Medieval sonorities and instruments

[Margo Schulter]

Hello, there, Cait and everyone.

Some discussions we've recently had on medieval sonorities and
instrumental techniques raise for me an interesting question: the
techniques of crafting a polyphonic texture, whether through
composition or improvisation.

In considering what kinds of polyphonic textures might have been
produced by instrumentalists, either in ensemble improvisations or in
performances on a single instrument, what is known about polyphonic
sonorities and their crafting in composed music might serve as a
possible starting point.

Here the availability of new or more thoroughly published sources, as
well as contributions to the analytical literature over the past four
decades and more by scholars such as Richard Crocker and Sarah Fuller,
permit an approach to written polyphony that might at least set the
question of improvised ensemble or solo instrumental polyphony in a
different context.

In speaking of "improvised instrumental polyphony," I include
accompaniments to monophonic songs as well as purely instrumental
music.

Before delving into some concepts regarding polyphonic sonorities, I
should observe that certain composed repertories have been proposed as
possibly derivative, or representative, of what some improvised
performances may have sounded like.

Most obviously, a 14th-century keyboard source such as the
Robertsbridge Codex suggests a style that keyboard players might have
followed either in adopting a vocal composition such as an Ars Nova
motet for solo performance, or for improvising part music based on
some kind of estampie genre like the dances in this collection. It has
been proposed that players of such instruments as the gittern might
look to the early keyboard sources in seeking out possible polyphonic
techniques for a late medieval milieu.

Additionally, certain genres of texted 13th-14th century polyphony
have been proposed as reflecting elements of styles involving
improvised instrumental accompaniment. Thus two-voice French motets in
the Codex Montpellier have been described as accompanied songs, and it
has been suggested by Richard Hoppin that the three-voice rondeaux of
Adam de la Halle might reflect techniques used in improvised
instrumental accompaniments.

Also, Hoppin proposes that the early 14th-century Italian madrigal
repertory, while some have compared it to the technique of the earlier
conductus, might more likely have developed "from secular monophony
with an improvised accompaniment."

Whatever "models" one considers for improvised instrumental polyphony,
there is the interesting question of how polyphonic sonorities and
their crafting were conceived of in composed polyphony, and how such
conceptions might have either influenced or been modified in
improvisatory textures, especially for a solo instrument such as the
organ or harp, or possibly a fretted instrument such as the citole or
gittern, for example.


------------------------------------------------------
1. Medieval sonority: neither random nor prefabricated
------------------------------------------------------

Two notions often influence modern scholarship regarding vertical
sonorities and progressions in medieval European polyphony. Either the
music represents a nascent if often inept or frustrated striving to
write "good harmony" according to 18th-19th century triadic rules; or
else it represents a "linear technique" in which vertical sonorities
result mainly as a "coincidence" of melodic lines.

However, both the music itself and some vital writings about
multi-voice sonorities from around 1300 and a bit later admit of
another perspective which I would like to present here.

In this alternative view, multi-voice sonorities in 13th-14th century
polyphony are neither random coincidences of the parts, nor the result
of a "prefabricated" chordal technique like that might be used to
fashion a 19th-century piano or guitar accompaniment in a major/minor
tonal style.

Rather we should consider such medieval concepts as the complete
trine, layered composition, the building of stable or unstable
multi-voice sonorities through partition or joining of intervals (to
be explained shortly), and sometimes differing preferences as to which
sonorities for three or more voices are pleasing or otherwise.

On the last point, theorists around 1300 are quite capable not only of
describing simultaneous sonorities for three or more voices, but of
expressing their preferences. Thus Jacobus of Liege (c. 1325) strongly
recommends a mildly unstable with an outer major ninth formed from two
euphonious fifths (e.g. D3-A3-E4, with C4 here showing middle C),
while a treatise from the same era "according to Johannes de Muris"
specifically cautions against this same sonority, rejecting the ninth
as "dissonant."

Both Jacobus and Johannes de Muris (or his student) agree that _all_
intervals in a recognized multi-voice sonority must be acceptably
concordant, but differ on whether the major ninth is to be regarded as
a partial concord or an outright discord. Additionally Jacobus,
reflecting the taste of his youth in the later 13th century, finds
that the outer major ninth "seems better to concord" when combined
with the two ideally concordant fifths; the "modern" Ars Nova treatise
may lean more toward sonorities with thirds or sixths.

Whatever stylistic implications such a dialogue might have -- and
Machaut, I would say, seems to agree with Jacobus about the major
ninth sonority and with Johannes de Muris or his disciple about a
greater emphasis on thirds and sixths -- it hardly seems
characteristic of a milieu where musicians are incapable of conceiving
three-voice simultaneities, or indifferent to overall vertical
euphony.

If we agree that multi-voice sonorities are relevant, then where do we
start in considering their crafting and use either in the notated
polyphonic repertory known to us, or in improvisatory instrumental
textures or accompaniments?


-------------------------------------------------------
2. Grocheio: The complete trine and layered composition
-------------------------------------------------------

A good starting point is provided by Johannes de Grocheio, who
explains that complete harmony or concord requires _three_ voices
forming a sonority I will call a _trine_ (from the _trina harmoniae
perfectio_ or "threefold perfection of harmony" which this sonority
manifests). This perfect harmony consists of an outer octave, lower
fifth, and upper fourth (e.g. D3-A3-D4).

One modern notation for indicating this vertical structure, 1-5-8,
could fit Grocheio's exposition of three-voice compositional
technique. One starts with the tenor, like the foundation of a house,
in building the musical edifice. Then one adds a duplum or motetus,
typically at a fifth above the tenor; followed by a triplum, typically
at an octave above the tenor. Together, these voices in their typical
dispositions form a trine, or _consonantia perfectissima_ as Grocheio
calls it, noting that it requires three voices to "perfect" this ideal
concord.

He also notes that the upper voices often cross and exchange roles,
explaining that a quadruplum or fourth voice is sometimes added, and
can help in perfecting the consonance (i.e. completing a trine) if
other voices are at a unison, or "truncate each other" (as in
hocketing, which he also describes).

Thus Grocheio expounds a layered process for building up a complex
texture in measured polyphony, as with a conductus, motet, or hocket:
first the tenor or foundation, then the duplum or motetus, and then
the triplum, with an optional quadruplum which can make possible more
consistently complete trinic concord.

This account, focusing mainly on rich and complete stable harmony,
suggests some possible techniques either for accompanying a monophonic
song on a harp or gittern, for example, or for improvising a solo
polyphonic texture. One might simply seek to add trines to the melody
at stategic points -- or possibly a drone, on the final or moveable --
or develop more intricate idioms involving contrasts between stability
and directed instability.

For example, consider a trine-to-fifth-to-trine figure like this, with
the melody in the upper part:

1 2 3 | 1 2 3 | 1

Melody: F4 E4 D4 E4 F4

C4 D4 C4
Accompaniment: F3 G3 F3

Here we open with the complete trine F3-C4-F4, with the momentary
seventh combination F3-C4-E4 contracting to the fifth G3-D4, followed
by the momentary sixth combination G3-D4-E4 expanding back to the
trine on F. While the unstable sonorities are quite transient, they
introduce a pleasant element of contrast to the harmonic rhythm:
concord at the opening of a rhythmic unit, and directed tension at the
end of a unit moving us forward toward the next stable concord.

We might also briefly note that the resolution of the major seventh
combination involves two elementary two-voice resolutions by stepwise
contrary motion (Maj7-5 + Maj3-1), as does also the later resolution
of the major sixth combination (Maj6-8 + Maj2-4).

Often, as here, this kind of texture might almost "write itself" --
and my example is based on the opening of a Montpellier motet -- or,
in improvisation, flow as it were out of the process of adding some
judicious concords to a melody. The accompanying instrument plays a
texture of simple fifths, with the melody moving above them in
contrary motion. One could also, of course, improvise all three voices
on a suitable instrument.


-----------------------------------
3. Jacobus: Partitions and joinings
-----------------------------------

While Grocheio tells us a great deal about the stable trine and its
role in composition, what about unstable sonorities? Here Jacobus of
Liege gives us invaluable help both in appreciating the musical use of
these sonorities, and in seeking ways to describe and notate their
structure which might be more congenial to medieval practice and
theory.

For Jacobus, a sonority of three or more voices can be described as a
"partition" (_partition_) or "splitting" (_fissio_) of an outer
interval into two or more adjacent intervals. A 1-5-8 trine, D3-A3-D4
for example, consists of an octave "split" into a fifth below and
fourth above.

To express this concept compactly in ASCII text, we might write

8|5_4

which can be read: "an outer octave partitioned or split into lower
fifth and upper fourth."

The same approach applies to unstable sonorities. Let us consider the
major sixth sonority of the three-voice passage above, G3-D4-E4.
Jacobus describes this type of partition or multi-voice sonority as a
major sixth split into fifth below and major second above, all
acceptably compatible intervals. Thus we have

M6|5_M2

This sonority is common in 13th-century writing, and also sometimes
used prominently by Machaut, but less favored by Ars Nova theorists
who regard the major second as an outright and full discord. For
Jacobus, as for some earlier theorists going back to Guido, however,
it has some degree of "compatibility," and so is a legitimate element
of recognized combinations.

In contrast, the other transient unstable sonority in our sample
passage, F3-C4-E4, would not be included in the catalogue of
partitions which Jacobus has provided, since he classifies the outer
major seventh as an outright discord. He specifically cautions that
two concordant intervals such as the fifth and major third can form a
discord such as the major seventh, so that one must take into account
_all_ intervals.

However, bold as well as more transient major seventh combinations are
found in 13th-century pieces, and we can notate this structure as an
outer major seventh split into lower fifth and upper major third, or

M7|5_M3

Now the question arises: all this is very interesting, but how might
it tie in with compositional, or possibly also improvisational,
technique? Jacobus himself tells us that partitions can be helpful in
making discant, which could mean either composed or improvised
polyphony.

If we assume a layered compositional technique of the kind described
by theorists such as Franco and Grocheio, then the applicability is
easy to see in a situation like this, where one is adding a triplum to
a two-voice texture:

E4 F4
G3 F3

Suppose that this is a cadence, or at any rate a point where we wish
to have a three-voice texture amplifying the Maj6-8 resolution from
instability to stability. Here knowing about the ideal stable trine,
and about some partitions of the octave and major sixth, can help us
in exploring some different solutions.

For example, the most common solution is this:

Triplum: B3 C4

Motetus: E4 F4
Tenor: G3 F3

M6|M3_4 8|5_4

Here the triplum splits the unstable major sixth into lower major
third and upper fourth, a partition included in the catalogue of
Jacobus, and then splits the resolving octave into the lower fifth and
upper fourth of a complete trine. In addition to filling out the
texture, this new part also has an excellent two-voice resolution of
its own with the lowest voice: Maj3-5.

Another solution, also typical of the 13th century and sometimes used
by Machaut as well as by certain English composers of the 14th-century
era, uses a different partition of the major sixth also, as noted
above, catalogued by Jacobus:

Triplum: D4 C4

Motetus: E4 F4
Tenor: G3 F3

M6|5_M2 8|5_4

In this kind of situation, the partition concept applies most
directly: our third voice "splits" an outer interval already formed by
the first two voices.

In other situations, another concept presented by Jacobus is helpful:
"joining" two adjacent intervals so as to form a new outer interval.
For example, let us consider this two-voice close:

1 2 3 | 1
C4 B3 C4
G3 F3

One colorful three-voice solution is this:

1 2 3 | 1
Triplum: D4 E4 F4
Motetus: C4 B3 C4
Tenor: G3 F3

5|4_M2 M6|M3_4 8|5_4

In the first sonority, the triplum adds an upper major second C4-D4
"joined" to the lower fourth G3-C4 so as to form an outer fifth G3-D4,
or a partition of 5|4_M2, catalogued by Jacobus.

In the penultimate cadential sonority, the triplum joins an upper
fourth B3-E4 to the lower major third G3-B3, forming the outer major
sixth G3-E4 -- a partition of M6|M3_4. This sonority resolves to a
complete trine on F, 8|5_4, where the triplum joins an upper fourth
C4-F4 to the lower fifth F3-C4, forming the outer octave of the trine.

We could also focus on the outer intervals formed by the tenor-triplum
pair and the partitions made by the motetus. Thus the first note of
the triplum forms the fifth G3-D4 with the tenor, split by the motetus
into 5|4_M2; the penultimate note forms the major sixth G3-E4, split
into M6|M3_4, and the last note the octave F3-F4, split into 8|5_4.

Thus the concepts of "partition" and "joining" of intervals provide a
model for how one can build up a musical texture in layers while
taking account of the sonorities generated in the process.

While the question of whether and how experienced composers from
Perotin to Ciconia may have conceived of their voices successively or
sometimes simultaneously is an intriguing one, my main point here has
been that successive composition does not necessarily imply
indifference to the vertical dimension in general or to multi-voice
sonorities in particular.

A concept of partition or the like, not necessarily articulated in a
formal theoretical manner like that of the encyclopedic Jacobus, might
also inform the technique of a 13th-century or 14th-century harpist,
for example, improvising a three-voice texture. Familiarity with
stable trines and with some unstable sonorities or partitions of an
outer fifth, sixth, and seventh, etc., and of typical resolutions,
could provide a ready basis for extempore solo polyphony.

My purpose here is to propose one starting point for considering what
improvising instrumentalists _might_ have done if pursuing polyphonic
styles influenced by or also quite possibly influencing the written
compositions of the 13th-14th century era.

Warmly thanking Cait and others, I invite discussion on specific
instruments or possible performance traditions in either a solo or
ensemble setting.

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Hi Margo;

Thanks for these. I'll get back to reading the rest of your post in minute,
but I since I have the tools, I took the liberty of drawing up a
supplemental figure, illustrating some of these materials on a 4ths tuned
fretted instrument, to accompany the text. One figure to start with, and
we'll see how it goes from there (comments or corrections welcome):

this example, from point #2 in your acticle: . . . .

Post by Margo Schulter
For example, consider a trine-to-fifth-to-trine figure like this, with
1 2 3 | 1 2 3 | 1
Melody: F4 E4 D4 E4 F4
C4 D4 C4
Accompaniment: F3 G3 F3

. . . is illustrated here:
Loading Image...

I kept it simple by using the 4 lowest pitched strings of guitar in standard
tuning, straight 4ths: E, A, D, G. Individual tones and their named
spellings (corresponding to yours) are synchronized accordingly in these
fretboard illustrations. Here's an E, A, D, G fretboard note speller if
needed
Loading Image...
The exact octave notations are off a little, relative to standard piano
range octave notation, but they are at least correct _relative to each
other_ on a fretboard. The charted sonorities are verbatim, per your post. I
took no liberties in arrangements. [remember to mute (don't play) the
highest pitched string in all voicing charts.]

That's a very pretty progression example Margo. The momentary (passing or
connecting chord) sonorities make a very big difference.

The only thing I might change initially (if I were to use this as a basis of
an instrumental accompaniment) is to use a trine at G as well (rather than
the plain 5th on G, the middle chord). I mentioned in an earlier post about
the appearent drop in volume (on my instrument), the thin or comparitively
weak sound, when 3 voices collapse to 2 (at the 5th: G, D, D). Much of this
has to do with the instantanious _decay_ of plucked string tones, compared
to singers voices -- the later being capable of maintaining sustain and
volume levels throughout, and even compensating volumes on the fly if
needed. So my arrangement preference here (and earlier as well) is not so
much an artistic choice, but rather (almost) a necessity. I could live with
the arrangement (as is), and executed on my instrument, but if I had a
choice, I would make that one change. I'd probably even go further then and
see if I could come up with some 4 voice sonorities that I could either
full-strum or just simply give a louder full stroke _attack_ (a good
deliberate downstroke for each voicing, without having to worry about muting
or avoiding the highest pitch string, i.e. pulling up short every on every
attack).

Thanks
Roger

Post by Margo Schulter
Hello, there, Cait and everyone.
Some discussions we've recently had on medieval sonorities and
instrumental techniques raise for me an interesting question: the
techniques of crafting a polyphonic texture, whether through
composition or improvisation.
In considering what kinds of polyphonic textures might have been
produced by instrumentalists, either in ensemble improvisations or in
performances on a single instrument, what is known about polyphonic
sonorities and their crafting in composed music might serve as a
possible starting point.
Here the availability of new or more thoroughly published sources, as
well as contributions to the analytical literature over the past four
decades and more by scholars such as Richard Crocker and Sarah Fuller,
permit an approach to written polyphony that might at least set the
question of improvised ensemble or solo instrumental polyphony in a
different context.
In speaking of "improvised instrumental polyphony," I include
accompaniments to monophonic songs as well as purely instrumental
music.
Before delving into some concepts regarding polyphonic sonorities, I
should observe that certain composed repertories have been proposed as
possibly derivative, or representative, of what some improvised
performances may have sounded like.
Most obviously, a 14th-century keyboard source such as the
Robertsbridge Codex suggests a style that keyboard players might have
followed either in adopting a vocal composition such as an Ars Nova
motet for solo performance, or for improvising part music based on
some kind of estampie genre like the dances in this collection. It has
been proposed that players of such instruments as the gittern might
look to the early keyboard sources in seeking out possible polyphonic
techniques for a late medieval milieu.
Additionally, certain genres of texted 13th-14th century polyphony
have been proposed as reflecting elements of styles involving
improvised instrumental accompaniment. Thus two-voice French motets in
the Codex Montpellier have been described as accompanied songs, and it
has been suggested by Richard Hoppin that the three-voice rondeaux of
Adam de la Halle might reflect techniques used in improvised
instrumental accompaniments.
Also, Hoppin proposes that the early 14th-century Italian madrigal
repertory, while some have compared it to the technique of the earlier
conductus, might more likely have developed "from secular monophony
with an improvised accompaniment."
Whatever "models" one considers for improvised instrumental polyphony,
there is the interesting question of how polyphonic sonorities and
their crafting were conceived of in composed polyphony, and how such
conceptions might have either influenced or been modified in
improvisatory textures, especially for a solo instrument such as the
organ or harp, or possibly a fretted instrument such as the citole or
gittern, for example.
------------------------------------------------------
1. Medieval sonority: neither random nor prefabricated
------------------------------------------------------
Two notions often influence modern scholarship regarding vertical
sonorities and progressions in medieval European polyphony. Either the
music represents a nascent if often inept or frustrated striving to
write "good harmony" according to 18th-19th century triadic rules; or
else it represents a "linear technique" in which vertical sonorities
result mainly as a "coincidence" of melodic lines.
However, both the music itself and some vital writings about
multi-voice sonorities from around 1300 and a bit later admit of
another perspective which I would like to present here.
In this alternative view, multi-voice sonorities in 13th-14th century
polyphony are neither random coincidences of the parts, nor the result
of a "prefabricated" chordal technique like that might be used to
fashion a 19th-century piano or guitar accompaniment in a major/minor
tonal style.
Rather we should consider such medieval concepts as the complete
trine, layered composition, the building of stable or unstable
multi-voice sonorities through partition or joining of intervals (to
be explained shortly), and sometimes differing preferences as to which
sonorities for three or more voices are pleasing or otherwise.
On the last point, theorists around 1300 are quite capable not only of
describing simultaneous sonorities for three or more voices, but of
expressing their preferences. Thus Jacobus of Liege (c. 1325) strongly
recommends a mildly unstable with an outer major ninth formed from two
euphonious fifths (e.g. D3-A3-E4, with C4 here showing middle C),
while a treatise from the same era "according to Johannes de Muris"
specifically cautions against this same sonority, rejecting the ninth
as "dissonant."
Both Jacobus and Johannes de Muris (or his student) agree that _all_
intervals in a recognized multi-voice sonority must be acceptably
concordant, but differ on whether the major ninth is to be regarded as
a partial concord or an outright discord. Additionally Jacobus,
reflecting the taste of his youth in the later 13th century, finds
that the outer major ninth "seems better to concord" when combined
with the two ideally concordant fifths; the "modern" Ars Nova treatise
may lean more toward sonorities with thirds or sixths.
Whatever stylistic implications such a dialogue might have -- and
Machaut, I would say, seems to agree with Jacobus about the major
ninth sonority and with Johannes de Muris or his disciple about a
greater emphasis on thirds and sixths -- it hardly seems
characteristic of a milieu where musicians are incapable of conceiving
three-voice simultaneities, or indifferent to overall vertical
euphony.
If we agree that multi-voice sonorities are relevant, then where do we
start in considering their crafting and use either in the notated
polyphonic repertory known to us, or in improvisatory instrumental
textures or accompaniments?
-------------------------------------------------------
2. Grocheio: The complete trine and layered composition
-------------------------------------------------------
A good starting point is provided by Johannes de Grocheio, who
explains that complete harmony or concord requires _three_ voices
forming a sonority I will call a _trine_ (from the _trina harmoniae
perfectio_ or "threefold perfection of harmony" which this sonority
manifests). This perfect harmony consists of an outer octave, lower
fifth, and upper fourth (e.g. D3-A3-D4).
One modern notation for indicating this vertical structure, 1-5-8,
could fit Grocheio's exposition of three-voice compositional
technique. One starts with the tenor, like the foundation of a house,
in building the musical edifice. Then one adds a duplum or motetus,
typically at a fifth above the tenor; followed by a triplum, typically
at an octave abov the tenor. Together, these voices in their typical
dispositions form a trine, or _consonantia perfectissima_ as Grocheio
calls it, noting that it requires three voices to "perfect" this ideal
concord.
He also notes that the upper voices often cross and exchange roles,
explaining that a quadruplum or fourth voice is sometimes added, and
can help in perfecting the consonance (i.e. completing a trine) if
other voices are at a unison, or "truncate each other" (as in
hocketing, which he also describes).
Thus Grocheio expounds a layered process for building up a complex
first the tenor or foundation, then the duplum or motetus, and then
the triplum, with an optional quadruplum which can make possible more
consistently complete trinic concord.
This account, focusing mainly on rich and complete stable harmony,
suggests some possible techniques either for accompanying a monophonic
song on a harp or gittern, for example, or for improvising a solo
polyphonic texture. One might simply seek to add trines to the melody
at stategic points -- or possibly a drone, on the final or moveable --
or develop more intricate idioms involving contrasts between stability
and directed instability.
For example, consider a trine-to-fifth-to-trine figure like this, with
1 2 3 | 1 2 3 | 1
Melody: F4 E4 D4 E4 F4
C4 D4 C4
Accompaniment: F3 G3 F3
Here we open with the complete trine F3-C4-F4, with the momentary
seventh combination F3-C4-E4 contracting to the fifth G3-D4, followed
by the momentary sixth combination G3-D4-E4 expanding back to the
trine on F. While the unstable sonorities are quite transient, they
concord at the opening of a rhythmic unit, and directed tension at the
end of a unit moving us forward toward the next stable concord.
We might also briefly note that the resolution of the major seventh
combination involves two elementary two-voice resolutions by stepwise
contrary motion (Maj7-5 + Maj3-1), as does also the later resolution
of the major sixth combination (Maj6-8 + Maj2-4).
Often, as here, this kind of texture might almost "write itself" --
and my example is based on the opening of a Montpellier motet -- or,
in improvisation, flow as it were out of the process of adding some
judicious concords to a melody. The accompanying instrument plays a
texture of simple fifths, with the melody moving above them in
contrary motion. One could also, of course, improvise all three voices
on a suitable instrument.
-----------------------------------
3. Jacobus: Partitions and joinings
-----------------------------------
While Grocheio tells us a great deal about the stable trine and its
role in composition, what about unstable sonorities? Here Jacobus of
Liege gives us invaluable help both in appreciating the musical use of
these sonorities, and in seeking ways to describe and notate their
structure which might be more congenial to medieval practice and
theory.
For Jacobus, a sonority of three or more voices can be described as a
"partition" (_partition_) or "splitting" (_fissio_) of an outer
interval into two or more adjacent intervals. A 1-5-8 trine, D3-A3-D4
for example, consists of an octave "split" into a fifth below and
fourth above.
To express this concept compactly in ASCII text, we might write
8|5_4
which can be read: "an outer octave partitioned or split into lower
fifth and upper fourth."
The same approach applies to unstable sonorities. Let us consider the
major sixth sonority of the three-voice passage above, G3-D4-E4.
Jacobus describes this type of partition or multi-voice sonority as a
major sixth split into fifth below and major second above, all
acceptably compatible intervals. Thus we have
M6|5_M2
This sonority is common in 13th-century writing, and also sometimes
used prominently by Machaut, but less favored by Ars Nova theorists
who regard the major second as an outright and full discord. For
Jacobus, as for some earlier theorists going back to Guido, however,
it has some degree of "compatibility," and so is a legitimate element
of recognized combinations.
In contrast, the other transient unstable sonority in our sample
passage, F3-C4-E4, would not be included in the catalogue of
partitions which Jacobus has provided, since he classifies the outer
major seventh as an outright discord. He specifically cautions that
two concordant intervals such as the fifth and major third can form a
discord such as the major seventh, so that one must take into account
_all_ intervals.
However, bold as well as more transient major seventh combinations are
found in 13th-century pieces, and we can notate this structure as an
outer major seventh split into lower fifth and upper major third, or
M7|5_M3
Now the question arises: all this is very interesting, but how might
it tie in with compositional, or possibly also improvisational,
technique? Jacobus himself tells us that partitions can be helpful in
making discant, which could mean either composed or improvised
polyphony.
If we assume a layered compositional technique of the kind described
by theorists such as Franco and Grocheio, then the applicability is
easy to see in a situation like this, where one is adding a triplum to
E4 F4
G3 F3
Suppose that this is a cadence, or at any rate a point where we wish
to have a three-voice texture amplifying the Maj6-8 resolution from
instability to stability. Here knowing about the ideal stable trine,
and about some partitions of the octave and major sixth, can help us
in exploring some different solutions.
Triplum: B3 C4
Motetus: E4 F4
Tenor: G3 F3
M6|M3_4 8|5_4
Here the triplum splits the unstable major sixth into lower major
third and upper fourth, a partition included in the catalogue of
Jacobus, and then splits the resolving octave into the lower fifth and
upper fourth of a complete trine. In addition to filling out the
texture, this new part also has an excellent two-voice resolution of
its own with the lowest voice: Maj3-5.
Another solution, also typical of the 13th century and sometimes used
by Machaut as well as by certain English composers of the 14th-century
era, uses a different partition of the major sixth also, as noted
Triplum: D4 C4
Motetus: E4 F4
Tenor: G3 F3
M6|5_M2 8|5_4
In this kind of situation, the partition concept applies most
directly: our third voice "splits" an outer interval already formed by
the first two voices.
"joining" two adjacent intervals so as to form a new outer interval.
1 2 3 | 1
C4 B3 C4
G3 F3
1 2 3 | 1
Triplum: D4 E4 F4
Motetus: C4 B3 C4
Tenor: G3 F3
5|4_M2 M6|M3_4 8|5_4
In the first sonority, the triplum adds an upper major second C4-D4
"joined" to the lower fourth G3-C4 so as to form an outer fifth G3-D4,
or a partition of 5|4_M2, catalogued by Jacobus.
In the penultimate cadential sonority, the triplum joins an upper
fourth B3-E4 to the lower major third G3-B3, forming the outer major
sixth G3-E4 -- a partition of M6|M3_4. This sonority resolves to a
complete trine on F, 8|5_4, where the triplum joins an upper fourth
C4-F4 to the lower fifth F3-C4, forming the outer octave of the trine.
We could also focus on the outer intervals formed by the tenor-triplum
pair and the partitions made by the motetus. Thus the first note of
the triplum forms the fifth G3-D4 with the tenor, split by the motetus
into 5|4_M2; the penultimate note forms the major sixth G3-E4, split
into M6|M3_4, and the last note the octave F3-F4, split into 8|5_4.
Thus the concepts of "partition" and "joining" of intervals provide a
model for how one can build up a musical texture in layers while
taking account of the sonorities generated in the process.
While the question of whether and how experienced composers from
Perotin to Ciconia may have conceived of their voices successively or
sometimes simultaneously is an intriguing one, my main point here has
been that successive composition does not necessarily imply
indifference to the vertical dimension in general or to multi-voice
sonorities in particular.
A concept of partition or the like, not necessarily articulated in a
formal theoretical manner like that of the encyclopedic Jacobus, might
also inform the technique of a 13th-century or 14th-century harpist,
for example, improvising a three-voice texture. Familiarity with
stable trines and with some unstable sonorities or partitions of an
outer fifth, sixth, and seventh, etc., and of typical resolutions,
could provide a ready basis for extempore solo polyphony.
My purpose here is to propose one starting point for considering what
improvising instrumentalists _might_ have done if pursuing polyphonic
styles influenced by or also quite possibly influencing the written
compositions of the 13th-14th century era.
Warmly thanking Cait and others, I invite discussion on specific
instruments or possible performance traditions in either a solo or
ensemble setting.
Most appreciatively,
Margo Schulter

[Roger E. Blumberg]

Hi again;

Here's the balance of the figures, 8 in total, combined into 3 drawings,
all 8 figures deal with point #3 in your above post:

Loading Image...
Loading Image...
Loading Image...

Overall, all I gotta say is (the same thing I said to myself earlier when I
first figured these out and played them) . . my my . . those are pretty
;')

And of course, I'm pleased as peaches that this little instrument can do all
that ;') I'm surprised actually, somehow I expected to get stumped
somewhere, i.e. not be able to construct a fingering for some particular
voicing. But we've lucked out so far. Same goes for any of the other
voicings I've tried so far from your other posted examples elsewhere.

Again, no-one can say for sure who or what influenced whom, but the mere
fact that this instrument can do these things, that it can be used to
compose, explore, experiment, and experience these and so many more
multi-voiced sonorities, says something (to me). It really would be ideal,
then as now, for composing a song melody for example, i.e. just start with a
short motif or fragment of a melody, an idea, pick up your chording-board
and see what you can come up with, see where it leads, sing along while play
passages over and over until you find just the thing you were hoping for,
and regardless of what you're accustomed to hearing or liking, the
instrument is versatile, it'll provide virtually anything you want,
seriously.

And, I could just as easily, in fact more easily in some cases, have used
4-3-4 lute tuning here, across 4 strings or courses. Sticking the 3rd in the
tuning pattern makes many voicings one fret narrower overall, therefore even
easier to finger. Meaning, some of these voicings might span a 4 fret length
of the fretboard now (within these illustrations), but if I used lute
tuning, those same voicings would compact to 3 frets span. I'm really only
using all-4ths (rather than lute tuning) because a couple of people here
have said that's what they're using.

I really liked (loved) the sonorities and progressions numbered 3.05 through
3.08. The last one, 3.08, is almost breathtakingly, breathtaking simply
because I was so surprised at what I was hearing. It's really beautiful, so
rich. [I think maybe I _will_ sit under that tree and play me some chords
;') ]

Thanks Margo, that was fun.
Roger

Post by Margo Schulter
Hello, there, Cait and everyone.
Some discussions we've recently had on medieval sonorities and
instrumental techniques raise for me an interesting question: the
techniques of crafting a polyphonic texture, whether through
composition or improvisation.
In considering what kinds of polyphonic textures might have been
produced by instrumentalists, either in ensemble improvisations or in
performances on a single instrument, what is known about polyphonic
sonorities and their crafting in composed music might serve as a
possible starting point.
Here the availability of new or more thoroughly published sources, as
well as contributions to the analytical literature over the past four
decades and more by scholars such as Richard Crocker and Sarah Fuller,
permit an approach to written polyphony that might at least set the
question of improvised ensemble or solo instrumental polyphony in a
different context.
In speaking of "improvised instrumental polyphony," I include
accompaniments to monophonic songs as well as purely instrumental
music.
Before delving into some concepts regarding polyphonic sonorities, I
should observe that certain composed repertories have been proposed as
possibly derivative, or representative, of what some improvised
performances may have sounded like.
Most obviously, a 14th-century keyboard source such as the
Robertsbridge Codex suggests a style that keyboard players might have
followed either in adopting a vocal composition such as an Ars Nova
motet for solo performance, or for improvising part music based on
some kind of estampie genre like the dances in this collection. It has
been proposed that players of such instruments as the gittern might
look to the early keyboard sources in seeking out possible polyphonic
techniques for a late medieval milieu.
Additionally, certain genres of texted 13th-14th century polyphony
have been proposed as reflecting elements of styles involving
improvised instrumental accompaniment. Thus two-voice French motets in
the Codex Montpellier have been described as accompanied songs, and it
has been suggested by Richard Hoppin that the three-voice rondeaux of
Adam de la Halle might reflect techniques used in improvised
instrumental accompaniments.
Also, Hoppin proposes that the early 14th-century Italian madrigal
repertory, while some have compared it to the technique of the earlier
conductus, might more likely have developed "from secular monophony
with an improvised accompaniment."
Whatever "models" one considers for improvised instrumental polyphony,
there is the interesting question of how polyphonic sonorities and
their crafting were conceived of in composed polyphony, and how such
conceptions might have either influenced or been modified in
improvisatory textures, especially for a solo instrument such as the
organ or harp, or possibly a fretted instrument such as the citole or
gittern, for example.
------------------------------------------------------
1. Medieval sonority: neither random nor prefabricated
------------------------------------------------------
Two notions often influence modern scholarship regarding vertical
sonorities and progressions in medieval European polyphony. Either the
music represents a nascent if often inept or frustrated striving to
write "good harmony" according to 18th-19th century triadic rules; or
else it represents a "linear technique" in which vertical sonorities
result mainly as a "coincidence" of melodic lines.
However, both the music itself and some vital writings about
multi-voice sonorities from around 1300 and a bit later admit of
another perspective which I would like to present here.
In this alternative view, multi-voice sonorities in 13th-14th century
polyphony are neither random coincidences of the parts, nor the result
of a "prefabricated" chordal technique like that might be used to
fashion a 19th-century piano or guitar accompaniment in a major/minor
tonal style.
Rather we should consider such medieval concepts as the complete
trine, layered composition, the building of stable or unstable
multi-voice sonorities through partition or joining of intervals (to
be explained shortly), and sometimes differing preferences as to which
sonorities for three or more voices are pleasing or otherwise.
On the last point, theorists around 1300 are quite capable not only of
describing simultaneous sonorities for three or more voices, but of
expressing their preferences. Thus Jacobus of Liege (c. 1325) strongly
recommends a mildly unstable with an outer major ninth formed from two
euphonious fifths (e.g. D3-A3-E4, with C4 here showing middle C),
while a treatise from the same era "according to Johannes de Muris"
specifically cautions against this same sonority, rejecting the ninth
as "dissonant."
Both Jacobus and Johannes de Muris (or his student) agree that _all_
intervals in a recognized multi-voice sonority must be acceptably
concordant, but differ on whether the major ninth is to be regarded as
a partial concord or an outright discord. Additionally Jacobus,
reflecting the taste of his youth in the later 13th century, finds
that the outer major ninth "seems better to concord" when combined
with the two ideally concordant fifths; the "modern" Ars Nova treatise
may lean more toward sonorities with thirds or sixths.
Whatever stylistic implications such a dialogue might have -- and
Machaut, I would say, seems to agree with Jacobus about the major
ninth sonority and with Johannes de Muris or his disciple about a
greater emphasis on thirds and sixths -- it hardly seems
characteristic of a milieu where musicians are incapable of conceiving
three-voice simultaneities, or indifferent to overall vertical
euphony.
If we agree that multi-voice sonorities are relevant, then where do we
start in considering their crafting and use either in the notated
polyphonic repertory known to us, or in improvisatory instrumental
textures or accompaniments?
-------------------------------------------------------
2. Grocheio: The complete trine and layered composition
-------------------------------------------------------
A good starting point is provided by Johannes de Grocheio, who
explains that complete harmony or concord requires _three_ voices
forming a sonority I will call a _trine_ (from the _trina harmoniae
perfectio_ or "threefold perfection of harmony" which this sonority
manifests). This perfect harmony consists of an outer octave, lower
fifth, and upper fourth (e.g. D3-A3-D4).
One modern notation for indicating this vertical structure, 1-5-8,
could fit Grocheio's exposition of three-voice compositional
technique. One starts with the tenor, like the foundation of a house,
in building the musical edifice. Then one adds a duplum or motetus,
typically at a fifth above the tenor; followed by a triplum, typically
at an octave above the tenor. Together, these voices in their typical
dispositions form a trine, or _consonantia perfectissima_ as Grocheio
calls it, noting that it requires three voices to "perfect" this ideal
c ncord.
He also notes that the upper voices often cross and exchange roles,
explaining that a quadruplum or fourth voice is sometimes added, and
can help in perfecting the consonance (i.e. completing a trine) if
other voices are at a unison, or "truncate each other" (as in
hocketing, which he also describes).
Thus Grocheio expounds a layered process for building up a complex
first the tenor or foundation, then the duplum or motetus, and then
the triplum, with an optional quadruplum which can make possible more
consistently complete trinic concord.
This account, focusing mainly on rich and complete stable harmony,
suggests some possible techniques either for accompanying a monophonic
song on a harp or gittern, for example, or for improvising a solo
polyphonic texture. One might simply seek to add trines to the melody
at stategic points -- or possibly a drone, on the final or moveable --
or develop more intricate idioms involving contrasts between stability
and directed instability.
For example, consider a trine-to-fifth-to-trine figure like this, with
1 2 3 | 1 2 3 | 1
Melody: F4 E4 D4 E4 F4
C4 D4 C4
Accompaniment: F3 G3 F3
Here we open with the complete trine F3-C4-F4, with the momentary
seventh combination F3-C4-E4 contracting to the fifth G3-D4, followed
by the momentary sixth combination G3-D4-E4 expanding back to the
trine on F. While the unstable sonorities are quite transient, they
concord at the opening of a rhythmic unit, and directed tension at the
end of a unit moving us forward toward the next stable concord.
We might also briefly note that the resolution of the major seventh
combination involves two elementary two-voice resolutions by stepwise
contrary motion (Maj7-5 + Maj3-1), as does also the later resolution
of the major sixth combination (Maj6-8 + Maj2-4).
Often, as here, this kind of texture might almost "write itself" --
and my example is based on the opening of a Montpellier motet -- or,
in improvisation, flow as it were out of the process of adding some
judicious concords to a melody. The accompanying instrument plays a
texture of simple fifths, with the melody moving above them in
contrary motion. One could also, of course, improvise all three voices
on a suitable instrument.
-----------------------------------
3. Jacobus: Partitions and joinings
-----------------------------------
While Grocheio tells us a great deal about the stable trine and its
role in composition, what about unstable sonorities? Here Jacobus of
Liege gives us invaluable help both in appreciating the musical use of
these sonorities, and in seeking ways to describe and notate their
structure which might be more congenial to medieval practice and
theory.
For Jacobus, a sonority of three or more voices can be described as a
"partition" (_partition_) or "splitting" (_fissio_) of an outer
interval into two or more adjacent intervals. A 1-5-8 trine, D3-A3-D4
for example, consists of an octave "split" into a fifth below and
fourth above.
To express this concept compactly in ASCII text, we might write
8|5_4
which can be read: "an outer octave partitioned or split into lower
fifth and upper fourth."
The same approach applies to unstable sonorities. Let us consider the
major sixth sonority of the three-voice passage above, G3-D4-E4.
Jacobus describes this type of partition or multi-voice sonority as a
major sixth split into fifth below and major second above, all
acceptably compatible intervals. Thus we have
M6|5_M2
This sonority is common in 13th-century writing, and also sometimes
used prominently by Machaut, but less favored by Ars Nova theorists
who regard the major second as an outright and full discord. For
Jacobus, as for some earlier theorists going back to Guido, however,
it has some degree of "compatibility," and so is a legitimate element
of recognized combinations.
In contrast, the other transient unstable sonority in our sample
passage, F3-C4-E4, would not be included in the catalogue of
partitions which Jacobus has provided, since he classifies the outer
major seventh as an outright discord. He specifically cautions that
two concordant intervals such as the fifth and major third can form a
discord such as the major seventh, so that one must take into account
_all_ intervals.
However, bold as well as more transient major seventh combinations are
found in 13th-century pieces, and we can notate this structure as an
outer major seventh split into lower fifth and upper major third, or
M7|5_M3
Now the question arises: all this is very interesting, but how might
it tie in with compositional, or possibly also improvisational,
technique? Jacobus himself tells us that partitions can be helpful in
making discant, which could mean either composed or improvised
polyphony.
If we assume a layered compositional technique of the kind described
by theorists such as Franco and Grocheio, then the applicability is
easy to see in a situation like this, where one is adding a triplum to
E4 F4
G3 F3
Suppose that this is a cadence, or at any rate a point where we wish
to have a three-voice texture amplifying the Maj6-8 resolution from
instability to stability. Here knowing about the ideal stable trine,
and about some partitions of the octave and major sixth, can help us
in exploring some different solutions.
Triplum: B3 C4
Motetus: E4 F4
Tenor: G3 F3
M6|M3_4 8|5_4
Here the triplum splits the unstable major sixth into lower major
third and upper fourth, a partition included in the catalogue of
Jacobus, and then splits the resolving octave into the lower fifth and
upper fourth of a complete trine. In addition to filling out the
texture, this new part also has an excellent two-voice resolution of
its own with the lowest voice: Maj3-5.
Another solution, also typical of the 13th century and sometimes used
by Machaut as well as by certain English composers of the 14th-century
era, uses a different partition of the major sixth also, as noted
Triplum: D4 C4
Motetus: E4 F4
Tenor: G3 F3
M6|5_M2 8|5_4
In this kind of situation, the partition concept applies most
directly: our third voice "splits" an outer interval already formed by
the first two voices.
"joining" two adjacent intervals so as to form a new outer interval.
1 2 3 | 1
C4 B3 C4
G3 F3
1 2 3 | 1
Triplum: D4 E4 F4
Motetus: C4 B3 C4
Tenor: G3 F3
5|4_M2 M6|M3_4 8|5_4
In the first sonority, the triplum adds an upper major second C4-D4
"joined" to the lower fourth G3-C4 so as to form an outer fifth G3-D4,
or a partition of 5|4_M2, catalogued by Jacobus.
In the penultimate cadential sonority, the triplum joins an upper
fourth B3-E4 to the lower major third G3-B3, forming the outer major
sixth G3-E4 -- a partition of M6|M3_4. This sonority resolves to a
complete trine on F, 8|5_4, where the triplum joins an upper fourth
C4-F4 to the lower fifth F3-C4, forming the outer octave of the trine.
We could also focus on the outer intervals formed by the tenor-triplum
pair and the partitions made by the motetus. Thus the first note of
the triplum forms the fifth G3-D4 with the tenor, split by the motetus
into 5|4_M2; the penultimate note forms the major sixth G3-E4, split
into M6|M3_4, and the last note the octave F3-F4, split into 8|5_4.
Thus the concepts of "partition" and "joining" of intervals provide a
model for how one can build up a musical texture in layers while
taking account of the sonorities generated in the process.
While the question of whether and how experienced composers from
Perotin to Ciconia may have conceived of their voices successively or
sometimes simultaneously is an intriguing one, my main point here has
been that successive composition does not necessarily imply
indifference to the vertical dimension in general or to multi-voice
sonorities in particular.
A concept of partition or the like, not necessarily articulated in a
formal theoretical manner like that of the encyclopedic Jacobus, might
also inform the technique of a 13th-century or 14th-century harpist,
for example, improvising a three-voice texture. Familiarity with
stable trines and with some unstable sonorities or partitions of an
outer fifth, sixth, and seventh, etc., and of typical resolutions,
could provide a ready basis for extempore solo polyphony.
My purpose here is to propose one starting point for considering what
improvising instrumentalists _might_ have done if pursuing polyphonic
styles influenced by or also quite possibly influencing the written
compositions of the 13th-14th century era.
Warmly thanking Cait and others, I invite discussion on specific
instruments or possible performance traditions in either a solo or
ensemble setting.
Most appreciatively,
Margo Schulter

[Margo Schulter]

Hello, there, Roger and All.

Thank you for such an enthusiastic response to my post. One of my main
purposes is actually to get people playing 13th-century music and
enjoying some of the basic progressions. Of course, these occur with
all kinds of variations and complications in the motets and other
music of the era, and Cait has also raised some interesting questions
as to organization and form that I'll address in another post.

Mainly, I want to thank you for not only reading and playing these
examples, but for making them available in a tablature form that
people with fretted strings (including modern guitars, for example)
can try out.

Before getting to some specific comments in your replies, I might
address a general philosophical question: in playing medieval music,
or improvising in medieval styles, on either period or modern
instruments, there can be levels of historically approximated or
educated performance.

One level is: "I strive to do only what is more or less clearly
documented for this type of instrument in literature of the period, or
reasonably 'inferred' from visual art, etc."

Another level is: "I strive to explore what with some likelihood _may_
have been done, although not necessarily recorded."

Yet another level is: "I strive to explore the musical repertory and
style of this era on this instrument without necessarily adhering to
documented or likely period technique, and possibly discovering new
techniques for playing in a traditional style on a period instrument."

While drawing lines is often both difficult and controversial, I'd
guess that playing trines or fifths here and there on a plucked string
instrument would be taken as a reasonable "Historically Approximated
Performance" (HAP, as I call it). This assumes, in the situation of
accompanying a monophonic song, that the person judging this point
considers _some_ instrumental accompaniment appropriate period
technique, often a debatable point for certain repertories, as we've
seen in recent threads.

In contrast, playing or improvising complex three-part polyphony in a
13th-century style on a medieval plucked instrument might be closer to
"Historically Educated Performance" (HEP): doing it well calls for a
fluid and fluent familiarity with the style, and the question would be
whether and to what extent people were likely to do this in the
medieval era.

One might say, "This is beautiful music, and a beautiful instrument,
and making the music and sharing it with others is a good thing --
which can be offered with a prudent disclaimer that this is period
style and a period instrument, but not necessarily period technique."

Post by Margo Schulter
1 2 3 | 1 2 3 | 1
Melody: F4 E4 D4 E4 F4
C4 D4 C4
Accompaniment: F3 G3 F3

<http://www.thecipher.com/mschulter_figs/ms_01-06-04_fig2.01.gif>

Thank you for intabulating these examples. I'll also quote your link

<http://www.thecipher.com/mschulter_figs/fretboard_spelled_EADG.gif>
The exact octave notations are off a little, relative to standard
piano range octave notation, but they are at least correct _relative
to each other_ on a fretboard. The charted sonorities are verbatim,
per your post. I took no liberties in arrangements. [remember to
mute (don't play) the highest pitched string in all voicing charts.]

Here my first reaction might be that various instruments can different
octave ranges and notations: recorders often an octave higher than
written and modern guitar an octave lower, as I recall. I wonder how a
medieval citole or gittern would compare with a modern guitar.

That's a very pretty progression example Margo. The momentary
(passing or connecting chord) sonorities make a very big difference.

Yes, and the interesting thing is that this is something that happens
all the time in written motets and the like, and could easily happen
in an improvised accompaniment. You don't necessarily have to analyze
it in order to do it and enjoy it, and I certainly don't analyze it
each time I play it in a keyboard improvisation, I mainly play and
enjoy.

A "passing chord," or more generally a "connecting chord" (sometimes
these unstable sonorities can be much more prominent and sustained),
is one good description of the basic effect. I'm trying to develop one
possible set of technical terms to analyze the way that the melodic
and vertical dimensions can interact in these kinds of 13th-century
progressions, by any choice including mine is likely to be quite
arbitrary.

In my own jargon, the unstable sonorities in the example we're
discussing are called "mediating sonorities." To explain what this
term means, lets look at an unadorned version with stable concords
only of a typical trine-to-fifth-to-trine progression. As a remark in
Cait's post suggests, this kind of figure is a mainstay in lots of
13th-century English and Continental polyphony -- often going back and
forth between F and G, for example, as here.

F4 D4 F4
C4 D4 C4
F3 G3 F3

(8-5 + 4-1) (5-8 + 1-4)

Here the outer voices move 8-5-8: from the outer octave of a 8|5_4
trine on F to a fifth on G, and then back to the octave of another
trine on F.

The two upper voices likewise move 4-1-4, from the upper fourth C4-F4
of the F trine to a unison on the upper note of the fifth G3-D4 and
back to the upper fourth of another F trine.

While this progression might occur as is, it illustrates a constraint
applying to medieval polyphony: you can't move from one stable concord
another (e.g. 8-5 or 5-8, 4-1 or 1-4) by _stepwise_ contrary motion.
While the two lower voices can move by step (F3-G3-F3, C4-D4-C4), the
highest voice has to leap down and then back up a third (F4-D4-F4).

Now let's look at what happens to the vertical progressions if we
"fill in" the melodic leaps of a third in the upper voice:

Md Md
F4 E4 D4 E4 F4
C4 D4 C4
F3 G3 F3

(M7-5 + M3-1) (M6-8 + M2-4)

Now all voices can move by step, and we also have a stimulating
element of vertical instability and resolution. To explain why I speak
of "mediating" tones or sonorities (Md for short), let's look at the
new two-voice progressions generated, starting with the outer voices.

Md Md
F4 E4 D4 E4 F4
F3 G3 G3

8 M7 5 M6 8

Here, in moving between the stable concords of the opening octave and
the fifth by contrary motion, the unstable major seventh F3-E3
"mediates" between these concords, making possible smoother motion and
also adding a transient M7-5 resolution.

Similarly, in moving back from fifth to octave, we have a mediating
major sixth G3-E4 adding a transient M6-8 resolution.

From a melodic view, we can speak of the note E4 in the upper part in
either progression as a "mediating tone": it makes this line smoother.
From a vertical view, we can speak of the unstable interval in which
this note participates as a "mediating interval": it adds the element
of a directed two-voice resolution M7-5 or M6-8.

More specifically, a mediating tone or interval makes smoother a
progression between two intervals by _contrary_ motion, here 8-5 or
5-8, with the mediating tone approached and left in the same
direction. This direction in the upper voice is descending for the
8-M7-5 figure (F4-E4-D4), and then ascending for the 5-M6-8 figure
(D4-E4-F4).

Now let's look at the upper two voices:

Md Md
F4 E4 D4 E4 F4
C4 D4 C3

4 M3 1 M2 4

Here we have a 4-1 progression with a mediating major third C4-E4 and
a transient M3-1 resolution, followed by a 1-4 progression with a
mediating major second D4-E4 and a transient M2-4 resolution. Again,
the mediating tones are approached and left in the same direction in
the upper voice; and the mediating sonorities make a progression
between two intervals (4-1 or 1-4) melodically smoother while adding
an element of directed vertical tension.

By the way, either the 8-7-5-6-8 type of mediating figure (here
between the outer pair of voices) or the 4-3-1-2-4 type (here between
the upper voices) might occur in a composition such as a two-voice
motet; in multi-voice music, these figures and others can be mixed,
matched, and combined.

Now let's look again at the whole three-voice picture:

Md Md
F4 E4 D4 E4 F4
C4 D4 C4
F3 G3 F3

(M7-5 + M3-1) (M6-8 + M2-4)

Here we get three-voice mediating sonorities and progressions: first
the M7|5_M3 sonority resolving to a fifth (M7-5 + M3-1), and then the
M6|5_M2 resolving to the complete F trine (M6-8 + M2-4). Melodic
smoothness, two-voice progressions, and three-voice sonority -- all
play a role in the total effect.

While mediating tones and sonorities are often quite transient,
typically (as here) leading from the end of one rhythmic unit to a
resolution at the beginning of the next, they can also be more
prominent. Let's change the rhythm a bit and make this a dramatic
cadence in something like 6/8 or 6/4 meter as it would be expressed in
a modern transcription, with the numbers at the top showing the main
beats and "r" showing a rest to get a characteristic pattern:

1 2 1 2
1 2 3 4 5 6 | 1 2 3 4 5 6 |
F4 E4 D4 E4 F4 r
C4 D4 C4 r
F3 G3 F3 r

The mediating seventh sonority is again quite brief, lending a bit of
impetus to the vertical rhythm, but the prolonged sixth sonority
G3-D4-E4 -- also a mediating sonority -- definitely stands out and
leads to a very effective cadence.

The only thing I might change initially (if I were to use this as a
basis of an instrumental accompaniment) is to use a trine at G as
well (rather than the plain 5th on G, the middle chord). I mentioned
in an earlier post about the appearent drop in volume (on my
instrument), the thin or comparitively weak sound, when 3 voices
collapse to 2 (at the 5th: G, D, D). Much of this has to do with the
instantanious _decay_ of plucked string tones, compared to singers
voices -- the later being capable of maintaining sustain and volume
levels throughout, and even compensating volumes on the fly if
needed.

While I'd let people who actually play these instruments comment on
the fine points of technique or possible period implications here, I
might just say that in various eras, instrumental renditions or
intabulations of vocal pieces do make adjustments and elaborations.
This had started by the beginning of the known keyboard repertory: the
Robertsbridge Codex has some adaptations of motets by Philippe de
Vitry. It's common in keyboard music to have "free voicing" where the
number of voices changes from two to three or four; the Robertsbridge
Codex sometimes shifts between two and three, and I've seen pieces in
the Buxheim Organ Book (early to middle 15th-century arrangements,
Mark Lindley suggests) mostly in two parts but with some four-voice
sonorities.

Also, for example, writers in the early 17th century discussing the
new art of continuo or thoroughbass playing note that an accompaniment
on the organ or another instrument isn't bound by all the standard
rules of vocal counterpoint.

Even in vocal music, or other ensemble music, composers might vary the
voice-leading in order to get richer sonority. For example, consider
this impressive 13th-century resolution featuring an acutely tense
major seventh (a "perfect discord," i.e. thoroughly discordant, as
period theorists put it):

E4 D4
C4 D4
F3 G3

(M7-5 + M3-1)

Actually this is the same progression that we've encountered
transiently in the example of mediating sonorities. In this
resolution, all voices move by step, and both unstable intervals
resolve by stepwise contrary motion. However, there's an interesting
variation:

E4 G4
C4 D4
F3 G3

Here, the progression looks less "efficient" as we might at least
judge it on paper (or in ASCII notation on screen): all three voices
move in the same direction (upward) and the unstable intervals thus
resolve by similar rather than contrary motion. Yet it's a beautiful
progression, and arrives at a complete trine on G.

One possible analysis if that in a typical directed resolution the
outer major seventh F3-E4 very nicely contracts to the fifth G3-D4 --
and here, in fact, we do have and hear the fifth G3-D4 in the second
sonority, only sounded by the _lower_ two voices, so that the upper is
free to move to the octave and complete a trine on G. One might call
this "symbiotic instability": the middle voice "covers" or "fills in"
for the upper voice by supplying the expected D4, letting the latter
move to G4.

Often the best conclusion is: however you analyze it, it sounds nice.

Anyway, while I'd let people who play medieval fretted instruments
attend to the possible period priorities, I'd say that taking a vocal
passage or piece and adapting it to an instrumental idiom rather than
simply giving a literal transcription has been typical, as suggested
by some of the arrangements from the Robertsbridge and Buxheim
collections, for example.

There's lots more to discuss here, and I hope that the discussion will
keep getting driven by experiments in actually playing or improvising
this kind of music, which could lead for suggestions regarding either
possible medieval techniques, or new techniques for playing in
medieval styles on period instruments (HEP rather than HAP).

Both you and Cait, for example, have mentioned the unison problem on a
solo plucked instrument -- thinning out of the texture -- and one
might encounter this with different progressions, with a range of
alternatives to be considered.

Most appreciatively,

Margo Schulter
***@calweb.com

[Margo Schulter]

Dear Roger and All,

Please let me explain that after my first long reply, I've decided to
make this a short and separate post mainly to say how excited I am
that you're playing this music and enjoying it!

Post by Roger E. Blumberg
Overall, all I gotta say is (the same thing I said to myself earlier
when I first figured these out and played them) . . my my . .
those are pretty ;')

What a delight to share some of this beauty. It's what I've tried to
communicate over the years, mainly through advocacy and analysis -- of
course, people who perform the music publicly do this in another and
very tangible way. By making those intabulations and making them so
easily available, you're a dynamic part of the process.

What I'm tempted to say is that medieval music is too important to be
left -- at least exclusively -- to those of us who call ourselves
"medievalists." Similarly, the enjoyment of Bach shouldn't be
restricted to people who have studied the 18th-century continuo
treatises, although for those interested there's lots of treasure to
be found in those treatises on ways of conceiving and performing the
music.

This isn't to put down people like Cait who are seeking to approximate
what specific period instrumental techniques may have been like, or
people like me who are interested in taking 13th-14th century theory
and carrying it a bit further -- as might have happened in the 15th
century, say, if Perotin and Machaut had been still studied as
"classics."

However, people like you are also part of the process, and your
advocacy of this music might be especially eloquent and telling for
people coming from other than "medievalist" backgrounds.

Isn't this 13th-century polyphony awesome: the range and diversity of
sonorities, and the color. What I've posted so far is a sample of
fairly "standard" things that you can find in three-voice motets, for
example.

Post by Roger E. Blumberg
And of course, I'm pleased as peaches that this little instrument
can do all that ;') I'm surprised actually, somehow I expected to
get stumped somewhere, i.e. not be able to construct a fingering for
some particular voicing. But we've lucked out so far. Same goes for
any of the other voicings I've tried so far from your other posted
examples elsewhere.

This is great news, and I'd say that what I've posted is fairly
typical. Generally the greatest range you'll need for a single
sonority is around a twelfth, as Jacobus notes. As samples, why don't
I give a couple of versions for a neat resolution of a "split ninth"
sonority M9|5_5 from around 1300, and a four-voice cadence typical of
the 14th century -- at least neither of these involves pesky unisons
<grin>.

G#4 A4
B4 C5 | G4 A4 | C#4 D4
E4 F4 C4 D4 G#3 A3
A3 F3 F3 D3 E3 D3

(Maj9-12) (Maj9-12) (Maj10-12 + Maj6-8 + Maj3-5)

Post by Roger E. Blumberg
I really liked (loved) the sonorities and progressions numbered 3.05
through 3.08. The last one, 3.08, is almost breathtakingly,
breathtaking simply because I was so surprised at what I was
hearing. It's really beautiful, so rich. [I think maybe I _will_ sit
under that tree and play me some chords ;') ]

Yes, 3.08 is one of my favorites, and very "jazzy" to me. Why don't I
quote your links, with 3.08 included in the last one:

<http://www.thecipher.com/mschulter_figs/ms_01-06-04_fig3.01-2-3.gif>
<http://www.thecipher.com/mschulter_figs/ms_01-06-04_fig3.04-5-6.gif>
<http://www.thecipher.com/mschulter_figs/ms_01-06-04_fig3.07-8.gif>

and also quickly quote the progression here in ASCII:

1 2 3 | 1 2 3 |
D4 E4 F4
C4 B3 C4
G3 F3

I can easily picture instrumental ensembles playing or improvising
this kind of thing under a tree, or elsewhere, and if the kind of
technique that Cait discussed of playing a three-voice conductus on a
harp, for example, was in vogue, then why not improvise a similar kind
of three-part texture? Written pieces have lots of figures and ideas
that lend themselves to neat improvisations.

From a HAP outlook, trying to approximate what people may actually
have done with specific instruments in the 13th century, the main
question might be whether people were playing three-voice textures on
single plucked string instruments, and if so, which ones? One recent
book on performance practices has a reference to "strumming" on a
medieval instrument like a gittern as one possibility, whatever that
might imply.

From a HEP outlook, if you can get under that tree and play or
improvise in a 13th-century style, and have the fluency and technique
to do a more or less complex three-voice texture, go to it. I'd love
to hear this kind of thing, and am in a way seeking an equivalent when
I use plucked string types of timbres for playing medieval pieces or
improvising on synthesizer. The tree of music has lots of branches.

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Post by Margo Schulter
Dear Roger and All,
Please let me explain that after my first long reply, I've decided to
make this a short and separate post mainly to say how excited I am
that you're playing this music and enjoying it!

Post by Roger E. Blumberg
Overall, all I gotta say is (the same thing I said to myself earlier
when I first figured these out and played them) . . my my . .
those are pretty ;')

What a delight to share some of this beauty. It's what I've tried to
communicate over the years, mainly through advocacy and analysis -- of
course, people who perform the music publicly do this in another and
very tangible way. By making those intabulations and making them so
easily available, you're a dynamic part of the process.

Thanks. I'm delighted that your delighted that I'm delighted with the
delights you're sharing with us. ;') It's a pleasure to be able to
contribute. Music is a treasure, to be sure.

Post by Margo Schulter
What I'm tempted to say is that medieval music is too important to be
left -- at least exclusively -- to those of us who call ourselves
"medievalists."

you're right, it should be made more accessible and available, exercised and
performed more, recieve greater exposure and wider appreciation as a result.


Similarly, the enjoyment of Bach shouldn't be

Post by Margo Schulter
restricted to people who have studied the 18th-century continuo
treatises, although for those interested there's lots of treasure to
be found in those treatises on ways of conceiving and performing the
music.
This isn't to put down people like Cait who are seeking to approximate
what specific period instrumental techniques may have been like, or
people like me who are interested in taking 13th-14th century theory
and carrying it a bit further -- as might have happened in the 15th
century, say, if Perotin and Machaut had been still studied as
"classics."

we'll have to make note of that; [Perotin and Machaut had been still studied
as "classics."]. Maybe some day they will be again.

Post by Margo Schulter
However, people like you are also part of the process, and your
advocacy of this music might be especially eloquent and telling for
people coming from other than "medievalist" backgrounds.
Isn't this 13th-century polyphony awesome: the range and diversity of
sonorities, and the color. What I've posted so far is a sample of
fairly "standard" things that you can find in three-voice motets, for
example.

yes, it is (awesome) actually. Even from these little snippets it's clear,
clear that colorful sonorities were not alien at all to the period nor to
it's native players and listeners. If this is "standard stuff" then one can
only imagine what the more radical expressions might have sounded like.

This stuff, (medieval polyphony, theory and practice, instrumentation and
improvisation, both vertical and horizontal constructs)," really should be
catalogued and presented in a more widely accessible format, e.g. the
fretboard examples that anyone with access to a guitar could experience,
covering a lot of territory in a short time as well. It took me 10 hours to
make yesterday's drawings and post them, but once they're done, the info
(the patterns and principles) can be demonstrated and digested in 10
minutes!
It makes all the difference -- easy access, and in an easy to digest
presentation. I'm simply doing another translation-step from your easy to
digest presentations here (among other things your presentation is in ASCII
rather than
staff notation, so it's already that much more accessible to all),
benefiting
from your accumulated years of knowledge and ability to distill it for us
as you are doing here and elsewhere. So it's going from your tens of years,
to my tens of hours, to the final recipient's tens of minutes (an
over-exaggeration, but what I'm saying is that I wouldn't be able to do it
_at all_ without your already having done the distilling and translating
steps that you already have done). So I guess this is another way of
agreeing that yes "medieval music is too important to be left exclusively to
those of us who call themselves "medievalists", and the next step might
almost have to be something akin to the supplementary entabulations I've
been doing here, if not from me then from someone else. But again that
someone will be dependant upon you'all for that accessible existing resource
pool to draw upon, shoulders to stand on, the right kind of teachers to
point back to and say . . . thanks.

Post by Margo Schulter

Post by Roger E. Blumberg
And of course, I'm pleased as peaches that this little instrument
can do all that ;') I'm surprised actually, somehow I expected to
get stumped somewhere, i.e. not be able to construct a fingering for
some particular voicing. But we've lucked out so far. Same goes for
any of the other voicings I've tried so far from your other posted
examples elsewhere.

This is great news, and I'd say that what I've posted is fairly
typical. Generally the greatest range you'll need for a single
sonority is around a twelfth, as Jacobus notes. As samples, why don't
I give a couple of versions for a neat resolution of a "split ninth"
sonority M9|5_5 from around 1300, and a four-voice cadence typical of
the 14th century -- at least neither of these involves pesky unisons
<grin>.
G#4 A4
B4 C5 | G4 A4 | C#4 D4
E4 F4 C4 D4 G#3 A3
A3 F3 F3 D3 E3 D3
(Maj9-12) (Maj9-12) (Maj10-12 + Maj6-8 + Maj3-5)

Great. Thanks for these. . .
And here, I've uploaded the accompanying fretboard illustrations again. I
omitted the second "Maj9-12" example, and for the third example, the 4
voice example, I transposed from E-D to A-G (easier to illustrate in this
tuning: E, A, D, G)
Loading Image...
and fretboard speller again
http://www.thecipher.com/mschulter_figs/fretboard_spelled_EADG.gif ]

I've labeled these three examples a, b, c.
Again, all of these examples are great.
Example "a" is distinct from all previous examples for it's rather distant
resolution, the lowest voice moving "A-down-to-F", a full Major 3rd or 2
whole-steps. It's another beauty -- and the possible next chord(s) are
writing themselves in my head as I play it.
Example "c", being 4 voiced, would allow a free-er or even more aggressive
attack (full strum or more deliberate down-stroke) if I want to or needed
maximum volume output. Again, the next chord is suggesting itself and I
would not let this go unused if I ever stumbled upon it myself ;') If I were
14 again, a virgin musician, in the year 1250, and someone showed these to
me
(or I found them on my own), the race would definitely be on! I'd be going
for all the gusto I could get.

Post by Margo Schulter

Post by Roger E. Blumberg
I really liked (loved) the sonorities and progressions numbered 3.05
through 3.08. The last one, 3.08, is almost breathtakingly,
breathtaking simply because I was so surprised at what I was
hearing. It's really beautiful, so rich. [I think maybe I _will_ sit
under that tree and play me some chords ;') ]

Yes, 3.08 is one of my favorites, and very "jazzy" to me. Why don't I
<http://www.thecipher.com/mschulter_figs/ms_01-06-04_fig3.01-2-3.gif>
<http://www.thecipher.com/mschulter_figs/ms_01-06-04_fig3.04-5-6.gif>
<http://www.thecipher.com/mschulter_figs/ms_01-06-04_fig3.07-8.gif>
1 2 3 | 1 2 3 |
D4 E4 F4
C4 B3 C4
G3 F3
I can easily picture instrumental ensembles playing or improvising
this kind of thing under a tree, or elsewhere, and if the kind of
technique that Cait discussed of playing a three-voice conductus on a
harp, for example, was in vogue, then why not improvise a similar kind
of three-part texture? Written pieces have lots of figures and ideas
that lend themselves to neat improvisations.

I agree. It's fun to ponder. In the end I'm sure that players then (like
ourselves now) worked out a basic "vocabulary", a common and comfortable
pallet of techniques and "stock" sonorities, fills, progressions, etc. that
they would reuse and recombine over and over in countless ways as required.
So these steps of attempting to identify and recapture those possible or
even probable vocabularies and common techniques (that they took for
granted) is essential. And this of course includes considerations and
capabilities specific to particular instruments known to have been used.

Post by Margo Schulter
From a HAP outlook, trying to approximate what people may actually
have done with specific instruments in the 13th century, the main
question might be whether people were playing three-voice textures on
single plucked string instruments, and if so, which ones? One recent
book on performance practices has a reference to "strumming" on a
medieval instrument like a gittern as one possibility, whatever that
might imply.

it implies a great deal to me, of course (single stringed, double
course, etc). Getting as much music (and volume) as you can from your
instrument makes sense to me. Struming is one way of doing that. It's also a
key and default technique for adding and expressing a wide varriety of
rhythmic patterns. Even if you had only one string you'd probably wind up
strumming it or plucking it rhythmically. The faster the music is the more
likely it (strumming) will occure. At some point it's another one of
those "unavoidables" I think. i.e. If you try it, and you like it, you'll
probably keep doing it. If I had a zither I might even tune three or four
sections of strings to different sonorities, if only trines (maybe remove
one string between sections to provide a visual and tactile break between
sonority sets) and strum away ;') But it's no secret that I like being in
command of mutiple voices at once. I like being able to fill my ears and
soul with lots of sound, texture and color. I can't get enough of it. But
the fact is, I wouldn't have needed to go to those lengths to achieve that
same effect. I would have know about, and gravitated to, the already
existing class of instrument that welcomes and greatly simplifies and
facilitates
that very technique, one of those fretted harp-zither thingies.

Post by Margo Schulter
From a HEP outlook, if you can get under that tree and play or
improvise in a 13th-century style, and have the fluency and technique
to do a more or less complex three-voice texture, go to it. I'd love
to hear this kind of thing, and am in a way seeking an equivalent when
I use plucked string types of timbres for playing medieval pieces or
improvising on synthesizer. The tree of music has lots of branches.

I'm confident that if I had been born in that period I'd have found a way.
It's really no more or less complex to learn (in the end) than today's
techniques are, I'm discovering. It's just trying to ascertain (now) what
the limits might
have been (then). After the initial learning curve, span of years,
accompaniment and even improvisation would be effortless, then as now. And
back then I would have learned a great deal by watching and listening to
others who had already laid a foundation. I would have picked it up by ear
quickly (whatever it might have been). I'm at a great disadvantage here and
now because my primary senses, my best learning tools, my ears and eyes, and
the one-on-one and hand-to-hand, are being denied me. I'm not able to absorb
the music in a "natural" way here and now, I haven't been absorbing it since
infancy, it hasn't been in the environment and all around me, as second
nature, easy. If I was young again I would take that challenge and run with
it "if you can
get under that tree and play or improvise in a 13th-century style, and have
the fluency and technique to do a more or less complex three-voice texture,

go to it". Someone in the next generations probably will do, and the more
help they get, the more likely it'll be.

Thanks
Roger

Post by Margo Schulter
Most appreciatively,
Margo Schulter

[Cait]

Margo -

Thanks for a really interesting discussion. I can only give a quick
reply at the moment but will try to follow up next week when I may
have more time. Your comments both on possible sources (such as
Robertsbridge) that might represent how 'accompaniment' was built,
and on the awareness of 'vertical' structure that is evidenced in
the theoretical writings is very useful.

I think your conception of 'split intervals' is a fascinating
one, certainly from a harpist's perspective. I often make strong
use of the 1-5-8 'trine' as the 'default' for accompaniment
to a monophonic song (e.g if playing the melody, adding the octave
and fifth on cadences); frequently one can get a good effect by
maintaining the same 1-5 as a drone as the tune moves, or moving
the 1-5 at a 'slower' rate than the tune as suggested in your

Post by Margo Schulter
1 2 3 | 1 2 3 | 1
Melody: F4 E4 D4 E4 F4
C4 D4 C4
Accompaniment: F3 G3 F3

I would be interested in whether you would agree with Bill Taylor
(an expert in early harp traditions in the British Isles) that
another way to think about this is in terms of a 'home' position
(F-C-F) and an 'away' position (G-D-(G)). It is often a convenient
way to discover a quick option for accompaniment, particularly of
simple tunes (like some cantigas), to look at how to break the tune
down into a sequence of 'home' and 'away' positions. On the other
hand I'm not always convinced that it is the best solution, and it
does raise the interesting problem of whether the third should be
considered part of 'home' or 'away'.

regards

Cait

[Todd Michel McComb]

I think your conception of 'split intervals' is a fascinating one,
certainly from a harpist's perspective.

Apropos this discussion, I thought I'd add that Tim Rayborn recently
released a recording which is entirely of improvisatory material
in a medieval style, on both harp and psaltery:

http://www.medieval.org/emfaq/cds/wbr0302.htm

At one point, Tim was around this newsgroup a little bit, but I
doubt he's reading this now, unfortunately. I hesitate to try to
summarize his efforts here.

Todd McComb
***@medieval.org

[Margo Schulter]

Post by Cait
Thanks for a really interesting discussion. I can only give a quick
reply at the moment but will try to follow up next week when I may
have more time. Your comments both on possible sources (such as
Robertsbridge) that might represent how 'accompaniment' was built,
and on the awareness of 'vertical' structure that is evidenced in
the theoretical writings is very useful.

Dear Cait and All,

Thank you for this encouraging reply: your participation here has
given me a lot of creative energy, and in discussing theory, it's
great to get feedback from people who play period instruments.

You ask some questions which really have me going on an essay of
sorts, but for the moment I'll be quick and enthusiastic about the
ideas you've brought in, and turn to that essay within the next 24
hours, I hope.

Post by Cait
I think your conception of 'split intervals' is a fascinating one,
certainly from a harpist's perspective. I often make strong use of
the 1-5-8 'trine' as the 'default' for accompaniment to a monophonic
song (e.g if playing the melody, adding the octave and fifth on
cadences); frequently one can get a good effect by maintaining the
same 1-5 as a drone as the tune moves, or moving the 1-5 at a

Post by Margo Schulter
1 2 3 | 1 2 3 | 1
Melody: F4 E4 D4 E4 F4
C4 D4 C4
Accompaniment: F3 G3 F3

Indeed, I'm fascinated with the question of how a harpist might relate
to the partitions of "split intervals" of Jacobus. You make the very
important point that someone playing trines or fifths in accompanying
a melody is apt to arrive at this kind of texture intuitively, as it
were.

Post by Cait
I would be interested in whether you would agree with Bill Taylor
(an expert in early harp traditions in the British Isles) that
another way to think about this is in terms of a 'home' position
(F-C-F) and an 'away' position (G-D-(G)). It is often a convenient
way to discover a quick option for accompaniment, particularly of
simple tunes (like some cantigas), to look at how to break the tune
down into a sequence of 'home' and 'away' positions.

My quick response is that this is a very typical pattern for lots of
polyphonic pieces, one that might lots of monophonic songs as a
starting point for an accompaniment, and also a great exercise for
improvisation: a medieval "ground bass" as it were!

Ernest Sanders has written about this kind of pattern in 13th-century
English polyphony, and while I'd lean in other directions than some of the
18th-century analytical language and value judgments in making comparisons
to the French repertory that people sometimes apply, the F-G-F thing is
indeed noteworthy. One famous example in English music is _Sumer is
icumen in_, where this is just what the two-voice _pes_ does: you could go
through the whole piece with exactly the technique you've described.

Lots of French motets have this kind of pattern, too, as well as a
rondeau of Adam de la Halle that immediately occurs to me. More on
this in my essay.

After reading your post, I found myself standing at a modest
glockenspiel, and simply alternating between F and G, and getting into
some neat improvisational ideas for an upper voice. Of course, in a
style where the favorite directed vertical progressions tend to
involve stepwise contrary motion, this "alternating step" business can
get you into lots of creative two-voice or three-voice improvising.

Post by Cait
On the other hand I'm not always convinced that it is the best
solution, and it does raise the interesting problem of whether the
third should be considered part of 'home' or 'away'.

Of course, it's one common and invaluable pattern rather than the key
to all 13th-century music: your mileage, or kilometrage, may vary. If
a piece has a "departure and return" kind of structure, starting on F
and returning to it, it might fit nicely. For a piece with a structure
more like an _In Seculum_ setting, starting on C and often emphasizing
that trine or fifth would fit better: here F is the "final" in the
sense of the place where you finally arrive, typically by a G-F
cadence of some kind, rather than the place that gets lots of emphasis
through the piece. In my essay, I'll try to clarify and develop this
more. Again, I'm looking at the structure of polyphony, but some of
this might apply to accompaniment of monophony also.

As to the third degree above the final, say A with a final of F, there
can be a range of answers. Sometimes in polyphony, if the lowest voice
moves F-G-A, we alternate stable and unstable sonorities so that F is
a stable "home," G unstable, and A a kind of "home away from home."
Now and then, A can definitely be "away," with an unstable sonority
resolving directly to F. Then, again, often we have A leading to G,
which leads in turn to F, which can get us into some fluid
progressions. Also, we might start a piece on an A trine, move around
a bit -- and conclude on a final of F, as Adam de la Halle does in one
rondeau.

I'll try to explain some of these options in my essay. Of course, a
more general answer is the one suggested by your remarks: try it with
a given melody, and see if it fits.

Post by Cait
regards

Most appreciatively,

Margo Schulter
***@calweb.com

[Margo Schulter]

-----------------------------------------
Medieval Polyphonic Patterns:
An Essay with Thanks to Cait
Part I: The F-G-F theme
-----------------------------------------

Please let me commence this promised essay by warmly thanking Cait for
an exciting dialogue, and specifically for inspiring this post by
sharing a suggestion of Bill Taylor, an expert in early harp music of
the British Isles, that one typical medieval pattern useful in
accompanying songs is a "home" sonority on F and an "away" sonority on
G -- for example, an alternation between F3-C4-F4 and G3-D4 or
G3-D4-G4.

In looking at this and other characteristic patterns in medieval
music, I'm going to focus on what happens in polyphonic compositions.
This recorded practice could serve as one guide to possible
instrumental accompaniment practices for monophonic songs, albeit a
guide which one might want to use with some caution and with due
artistic judgment.

When I speak of caution and judgment, I have in mind especially some
predilections and at least potential biases of my own to which the
reader should be alerted.

First, for 35 years and a bit more, I've been improvising polyphonic
textures in a medieval vocal kind of style on keyboards. If I produce
something that evokes for me an ensemble organum, clausula, conductus,
motet, or cantilena, etc., then I'm happy. Also, my compositional and
analytical efforts have focused on written polyphony.

Secondly, my responses to improvised accompaniments in performances of
monophonic song might reflect more a delight in familiar textures --
"how neat to have this trouvere song sound like an extempore conductus
or motet" -- rather than a judicious evaluation of likely performance
practices for a particular genre at a particular epoch.

To take what might some might consider an especially telling example:
I have taken great pleasure in a rendition of a trobador song by
Marcabru, from around the middle of the 12th century, performed in a
lilting modal rhythm with a plucked string accompaniment, as I recall,
in a nice discant style (as noted in the performance notes) which I
found a bit like a conductus.

Someone looking more critically at likely period style might ask
whether trobador songs in this era were likely to be accompanied at
all (a debatable question, as we've seen in recent threads), and
whether a modal rhythm would prevail rather than a freer declamatory
reading.

Anyway, there are some implicit assumptions in what follows that I'd
like to make a bit more explicit. I tend to assume some kind of modal
or mensural rhythm which could invite something like a composed
polyphonic texture in this type of rhythm, and an approach where
techniques like three-voice sonorities and progressions would not be
out of place. These are the things that I'm accustomed to do, not
necessarily the ones you'd want to do in a given situation.

For more freely declamatory songs, there could be other models. One
could look at polyphonic settings from the 13th century or a bit later
of Psalm recitation tones or the like, or even consider a trinic
equivalent of the "dry recitative" of the 17th century or later.

With these caveats, I'll first consider the F-G-F pattern, and then,
in Part II, another question which you have raised, Cait: the
relationship between steps a third apart, such as F and A.

It's prudent to conclude this preface by saying that the possibilities
suggested below are meant to be illustrative rather than exhaustive.


--------------------
1. The F-G-F pattern
--------------------

In recommending the "F home, G away" pattern, Bill Taylor has called
attention to a theme characteristic of much Continental as well as
English music in the 13th century.

We might actually take this as a theme within a yet more pervasive
theme: the frequent alternation between steps a degree apart, typical
of a style where progressions by stepwise contrary motion define the
ideal for efficient and compelling cadential action. Thus if our final
or trinic center of repose in on F, we'd expect unstable cadential
sonorities on the adjacent steps of G or E, and this is in fact what
tends to happen in standard practice.

Likewise, if the final is G, we might expect to find and do find that
the most popular cadences involve unstable sonorities on the adjacent
steps of A or F, and so on.


--------------------------------
1.1. A Montpellier manifestation
--------------------------------

Here we'll focus on the F-G-F theme, and some of its documented or
possible expressions. First, I'll quickly recall an example adapted
from the opening of a 13th-century Montpellier motet, #103, _Aimi!
las! vivrai_/_Doucement me tient_/OMNES, which I seem first to have
encountered through an analysis of Richard Crocker in his _A History
of Musical Style_:

1 2 3 | 1 2 3 | 1 ...
F4 E4 D4 E4 F4
C4 D4 C4
F3 G3 F4

(Maj7-5 + Maj3-1) (Maj6-8 + Maj2-4)

Here I've indicated the transient directed progressions introduced by
the seventh sonority F3-C4-E4 at the end of the first unit and the
sixth sonority G3-D4-E4 at the end of the second, each lending impetus
to the musical motion forward into the next unit. The momentary
partitions of M7|5_M3 and M6|5_M2 add a bit of color to the stable
consonances, and the directed resolutions briding from one unit to the
next could be described as _cadentiae_ in a medieval meaning of that
term: apt progressions from more tense to more concordant intervals.


----------------------
1.2. A different style
----------------------

Taking the same framework for the two outer voices, we can also arrive
at a passage from one of the most famous F-G-F pieces of the era, here
transcribed in a 6/8 or 6/4 meter with two main beats to each measure:

1 2
1 2 3 4 5 6 | 1 ...
F4 E4 D4 E4 F4
C4 Bb3 C4
F3 G3 F4

(Maj6-8 + min3-5)

From a conventional Continental point of view, we start at "home" on
the F trine, and move to "away" on a mildly unstable sonority: the
split fifth G3-Bb3-D4, with its two unstable thirds, 5|m3_M3. Then
the E4 in the upper voice gives us the momentary sixth sonority
G3-Bb3-E4 or M6|m3_4, resolving in usual fashion to arrive back at our
trinic "home" on F (Maj6-8 + min3-5).

In fact, however, this is the opening of the English round _Sumer is
icumen in_, if one starts with the entry of the first voice singing
the main canonic melody above the repeated _pes_ in the lower two
voices. (If we elect to sing the pes voices alone first to give a feel
for the "ground bass" pattern, then this passage would be a bit after
the opening.)

While this three-voice passage at the beginning of the canon might
suggest an F-G-F theme of trine-split fifth-trine, as more voices
enter it quickly becomes clear that we have a different vertical style
with pervasive tertian sonorities as the norm, the kind of thing
reported by Anonymous IV for the "Westcountry" of England. This kind
of writing, where thirds are treated as stable and conclusive,
contrasts with other kinds of styles in England as well as on the
Continent where these intervals are regarded as mildly unstable, and
often participate in directed progressions to stable sonorities such
as trines.


-------------------------------
1.3. A diversion after midnight
-------------------------------

Getting back to the latter kind of style, we could harmonize the
framework of the outer two voices in many ways, for example this:

1 2 3 | 1 2 3 | 1 ...
F4 E4 D4 E4 F4
C4 D4 C4 B3 C4
F3 G3 F4

(Maj7-5 + Maj3-1) (Maj6-8 + Maj3-5)

This solution might come out of the same stylistic milieu as our first
example adapted from Montpellier: as in that example, the quick
directed resolutions leading from one rhythmic unit to the next help
move the harmonic rhythm along, and also to provide moments of unity
knitting the voices together in their often diverse motions.

The theme of alternating between F and G can be a taking off point for
lots of ideas. For example, here's something I came up with very early
this morning as a kind of belated midnight discant diversion, with "r"
in this notation showing a rest:

1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 |
D4 E4 F4 r G4 D4 E4 F4
D4 B3 C4 E4 D4 C4 B3 C4
G3 F3 G3 F3

(Maj6-8 + Maj3-5) (Maj7-5) (Maj6-8 + Maj3-5)

Again I'm showing the directed resolutions because this is an aspect
of technique in lots of motets and the like which it seems to me it
wouldn't hurt to do my part in emphasizing. Certainly I wouldn't want
to suggest this kind of harmonic rhythm -- directed tension at the end
of a unit resolved at the beginning of the next -- as any kind of
"rule"; it's just a common and useful technique.

Other nuances here are the rest in the highest voice, followed by its
entry to supply the octave of a complete trine, and then by a turn of
phrase in this voice yielding a momentary sonority of G3-C4-D4, or
5|4_M2. From any usual standpoint this kind of sonority in the middle
of a unit is quite incidental, and one might well have the voices
proceed in the sam way for melodic reasons quite apart from this
vertical detail. However, I must confess to a weakness for 5|4_M2, and
find it a nice touch of color.


-----------------------------------------
1.4. Adam de la Halle: An artful contrast
-----------------------------------------

A complete three-voice rondeau by Adam de la Halle might illustrate
the F-G-F theme in another guise while also demonstrating an artful
use of form to give shape to the "home-away-home" scenario.

Readings of the rhythmic fine points in this rondeau, _He, Diex! quant
verrai_, can vary, so that this version is only one possible solution,
with each of the indicated semibreves dividing a breve taken as having
equal duration (e.g. triplets at the end of the second unit):

Musical Form: AB AAAB AB

A | B

1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 + 2 + 3 | 123 ||
C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3 C4
F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4 F4
F3 F3 A3 G3 A3 G3 G3 F3

Here the middle voice has the main melody, and we have a "departure
and return" kind of scenario starting on F and eventually returning
there. Of special interest, and marking a pivotal point in both the
vertical structure and the form, is the unstable split fifth sonority
G3-B3-D4 or 5|M3_m3, strategically situated at the middle of the
piece.

This mildly unstable sonority, which Jacobus as a passionate advocate
for this late 13th-century era will note as a pleasant element of
style when aptly handled, marks a pregnant pause in the form: it
occurs at the end of the "A" section of the rondeau, and signals that
there is more to come.

Moving into the "B" section, we first proceed to another split fifth
sonority on A, the step above G, which leads by a very transient sixth
sonority A3-C4-F4 or m6|m3_4 to a momentary resolution on a G trine
(min6-8 + min3-5), then bringing the music back home with a usual
cadence from a sixth sonority on G to F (Maj6-8 + Maj3-5).

A neat touch of cadential strategy occurs in the portion of the
musical form -- AB AAAB AB -- where the "A" section is thrice
repeated. Here the conclusion of this section is directly followed by
a return to the beginning -- resulting in another standard
13th-century cadence (voice-crossing disregarded for the moment):

D4... F4
B3... C4
G3... F3

(Maj3-5)

In this formula for a G-F cadence, or more generally a cadence where
the lowest voice descends by a step, the lower third of the _quinta
fissa_ (here major) expands to a fifth, while the outer fifth expands
to the octave of a complete trine. While not quite as "efficient" as
cadences where all unstable intervals resolve by stepwise contrary
motion -- here the upper minor third resolves by similar motion to the
upper fourth of the trine, and the highest voice leaps by a third --
this progression is common, and serves as a close in motets.

Here it serves at once to resolve the suspense caused by the
conclusion of the "A" section on an unstable sonority, to reaffirm the
contrast between F as "home" and G as "away," and also to give the
piece a pleasant profile through the minor third motion D4-F4 in the
highest voice of this formula. The actual voice-leading here involves
a crossing of parts:

D4... C4
B3... F4
G3... F3

As a kind of lead-in to Part II, I'll briefly note two possible roles
for the step A in this piece on F.

In the "A" section at the second unit, the trine A3-E4-A4 might be
considered a momentary "home away from home": it is approached by a
transient Maj2-4 resolution between the upper voices. When the A trine
does play this role, it might be considered as something of a
polyphonic equivalent of a confinal -- or, I might say, co-center. For
example, we might have F as center or final, A as co-center, and G as
an active step contrasting with either.

In the "B" section we see another possible role for the step A, by no
means necessarily incompatible with the previous role: a step in
cadential progressions leading to G, which in turn leads to F. Thus if
we try to come up with a simplified version of the "B" section, we
might get something like this:

... 3 | 1 2 3 | 1 2 3 ||
E4 F4 G4 E4 F4
C4 D4 B3 C4
A3 G3 F3

Here a sixth sonority on A resolves to a trine on G, and the upper
voices then move to another sixth sonority on G which resolves to F.
One might say that A is to G somewhat as G is to F.

In this piece, we might call F the "ultimate" goal, and G the
"penultimate," since it is the step with the cadential sixth sonority
leading directly to this goal.

Since the step A in this sequence likewise has an unstable sonority
resolving to a trine on the step G, we might if so inclined call it
"the penultimate of the penultimate."

Of course, this simplified version of the "B" section disregards
Adam's elegant ornamentation of the close, and also the variety
brought about by the voice-crossing. As Richard Crocker has well said
in regard to the 13th-century motet, the composers are adept in
finding rich variations on standard passages and progressions.

Influences proposed for these three-voice rondeaux of Adam include the
conductus, the polyphonic rondellus, and improvised accompaniments of
monophonic dance songs. If the last influence were significant,
these masterpieces might record some of what improvising musicians
were doing -- or one version of this, as adapted by a composer skilled
in both the trouvere song and the motet.

At any rate, the F-G-F or more generally "adjacent home and away
steps" theme is a fertile start for improvising or composing: the
dilemma remains, of course, as to which types of improvised polyphonic
techniques, or possibly newly composed arrangements, one considers
appropriate for a given genre in a given performance situation, with
"HAP or HEP" questions[1] likely playing a role in one's choices.


---------------------------------------
1.5. An aside: Fluidity and oscillation
---------------------------------------

Having traced out some of the possibilities of the F-G-F theme, I
should add that in some pieces we have a fluid oscillation or
"see-sawing" between F and G in which either might prove to be "home."

Part of this picture is that just as G is a favorite penultimate for a
center on F, so F is an adjacent degree and common penultimate for a
center on G. Consider this final cadence of a kind often found, for
example, in conducti:

C4 D4
A3 G3
F3 G3

(Maj3-1 + min3-5)

Here a split fifth on F, 5|M3_m3, resolves to a stable fifth on G;
thus G is the ultimate, and F the cadential penultimate.

In some pieces, there's a charming fluidity, moving back and forth
between F and G and eventually settling on one or the other at the
final cadence. This happens in a most elegant motet, _On parole/A
Paris/FRESE NOUVELE, Montpellier #319.

The piece opens with a trine on F, and soon displays a felicitous
point of form facilitated by the structure of the French tenor,
apparently a street cry advertising "Fresh strawberries, wild
blackberries" -- or, it has been suggested by one commentator,
possibly recording some kind of political slogan.

To see (and hear) this point of form, let us consider the progression
at the conclusion of the first statement of the tenor melody, measures
7-9 in a modern transcription barred in 3/4:

1 2 3 + | 1 2 3 | 1 2 3 |
A4 A4 G4 F4 G4 D4 E4 F4
E4 D4 C4 D4 r C4
A3 G3 r F3

Here we start with a trine on A, with the upper voices moving by the
end of the unit to a very quick sixth sonority resolving to a trine on
G (min6-8 + min3-5). While the lower two voices pause at the end of
the measure, the note E4 in the highest voice exerts a very satisfying
pull to the full trine on F.

This formula thus might resemble the "B" section of the rondeau by
Adam de la Halle (Section 1.4): there is again a descent in the lowest
voice of A-G-F, with A leading to a momentary resolution to G, and G
to a trine on F.

However, the second and third rhythmic units of this example actually
splice together the conclusion of the first statement of the tenor,
ending on G, as marked by the rest, and the commencement of the next
statement starting on F. At the conclusion of this delightful motet,
one of the most beautiful pieces of music I have heard, we settle
agreebly on a final cadence to G:

1 + 2 3 + | 1 2 3 ||
G4 A4 A4 G4 F4 G4
A3 B3 C4 D4
A3 G3

In addition to illustrating the fluid interplay between F and G, this
piece has a feature making it appropriate to quote here: in the first
excerpt, the melodic turn in the highest line of G4-D4-E4-F4 provides
one not unlikely source for my own use of this figure (Section 1.3).


----
Note
----

1. "Historically Appropriate Performance" (HAP) aims to do, and do
well, what reasonably _may_ have been done in a given era and genre;
"Historically Educated Performance" (HEP) seeks to canvass period
sources and then do something that "fits the music in an informed
way," quite possibly using new techniques, or techniques of a group
such as the Studio for Early Music which some might hold more typical
of 1970 than 1270.

[Roger E. Blumberg]

Hi Margo;
(and thanks as usual)

I've tried to realign the ASCII example that you gave for fig.1.4 (the
complete three-voice rondeau by Adam de la Halle), here quoted below, so I
can begin asking questions about it. I've done the realigning judging by
what I see when I view it from my Mac. PC and PC fonts seem to be mucking
things up a bit (when I view it from my PC). If you Margo are viewing this
on a Mac, I don't know how it will appear to you, better or worse, Does this
realignment look correct and representative to you? Are you on a Mac?)

A | B
1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 +

2 + 3 | 123 ||

C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3 C4
F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4

F4

F3 F3 A3 G3 A3 G3

G3 F3


anyhow, here goes.
First, I got stuck on the opening bar, this part below. . . . .
the crossed voices and unisons had me tearing my hair out ;')

1 2 3 + | 1
C4 F4 G4 A4
F4 F4 E4
F3 F3 A3

Is there any way to simplify that opening (before the "A" trine)? I'm
thinking that the real heart of this example begins just after, at that AEA
trine. There's some fabulous stuff going on in that example, and the opening
just doesn't seem to do it justice (in addition to being difficult to
execute) i.e. It would be a shame to miss the good stuff because of the
opening (if people can't get past the opening). Do you think I or we would
loose anything by changing the opening to 2 trines, on F and G? When I do
that I still get the impetus, the drive, to the AEA trine where the action
really begins. You said the center voice has the melody generally, but the
top voice is carrying it in the opening, including that huge jump C4 to F4.
At any rate, a "G" trine seems to suffice to get you from the opening "F"
trine to the "A" trine and even implys that melody line C, F, G, A (to me at
least). Perhaps even the Guido trine on "G" (I don't know what the correct
term is but it's the 8|4_5 split rather than 8|5_4 )? I don't mean to
rewrite history, I'm just looking for a way to allow the good stuff to rise
the top more easily, be more accessible, give the real focal point of the
exercise the focus (if I'm reading your intent right, i.e. why you chose
this particular example and what you're really wanting us to hear. Even on a
piano that opening, with it's unison, would be impossible to perform, hence
hear).

Also, I'm wondering about the A3 to G3 (lowest voice). Should I be pedaling
that A3 all the way through to G3? Similarly, all voices are being
maintained throughout, so at all points there's still a 3 voice vertical
sonority happening, i.e. if I were to map this out on a fretboard I could
still block it out 3 voices per any moment in time? I'm assuming yes, but I
just want to be sure. In another example you specifically include a rest (r)
at points where voices fall silent.

Lastly, I don't seem to get the turn-around in this piece, beginning at the
"G3, D3, G3" stack. Everything is beautiful up to that point, really cooking
along, and then it looses me completely. Either something's not working in
the composition or I'm not doing the rhythm properly, but every time I get
to that part it "goes in the dumpster" if you will. The whole last 5 chord
passage just doesn't seem to belong there, it doesn't get you back to the F
trine in any satisfactory way (to me), no preparation or something. It's
almost like two people wrote this piece, some master did the central part
and then someone else wrote the opening and the close ;') Sorry, but
something isn't working there for me. Got any ideas what I'm doing wrong,
(I'm hoping that it _is_ me, because the center part is so cool)? I hear
three possible "next chords" (or simply general melodic movements) that
might follow the "G3, D3, G3" stack smoothly, but none of them are what's
being used and none of them get you back to the F trine either. That's what
I mean, there's no natural impetus to want you to return to the F trine yet,
and the turnaround or transition provided doesn't seem to be working either
(for me). In fact, the peice seems to me to have "A" as it's "home", not F.
The turnaround I like best from the "G3, D3, G3" stack is "E trine" then
right back to the "A trine" passage (I love that part, I want to hear it and
play it over and over again ;') But I still can't bring myself to want or
need to get back to F as home.

Thanks
Roger

-----------------------------------------
An Essay with Thanks to Cait
Part I: The F-G-F theme
-----------------------------------------
Please let me commence this promised essay by warmly thanking Cait for
an exciting dialogue, and specifically for inspiring this post by
sharing a suggestion of Bill Taylor, an expert in early harp music of
the British Isles, that one typical medieval pattern useful in
accompanying songs is a "home" sonority on F and an "away" sonority on
G -- for example, an alternation between F3-C4-F4 and G3-D4 or
G3-D4-G4.
In looking at this and other characteristic patterns in medieval
music, I'm going to focus on what happens in polyphonic compositions.
This recorded practice could serve as one guide to possible
instrumental accompaniment practices for monophonic songs, albeit a
guide which one might want to use with some caution and with due
artistic judgment.
When I speak of caution and judgment, I have in mind especially some
predilections and at least potential biases of my own to which the
reader should be alerted.
First, for 35 years and a bit more, I've been improvising polyphonic
textures in a medieval vocal kind of style on keyboards. If I produce
something that evokes for me an ensemble organum, clausula, conductus,
motet, or cantilena, etc., then I'm happy. Also, my compositional and
analytical efforts have focused on written polyphony.
Secondly, my responses to improvised accompaniments in performances of
monophonic song might reflect more a delight in familiar textures --
"how neat to have this trouvere song sound like an extempore conductus
or motet" -- rather than a judicious evaluation of likely performance
practices for a particular genre at a particular epoch.
I have taken great pleasure in a rendition of a trobador song by
Marcabru, from around the middle of the 12th century, performed in a
lilting modal rhythm with a plucked string accompaniment, as I recall,
in a nice discant style (as noted in the performance notes) which I
found a bit like a conductus.
Someone looking more critically at likely period style might ask
whether trobador songs in this era were likely to be accompanied at
all (a debatable question, as we've seen in recent threads), and
whether a modal rhythm would prevail rather than a freer declamatory
reading.
Anyway, there are some implicit assumptions in what follows that I'd
like to make a bit more explicit. I tend to assume some kind of modal
or mensural rhythm which could invite something like a composed
polyphonic texture in this type of rhythm, and an approach where
techniques like three-voice sonorities and progressions would not be
out of place. These are the things that I'm accustomed to do, not
necessarily the ones you'd want to do in a given situation.
For more freely declamatory songs, there could be other models. One
could look at polyphonic settings from the 13th century or a bit later
of Psalm recitation tones or the like, or even consider a trinic
equivalent of the "dry recitative" of the 17th century or later.
With these caveats, I'll first consider the F-G-F pattern, and then,
in Part II, another question which you have raised, Cait: the
relationship between steps a third apart, such as F and A.
It's prudent to conclude this preface by saying that the possibilities
suggested below are meant to be illustrative rather than exhaustive.
--------------------
1. The F-G-F pattern
--------------------
In recommending the "F home, G away" pattern, Bill Taylor has called
attention to a theme characteristic of much Continental as well as
English music in the 13th century.
We might actually take this as a theme within a yet more pervasive
theme: the frequent alternation between steps a degree apart, typical
of a style where progressions by stepwise contrary motion define the
ideal for efficient and compelling cadential action. Thus if our final
or trinic center of repose in on F, we'd expect unstable cadential
sonorities on the adjacent steps of G or E, and this is in fact what
tends to happen in standard practice.
Likewise, if the final is G, we might expect to find and do find that
the most popular cadences involve unstable sonorities on the adjacent
steps of A or F, and so on.
--------------------------------
1.1. A Montpellier manifestation
--------------------------------
Here we'll focus on the F-G-F theme, and some of its documented or
possible expressions. First, I'll quickly recall an example adapted
from the opening of a 13th-century Montpellier motet, #103, _Aimi!
las! vivrai_/_Doucement me tient_/OMNES, which I seem first to have
encountered through an analysis of Richard Crocker in his _A History
1 2 3 | 1 2 3 | 1 ...
F4 E4 D4 E4 F4
C4 D4 C4
F3 G3 F4
(Maj7-5 + Maj3-1) (Maj6-8 + Maj2-4)
Here I've indicated the transient directed progressions introduced by
the seventh sonority F3-C4-E4 at the end of the first unit and the
sixth sonority G3-D4-E4 at the end of the second, each lending impetus
to the musical motion forward into the next unit. The momentary
partitions of M7|5_M3 and M6|5_M2 add a bit of color to the stable
consonances, and the directed resolutions briding from one unit to the
next could be described as _cadentiae_ in a medieval meaning of that
term: apt progressions from more tense to more concordant intervals.
----------------------
1.2. A different style
----------------------
Taking the same framework for the two outer voices, we can also arrive
at a passage from one of the most famous F-G-F pieces of the era, here
1 2
1 2 3 4 5 6 | 1 ...
F4 E4 D4 E4 F4
C4 Bb3 C4
F3 G3 F4
(Maj6-8 + min3-5)
From a conventional Continental point of view, we start at "home" on
the F trine, and move to "away" on a mildly unstable sonority: the
split fifth G3-Bb3-D4, with its two unstable thirds, 5|m3_M3. Then
the E4 in the upper voice gives us the momentary sixth sonority
G3-Bb3-E4 or M6|m3_4, resolving in usual fashion to arrive back at our
trinic "home" on F (Maj6-8 + min3-5).
In fact, however, this is the opening of the English round _Sumer is
icumen in_, if one starts with the entry of the first voice singing
the main canonic melody above the repeated _pes_ in the lower two
voices. (If we elect to sing the pes voices alone first to give a feel
for the "ground bass" pattern, then this passage would be a bit after
the opening.)
While this three-voice passage at the beginning of the canon might
suggest an F-G-F theme of trine-split fifth-trine, as more voices
enter it quickly becomes clear that we have a different vertical style
with pervasive tertian sonorities as the norm, the kind of thing
reported by Anonymous IV for the "Westcountry" of England. This kind
of writing, where thirds are treated as stable and conclusive,
contrasts with other kinds of s yles in England as well as on the
Continent where these intervals are regarded as mildly unstable, and
often participate in directed progressions to stable sonorities such
as trines.
-------------------------------
1.3. A diversion after midnight
-------------------------------
Getting back to the latter kind of style, we could harmonize the
1 2 3 | 1 2 3 | 1 ...
F4 E4 D4 E4 F4
C4 D4 C4 B3 C4
F3 G3 F4
(Maj7-5 + Maj3-1) (Maj6-8 + Maj3-5)
This solution might come out of the same stylistic milieu as our first
example adapted from Montpellier: as in that example, the quick
directed resolutions leading from one rhythmic unit to the next help
move the harmonic rhythm along, and also to provide moments of unity
knitting the voices together in their often diverse motions.
The theme of alternating between F and G can be a taking off point for
lots of ideas. For example, here's something I came up with very early
this morning as a kind of belated midnight discant diversion, with "r"
1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 |
D4 E4 F4 r G4 D4 E4 F4
D4 B3 C4 E4 D4 C4 B3 C4
G3 F3 G3 F3
(Maj6-8 + Maj3-5) (Maj7-5) (Maj6-8 + Maj3-5)
Again I'm showing the directed resolutions because this is an aspect
of technique in lots of motets and the like which it seems to me it
wouldn't hurt to do my part in emphasizing. Certainly I wouldn't want
to suggest this kind of harmonic rhythm -- directed tension at the end
of a unit resolved at the beginning of the next -- as any kind of
"rule"; it's just a common and useful technique.
Other nuances here are the rest in the highest voice, followed by its
entry to supply the octave of a complete trine, and then by a turn of
phrase in this voice yielding a momentary sonority of G3-C4-D4, or
5|4_M2. From any usual standpoint this kind of sonority in the middle
of a unit is quite incidental, and one might well have the voices
proceed in the same way for melodic reasons quite apart from this
vertical detail. However, I must confess to a weakness for 5|4_M2, and
find it a nice touch of color.
-----------------------------------------
1.4. Adam de la Halle: An artful contrast
-----------------------------------------
A complete three-voice rondeau by Adam de la Halle might illustrate
the F-G-F theme in another guise while also demonstrating an artful
use of form to give shape to the "home-away-home" scenario.
Readings of the rhythmic fine points in this rondeau, _He, Diex! quant
verrai_, can vary, so that this version is only one possible solution,
with each of the indicated semibreves dividing a breve taken as having
Musical Form: AB AAAB AB
A | B
1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 + 2 + 3 | 123 ||
C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3 C4
F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4 F4
F3 F3 A3 G3 A3 G3 G3 F3
Here the middle voice has the main melody, and we have a "departure
and return" kind of scenario starting on F and eventually returning
there. Of special interest, and marking a pivotal point in both the
vertical structure and the form, is the unstable split fifth sonority
G3-B3-D4 or 5|M3_m3, strategically situated at the middle of the
piece.
This mildly unstable sonority, which Jacobus as a passionate advocate
for this late 13th-century era will note as a pleasant element of
style when aptly handled, marks a pregnant pause in the form: it
occurs at the end of the "A" section of the rondeau, and signals that
there is more to come.
Moving into the "B" section, we first proceed to another split fifth
sonority on A, the step above G, which leads by a very transient sixth
sonority A3-C4-F4 or m6|m3_4 to a momentary resolution on a G trine
(min6-8 + min3-5), then bringing the music back home with a usual
cadence from a sixth sonority on G to F (Maj6-8 + Maj3-5).
A neat touch of cadential strategy occurs in the portion of the
musical form -- AB AAAB AB -- where the "A" section is thrice
repeated. Here the conclusion of this section is directly followed by
a return to the beginning -- resulting in another standard
D4... F4
B3... C4
G3... F3
(Maj3-5)
In this formula for a G-F cadence, or more generally a cadence where
the lowest voice descends by a step, the lower third of the _quinta
fissa_ (here major) expands to a fifth, while the outer fifth expands
to the octave of a complete trine. While not quite as "efficient" as
cadences where all unstable intervals resolve by stepwise contrary
motion -- here the upper minor third resolves by similar motion to the
upper fourth of the trine, and the highest voice leaps by a third --
this progression is common, and serves as a close in motets.
Here it serves at once to resolve the suspense caused by the
conclusion of the "A" section on an unstable sonority, to reaffirm the
contrast between F as "home" and G as "away," and also to give the
piece a pleasant profile through the minor third motion D4-F4 in the
highest voice of this formula. The actual voice-leading here involves
D4... C4
B3... F4
G3... F3
As a kind of lead-in to Part II, I'll briefly note two possible roles
for the step A in this piece on F.
In the "A" section at the second unit, the trine A3-E4-A4 might be
considered a momentary "home away from home": it is approached by a
transient Maj2-4 resolution between the upper voices. When the A trine
does play this role, it might be considered as something of a
polyphonic equivalent of a confinal -- or, I might say, co-center. For
example, we might have F as center or final, A as co-center, and G as
an active step contrasting with either.
In the "B" section we see another possible role for the step A, by no
means necessarily incompatible with the previous role: a step in
cadential progressions leading to G, which in turn leads to F. Thus if
we try to come up with a simplified version of the "B" section, we
... 3 | 1 2 3 | 1 2 3 ||
E4 F4 G4 E4 F4
C4 D4 B3 C4
A3 G3 F3
Here a sixth sonority on A resolves to a trine on G, and the upper
voices then move to another sixth sonority on G which resolves to F.
One might say that A is to G somewhat as G is to F.
In this piece, we might call F the "ultimate" goal, and G the
"penultimate," since it is the step with the cadential sixth sonority
leading directly to this goal.
Since the step A in this sequence likewise has an unstable sonority
resolving to a trine on the step G, we might if so inclined call it
"the penultimate of the penultimate."
Of course, this simplified version of the "B" section disregards
Adam's elegant ornamentation of the close, and also the variety
brought about by the voice-crossing. As Richard Crocker has well said
in regard to the 13th-century motet, the composers are adept in
finding rich variations on standard passages and progressions.
Influences proposed for these three-voice rondeaux of Adam include the
conductus, the polyphonic rondellus, and improvised accompaniments of
monophonic dance songs. If the last influence were significant,
these masterpieces might record some of what improvising musicians
were doing -- or one version of this, as adapted by a composer skilled
in both the trouvere song and the motet.
At any rate, the F-G-F or more generally "adjacent home and away
steps" theme is a fertile start for improvising or composing: the
dilemma remains, of course, as to which types of improvised polyphonic
techniques, or possibly newly composed arrangements, one considers
appropriate for a given genre in a given performance situation, with
"HAP or HEP" questions[1] likely playing a role in one's choices.
---------------------------------------
1.5. An aside: Fluidity and oscillation
---------------------------------------
Having traced out some of the possibilities of the F-G-F theme, I
should add that in some pieces we have a fluid oscillation or
"see-sawing" between F and G in which either might prove to be "home."
Part of this picture is that just as G is a favorite penultimate for a
center on F, so F is an adjacent degree and common penultimate for a
center on G. Consider this final cadence of a kind often found, for
C4 D4
A3 G3
F3 G3
(Maj3-1 + min3-5)
Here a split fifth on F, 5|M3_m3, resolves to a stable fifth on G;
thus G is the ultimate, and F the cadential penultimate.
In some pieces, there's a charming fluidity, moving back and forth
between F and G and eventually settling on one or the other at the
final cadence. This happens in a most elegant motet, _On parole/A
Paris/FRESE NOUVELE, Montpellier #319.
The piece opens with a trine on F, and soon displays a felicitous
point of form facilitated by the structure of the French tenor,
apparently a street cry advertising "Fresh strawberries, wild
blackberries" -- or, it has been suggested by one commentator,
possibly recording some kind of political slogan.
To see (and hear) this point of form, let us consider the progression
at the conclusion of the first statement of the tenor melody, measures
1 2 3 + | 1 2 3 | 1 2 3 |
A4 A4 G4 F4 G4 D4 E4 F4
E4 D4 C4 D4 r C4
A3 G3 r F3
Here we start with a trine on A, with the upper voices moving by the
end of the unit to a very quick sixth sonority resolving to a trine on
G (min6-8 + min3-5). While the lower two voices pause at the end of
the measure, the note E4 in the highest voice exerts a very satisfying
pull to the full trine on F.
This formula thus might resemble the "B" section of the rondeau by
Adam de la Halle (Section 1.4): there is again a descent in the lowest
voice of A-G-F, with A leading to a momentary resolution to G, and G
to a trine on F.
However, the second and third rhythmic units of this example actually
splice together the conclusion of the first statement of the tenor,
ending on G, as marked by the rest, and the commencement of the next
statement starting on F. At the conclusion of this delightful motet,
one of the most beautiful pieces of music I have heard, we settle
1 + 2 3 + | 1 2 3 ||
G4 A4 A4 G4 F4 G4
A3 B3 C4 D4
A3 G3
In addition to illustrating the fluid interplay between F and G, this
piece has a feature making it appropriate to quote here: in the first
excerpt, the melodic turn in the highest line of G4-D4-E4-F4 provides
one not unlikely source for my own use of this figure (Section 1.3).
----
Note
----
1. "Historically Appropriate Performance" (HAP) aims to do, and do
well, what reasonably _may_ have been done in a given era and genre;
"Historically Educated Performance" (HEP) seeks to canvass period
sources and then do something that "fits the music in an informed
way," quite possibly using new techniques, or techniques of a group
such as the Studio for Early Music which some might hold more typical
of 1970 than 1270.

[Roger E. Blumberg]

sorry, that realignment job of the full passage didn't make it through the
wash, it looks worse now (in my post above) than it did before.
The smaller isolated bits in the message turned out ok though.

Roger

Post by Roger E. Blumberg
Hi Margo;
(and thanks as usual)
I've tried to realign the ASCII example that you gave for fig.1.4 (the
complete three-voice rondeau by Adam de la Halle), here quoted below, so I
can begin asking questions about it. I've done the realigning judging by
what I see when I view it from my Mac. PC and PC fonts seem to be mucking
things up a bit (when I view it from my PC). If you Margo are viewing this
on a Mac, I don't know how it will appear to you, better or worse, Does this
realignment look correct and representative to you? Are you on a Mac?)

A | B
1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 +

2 + 3 | 123 ||

C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3

C4

Post by Roger E. Blumberg

F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4

F4

F3 F3 A3 G3 A3 G3

G3 F3
anyhow, here goes.
First, I got stuck on the opening bar, this part below. . . . .
the crossed voices and unisons had me tearing my hair out ;')
1 2 3 + | 1
C4 F4 G4 A4
F4 F4 E4
F3 F3 A3
Is there any way to simplify that opening (before the "A" trine)? I'm
thinking that the real heart of this example begins just after, at that AEA
trine. There's some fabulous stuff going on in that example, and the opening
just doesn't seem to do it justice (in addition to being difficult to
execute) i.e. It would be a shame to miss the good stuff because of the
opening (if people can't get past the opening). Do you think I or we would
loose anything by changing the opening to 2 trines, on F and G? When I do
that I still get the impetus, the drive, to the AEA trine where the action
really begins. You said the center voice has the melody generally, but the
top voice is carrying it in the opening, including that huge jump C4 to F4.
At any rate, a "G" trine seems to suffice to get you from the opening "F"
trine to the "A" trine and even implys that melody line C, F, G, A (to me at
least). Perhaps even the Guido trine on "G" (I don't know what the correct
term is but it's the 8|4_5 split rather than 8|5_4 )? I don't mean to
rewrite history, I'm just looking for a way to allow the good stuff to rise
the top more easily, be more accessible, give the real focal point of the
exercise the focus (if I'm reading your intent right, i.e. why you chose
this particular example and what you're really wanting us to hear. Even on a
piano that opening, with it's unison, would be impossible to perform, hence
hear).
Also, I'm wondering about the A3 to G3 (lowest voice). Should I be pedaling
that A3 all the way through to G3? Similarly, all voices are being
maintained throughout, so at all points there's still a 3 voice vertical
sonority happening, i.e. if I were to map this out on a fretboard I could
still block it out 3 voices per any moment in time? I'm assuming yes, but I
just want to be sure. In another example you specifically include a rest (r)
at points where voices fall silent.
Lastly, I don't seem to get the turn-around in this piece, beginning at the
"G3, D3, G3" stack. Everything is beautiful up to that point, really cooking
along, and then it looses me completely. Either something's not working in
the composition or I'm not doing the rhythm properly, but every time I get
to that part it "goes in the dumpster" if you will. The whole last 5 chord
passage just doesn't seem to belong there, it doesn't get you back to the F
trine in any satisfactory way (to me), no preparation or something. It's
almost like two people wrote this piece, some master did the central part
and then someone else wrote the opening and the close ;') Sorry, but
something isn't working there for me. Got any ideas what I'm doing wrong,
(I'm hoping that it _is_ me, because the center part is so cool)? I hear
three possible "next chords" (or simply general melodic movements) that
might follow the "G3, D3, G3" stack smoothly, but none of them are what's
being used and none of them get you back to the F trine either. That's what
I mean, there's no natural impetus to want you to return to the F trine yet,
and the turnaround or transition provided doesn't seem to be working either
(for me). In fact, the peice seems to me to have "A" as it's "home", not F.
The turnaround I like best from the "G3, D3, G3" stack is "E trine" then
right back to the "A trine" passage (I love that part, I want to hear it and
play it over and over again ;') But I still can't bring myself to want or
need to get back to F as home.
Thanks
Roger

-----------------------------------------
An Essay with Thanks to Cait
Part I: The F-G-F theme
-----------------------------------------
Please let me commence this promised essay by warmly thanking Cait for
an exciting dialogue, and specifically for inspiring this post by
sharing a suggestion of Bill Taylor, an expert in early harp music of
the British Isles, that one typical medieval pattern useful in
accompanying songs is a "home" sonority on F and an "away" sonority on
G -- for example, an alternation between F3-C4-F4 and G3-D4 or
G3-D4-G4.
In looking at this and other characteristic patterns in medieval
music, I'm going to focus on what happens in polyphonic compositions.
This recorded practice could serve as one guide to possible
instrumental accompaniment practices for monophonic songs, albeit a
guide which one might want to use with some caution and with due
artistic judgment.
When I speak of caution and judgment, I have in mind especially some
predilections and at least potential biases of my own to which the
reader should be alerted.
First, for 35 years and a bit more, I've been improvising polyphonic
textures in a medieval vocal kind of style on keyboards. If I produce
something that evokes for me an ensemble organum, clausula, conductus,
motet, or cantilena, etc., then I'm happy. Also, my compositional and
analytical efforts have focused on written polyphony.
Secondly, my responses to improvised accompaniments in performances of
monophonic song might reflect more a delight in familiar textures --
"how neat to have this trouvere song sound like an extempore conductus
or motet" -- rather than a judicious evaluation of likely performance
practices for a particular genre at a particular epoch.
I have taken great pleasure in a rendition of a trobador song by
Marcabru, from around the middle of the 12th century, performed in a
lilting modal rhythm with a plucked string accompaniment, as I recall,
in a nice discant style (as noted in the performance notes) which I
found a bit like a conductus.
Someone looking more critically at likely period style might ask
whether trobador songs in this era were likely to be accompanied at
all (a debatable question, as we've seen in recent threads), and
whether a modal rhythm would prevail rather than a freer declamatory
reading.
Anyway, there are some implicit assumptions in what follows that I'd
like to make a bit more explicit. I tend to assume some kind of modal
or mensural rhythm which could invite something like a composed
polyphonic texture in this type of rhythm, and an approach where
techniques like three-voice sonorities and progressions would not be
out of place. These are the things that I'm accustomed to do, not
necessarily the ones you'd want to do in a given situation.
For more freely declamatory songs, there could be other models. One
could look at polyphonic settings from the 13th century or a bit later
of Psalm recitation tones or the like, or even consider a trinic
equivalent of the "dry recitative" of the 17th century or later.
With these caveats, I'll first consider the F-G-F pattern, and then,
in Part II, another question which you have raised, Cait: the
relationship between steps a third apart, such as F and A.
It's prudent to conclude this preface by saying that the possibilities
suggested below are meant to be illustrative rather than exhaustive.
--------------------
1. The F-G-F pattern
--------------------
In recommending the "F home, G away" pattern, Bill Taylor has called
attention to a theme characteristic of much Continental as well as
English music in the 13th century.
We might actually take this as a theme within a yet more pervasive
theme: the frequent alternation between steps a degree apart, typical
of a style where progressions by stepwise contrary motion define the
ideal for efficient and compelling cadential action. Thus if our final
or trinic center of repose in on F, we'd expect unstable cadential
sonorities on the adjacent steps of G or E, and this is in fact what
tends to happen in standard practice.
Likewise, if the final is G, we might expect to find and do find that
the most popular cadences involve unstable sonorities on the adjacent
steps of A or F, and so on.
--------------------------------
1.1. A Montpellier manifestation
--------------------------------
Here we'll focus on the F-G-F theme, and some of its documented or
possible expressions. First, I'll quickly recall an example adapted
from the opening of a 13th-century Montpellier motet, #103, _Aimi!
las! vivrai_/_Doucement me tient_/OMNES, which I seem first to have
encountered through an analysis of Richard Crocker in his _A History
1 2 3 | 1 2 3 | 1 ...
F4 E4 D4 E4 F4
C4 D4 C4
F3 G3 F4
(Maj7-5 + Maj3-1) (Maj6-8 + Maj2-4)
Here I've indicated the transient directed progressions introduced by
the seventh sonority F3-C4-E4 at the end of the first unit and the
sixth sonority G3-D4-E4 at the end of the second, each lending impetus
to the musical motion forward into the next unit. The momentary
partitions of M7|5_M3 and M6|5_M2 add a bit of color to the stable
consonances, and the directed resolutions briding from one unit to the
next could be described as _cadentiae_ in a medieval meaning of that
term: apt progressions from more tense to more concordant intervals.
----------------------
1.2. A different style
----------------------
Taking the same framework for the two outer voices, we can also arrive
at a passage from one of the most famous F-G-F pieces of the era, here
1 2
1 2 3 4 5 6 | 1 ...
F4 E4 D4 E4 F4
C4 Bb3 C4
F3 G3 F4
(Maj6-8 + min3-5)
From a conventional Continental point of view, we start at "home" on
the F trine, and move to "away" on a mildly unstable sonority: the
split fifth G3-Bb3-D4, with its two unstable thirds, 5|m3_M3. Then
the E4 in the upper voice gives us the momentary sixth sonority
G3-Bb3-E4 or M6|m3_4, resolving in usual fashion to arrive back at our
trinic "home" on F (Maj6-8 + min3-5).
In fact, however, this is the opening of the English round _Sumer is
icumen in_, if one starts with the entry of the first voice singing
the main canonic melody above the repeated _pes_ in the lower two
voices. (If we elect to sing the pes voices alone first to give a feel
for the "ground bass" pattern, then this passage would be a bit after
the opening.)
While this three-voice passage at the beginning of the canon might
suggest an F-G-F theme of trine-split fifth-trine, as more voices
enter it quickly becomes clear that we have a different vertical style
with pervasive tertian sonorities as the norm, the kind of thing
reported by Anonymo s IV for the "Westcountry" of England. This kind
of writing, where thirds are treated as stable and conclusive,
contrasts with other kinds of styles in England as well as on the
Continent where these intervals are regarded as mildly unstable, and
often participate in directed progressions to stable sonorities such
as trines.
-------------------------------
1.3. A diversion after midnight
-------------------------------
Getting back to the latter kind of style, we could harmonize the
1 2 3 | 1 2 3 | 1 ...
F4 E4 D4 E4 F4
C4 D4 C4 B3 C4
F3 G3 F4
(Maj7-5 + Maj3-1) (Maj6-8 + Maj3-5)
This solution might come out of the same stylistic milieu as our first
example adapted from Montpellier: as in that example, the quick
directed resolutions leading from one rhythmic unit to the next help
move the harmonic rhythm along, and also to provide moments of unity
knitting the voices together in their often diverse motions.
The theme of alternating between F and G can be a taking off point for
lots of ideas. For example, here's something I came up with very early
this morning as a kind of belated midnight discant diversion, with "r"
1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 |
D4 E4 F4 r G4 D4 E4 F4
D4 B3 C4 E4 D4 C4 B3 C4
G3 F3 G3 F3
(Maj6-8 + Maj3-5) (Maj7-5) (Maj6-8 + Maj3-5)
Again I'm showing the directed resolutions because this is an aspect
of technique in lots of motets and the like which it seems to me it
wouldn't hurt to do my part in emphasizing. Certainly I wouldn't want
to suggest this kind of harmonic rhythm -- directed tension at the end
of a unit resolved at the beginning of the next -- as any kind of
"rule"; it's just a common and useful technique.
Other nuances here are the rest in the highest voice, followed by its
entry to supply the octave of a complete trine, and then by a turn of
phrase in this voice yielding a momentary sonority of G3-C4-D4, or
5|4_M2. From any usual standpoint this kind of sonority in the middle
of a unit is quite incidental, and one might well have the voices
proceed in the same way for melodic reasons quite apart from this
vertical detail. However, I must confess to a weakness for 5|4_M2, and
find it a nice touch of color.
-----------------------------------------
1.4. Adam de la Halle: An artful contrast
-----------------------------------------
A complete three-voice rondeau by Adam de la Halle might illustrate
the F-G-F theme in another guise while also demonstrating an artful
use of form to give shape to the "home-away-home" scenario.
Readings of the rhythmic fine points in this rondeau, _He, Diex! quant
verrai_, can vary, so that this version is only one possible solution,
with each of the indicated semibreves dividing a breve taken as having
Musical Form: AB AAAB AB
A | B
1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 + 2 + 3 | 123 ||
C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3 C4
F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4 F4
F3 F3 A3 G3 A3 G3 G3 F3
Here the middle voice has the main melody, and we have a "departure
and return" kind of scenario starting on F and eventually returning
there. Of special interest, and marking a pivotal point in both the
vertical structure and the form, is the unstable split fifth sonority
G3-B3-D4 or 5|M3_m3, strategically situated at the middle of the
piece.
This mildly unstable sonority, which Jacobus as a passionate advocate
for this late 13th-century era will note as a pleasant element of
style when aptly handled, marks a pregnant pause in the form: it
occurs at the end of the "A" section of the rondeau, and signals that
there is more to come.
Moving into the "B" section, we first proceed to another split fifth
sonority on A, the step above G, which leads by a very transient sixth
sonority A3-C4-F4 or m6|m3_4 to a momentary resolution on a G trine
(min6-8 + min3-5), then bringing the music back home with a usual
cadence from a sixth sonority on G to F (Maj6-8 + Maj3-5).
A neat touch of cadential strategy occurs in the portion of the
musical form -- AB AAAB AB -- where the "A" section is thrice
repeated. Here the conclusion of this section is directly followed by
a return to the beginning -- resulting in another standard
D4... F4
B3... C4
G3... F3
(Maj3-5)
In this formula for a G-F cadence, or more generally a cadence where
the lowest voice descends by a step, the lower third of the _quinta
fissa_ (here major) expands to a fifth, while the outer fifth expands
to the octave of a complete trine. While not quite as "efficient" as
cadences where all unstable intervals resolve by stepwise contrary
motion -- here the upper minor third resolves by similar motion to the
upper fourth of the trine, and the highest voice leaps by a third --
this progression is common, and serves as a close in motets.
Here it serves at once to resolve the suspense caused by the
conclusion of the "A" section on an unstable sonority, to reaffirm the
contrast between F as "home" and G as "away," and also to give the
piece a pleasant profile through the minor third motion D4-F4 in the
highest voice of this formula. The actual voice-leading here involves
D4... C4
B3... F4
G3... F3
As a kind of lead-in to Part II, I'll briefly note two possible roles
for the step A in this piece on F.
In the "A" section at the second unit, the trine A3-E4-A4 might be
considered a momentary "home away from home": it is approached by a
transient Maj2-4 resolution between the upper voices. When the A trine
does play this role, it might be considered as something of a
polyphonic equivalent of a confinal -- or, I might say, co-center. For
example, we might have F as center or final, A as co-center, and G as
an active step contrasting with either.
In the "B" section we see another possible role for the step A, by no
means necessarily incompatible with the previous role: a step in
cadential progressions leading to G, which in turn leads to F. Thus if
we try to come up with a simplified version of the "B" section, we
... 3 | 1 2 3 | 1 2 3 ||
E4 F4 G4 E4 F4
C4 D4 B3 C4
A3 G3 F3
Here a sixth sonority on A resolves to a trine on G, and the upper
voices then move to another sixth sonority on G which resolves to F.
One might say that A is to G somewhat as G is to F.
In this piece, we might call F the "ultimate" goal, and G the
"penultimate," since it is the step with the cadential sixth sonority
leading directly to this goal.
Since the step A in this sequence likewise has an unstable sonority
resolving to a trine on the step G, we might if so inclined call it
"the penultimate of the penultimate."
Of course, this simplified version of the "B" section disregards
Adam's elegant ornamentation of the close, and also the variety
brought about by the voice-crossing. As Richard Crocker has well said
in regard to the 13th-century motet, the composers are adept in
finding rich variations on standard passages and progressions.
Influences proposed for these three-voice rondeaux of Adam include the
conductus, the polyphonic rondellus, and improvised accompaniments of
monophonic dance songs. If the last influence were significant,
these masterpieces might record some of what improvising musicians
were doing -- or one version of this, as adapted by a composer skilled
in both the trouvere song and the motet.
At any rate, the F-G-F or more generally "adjacent home and away
steps" theme is a fertile start for improvising or composing: the
dilemma remains, of course, as to which types of improvised polyphonic
techniques, or possibly newly composed arrangements, one considers
appropriate for a given genre in a given performance situation, with
"HAP or HEP" questions[1] likely playing a role in one's choices.
---------------------------------------
1.5. An aside: Fluidity and oscillation
---------------------------------------
Having traced out some of the possibilities of the F-G-F theme, I
should add that in some pieces we have a fluid oscillation or
"see-sawing" between F and G in which either might prove to be "home."
Part of this picture is that just as G is a favorite penultimate for a
center on F, so F is an adjacent degree and common penultimate for a
center on G. Consider this final cadence of a kind often found, for
C4 D4
A3 G3
F3 G3
(Maj3-1 + min3-5)
Here a split fifth on F, 5|M3_m3, resolves to a stable fifth on G;
thus G is the ultimate, and F the cadential penultimate.
In some pieces, there's a charming fluidity, moving back and forth
between F and G and eventually settling on one or the other at the
final cadence. This happens in a most elegant motet, _On parole/A
Paris/FRESE NOUVELE, Montpellier #319.
The piece opens with a trine on F, and soon displays a felicitous
point of form facilitated by the structure of the French tenor,
apparently a street cry advertising "Fresh strawberries, wild
blackberries" -- or, it has been suggested by one commentator,
possibly recording some kind of political slogan.
To see (and hear) this point of form, let us consider the progression
at the conclusion of the first statement of the tenor melody, measures
1 2 3 + | 1 2 3 | 1 2 3 |
A4 A4 G4 F4 G4 D4 E4 F4
E4 D4 C4 D4 r C4
A3 G3 r F3
Here we start with a trine on A, with the upper voices moving by the
end of the unit to a very quick sixth sonority resolving to a trine on
G (min6-8 + min3-5). While the lower two voices pause at the end of
the measure, the note E4 in the highest voice exerts a very satisfying
pull to the full trine on F.
This formula thus might resemble the "B" section of the rondeau by
Adam de la Halle (Section 1.4): there is again a descent in the lowest
voice of A-G-F, with A leading to a momentary resolution to G, and G
to a trine on F.
However, the second and third rhythmic units of this example actually
splice together the conclusion of the first statement of the tenor,
ending on G, as marked by the rest, and the commencement of the next
statement starting on F. At the conclusion of this delightful motet,
one of the most beautiful pieces of music I have heard, we settle
1 + 2 3 + | 1 2 3 ||
G4 A4 A4 G4 F4 G4
A3 B3 C4 D4
A3 G3
In addition to illustrating the fluid interplay between F and G, this
piece has a feature making it appropriate to quote here: in the first
excerpt, the melodic turn in the highest line of G4-D4-E4-F4 provides
one not unlikely source for my own use of this figure (Section 1.3).
----
Note
----
1. "Historically Appropriate Performance" (HAP) aims to do, and do
well, what reasonably _may_ have been done in a given era and genre;
"Historically Educated Performance" (HEP) seeks to canvass period
sources and then do something that "fits the music in an informed
way," quite possibly using new techniques, or techniques of a group
such as the Studio for Early Music which some might hold more typical
of 1970 than 1270.

[Roger E. Blumberg]

and instances of this -- > "G3, D3, G3" stack
should read: "G3, D4, G4" stack

sorry
Roger

Post by Roger E. Blumberg
Hi Margo;
(and thanks as usual)
I've tried to realign the ASCII example that you gave for fig.1.4 (the
complete three-voice rondeau by Adam de la Halle), here quoted below, so I
can begin asking questions about it. I've done the realigning judging by
what I see when I view it from my Mac. PC and PC fonts seem to be mucking
things up a bit (when I view it from my PC). If you Margo are viewing this
on a Mac, I don't know how it will appear to you, better or worse, Does this
realignment look correct and representative to you? Are you on a Mac?)

A | B
1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 +

2 + 3 | 123 ||

C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3

C4

Post by Roger E. Blumberg

F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4

F4

F3 F3 A3 G3 A3 G3

G3 F3
anyhow, here goes.
First, I got stuck on the opening bar, this part below. . . . .
the crossed voices and unisons had me tearing my hair out ;')
1 2 3 + | 1
C4 F4 G4 A4
F4 F4 E4
F3 F3 A3
Is there any way to simplify that opening (before the "A" trine)? I'm
thinking that the real heart of this example begins just after, at that AEA
trine. There's some fabulous stuff going on in that example, and the opening
just doesn't seem to do it justice (in addition to being difficult to
execute) i.e. It would be a shame to miss the good stuff because of the
opening (if people can't get past the opening). Do you think I or we would
loose anything by changing the opening to 2 trines, on F and G? When I do
that I still get the impetus, the drive, to the AEA trine where the action
really begins. You said the center voice has the melody generally, but the
top voice is carrying it in the opening, including that huge jump C4 to F4.
At any rate, a "G" trine seems to suffice to get you from the opening "F"
trine to the "A" trine and even implys that melody line C, F, G, A (to me at
least). Perhaps even the Guido trine on "G" (I don't know what the correct
term is but it's the 8|4_5 split rather than 8|5_4 )? I don't mean to
rewrite history, I'm just looking for a way to allow the good stuff to rise
the top more easily, be more accessible, give the real focal point of the
exercise the focus (if I'm reading your intent right, i.e. why you chose
this particular example and what you're really wanting us to hear. Even on a
piano that opening, with it's unison, would be impossible to perform, hence
hear).
Also, I'm wondering about the A3 to G3 (lowest voice). Should I be pedaling
that A3 all the way through to G3? Similarly, all voices are being
maintained throughout, so at all points there's still a 3 voice vertical
sonority happening, i.e. if I were to map this out on a fretboard I could
still block it out 3 voices per any moment in time? I'm assuming yes, but I
just want to be sure. In another example you specifically include a rest (r)
at points where voices fall silent.
Lastly, I don't seem to get the turn-around in this piece, beginning at the
"G3, D3, G3" stack. Everything is beautiful up to that point, really cooking
along, and then it looses me completely. Either something's not working in
the composition or I'm not doing the rhythm properly, but every time I get
to that part it "goes in the dumpster" if you will. The whole last 5 chord
passage just doesn't seem to belong there, it doesn't get you back to the F
trine in any satisfactory way (to me), no preparation or something. It's
almost like two people wrote this piece, some master did the central part
and then someone else wrote the opening and the close ;') Sorry, but
something isn't working there for me. Got any ideas what I'm doing wrong,
(I'm hoping that it _is_ me, because the center part is so cool)? I hear
three possible "next chords" (or simply general melodic movements) that
might follow the "G3, D3, G3" stack smoothly, but none of them are what's
being used and none of them get you back to the F trine either. That's what
I mean, there's no natural impetus to want you to return to the F trine yet,
and the turnaround or transition provided doesn't seem to be working either
(for me). In fact, the peice seems to me to have "A" as it's "home", not F.
The turnaround I like best from the "G3, D3, G3" stack is "E trine" then
right back to the "A trine" passage (I love that part, I want to hear it and
play it over and over again ;') But I still can't bring myself to want or
need to get back to F as home.
Thanks
Roger

-----------------------------------------
An Essay with Thanks to Cait
Part I: The F-G-F theme
-----------------------------------------
Please let me commence this promised essay by warmly thanking Cait for
an exciting dialogue, and specifically for inspiring this post by
sharing a suggestion of Bill Taylor, an expert in early harp music of
the British Isles, that one typical medieval pattern useful in
accompanying songs is a "home" sonority on F and an "away" sonority on
G -- for example, an alternation between F3-C4-F4 and G3-D4 or
G3-D4-G4.
In looking at this and other characteristic patterns in medieval
music, I'm going to focus on what happens in polyphonic compositions.
This recorded practice could serve as one guide to possible
instrumental accompaniment practices for monophonic songs, albeit a
guide which one might want to use with some caution and with due
artistic judgment.
When I speak of caution and judgment, I have in mind especially some
predilections and at least potential biases of my own to which the
reader should be alerted.
First, for 35 years and a bit more, I've been improvising polyphonic
textures in a medieval vocal kind of style on keyboards. If I produce
something that evokes for me an ensemble organum, clausula, conductus,
motet, or cantilena, etc., then I'm happy. Also, my compositional and
analytical efforts have focused on written polyphony.
Secondly, my responses to improvised accompaniments in performances of
monophonic song might reflect more a delight in familiar textures --
"how neat to have this trouvere song sound like an extempore conductus
or motet" -- rather than a judicious evaluation of likely performance
practices for a particular genre at a particular epoch.
I have taken great pleasure in a rendition of a trobador song by
Marcabru, from around the middle of the 12th century, performed in a
lilting modal rhythm with a plucked string accompaniment, as I recall,
in a nice discant style (as noted in the performance notes) which I
found a bit like a conductus.
Someone looking more critically at likely period style might ask
whether trobador songs in this era were likely to be accompanied at
all (a debatable question, as we've seen in recent threads), and
whether a modal rhythm would prevail rather than a freer declamatory
reading.
Anyway, there are some implicit assumptions in what follows that I'd
like to make a bit more explicit. I tend to assume some kind of modal
or mensural rhythm which could invite something like a composed
polyphonic texture in this type of rhythm, and an approach where
techniques like three-voice sonorities and progressions would not be
out of place. These are the things that I'm accustomed to do, not
necessarily the ones you'd want to do in a given situation.
For more freely declamatory songs, there could be other models. One
could look at polyphonic settings from the 13th century or a bit later
of Psalm recitation tones or the like, or even consider a trinic
equivalent of the "dry recitative" of the 17th century or later.
With these caveats, I'll first consider the F-G-F pattern, and then,
in Part II, another question which you have raised, Cait: the
relationship between steps a third apart, such as F and A.
It's prudent to conclude this preface by saying that the possibilities
suggested below are meant to be illustrative rather than exhaustive.
--------------------
1. The F-G-F pattern
--------------------
In recommending the "F home, G away" pattern, Bill Taylor has called
attention to a theme characteristic of much Continental as well as
English music in the 13th century.
We might actually take this as a theme within a yet more pervasive
theme: the frequent alternation between steps a degree apart, typical
of a style where progressions by stepwise contrary motion define the
ideal for efficient and compelling cadential action. Thus if our final
or trinic center of repose in on F, we'd expect unstable cadential
sonorities on the adjacent steps of G or E, and this is in fact what
tends to happen in standard practice.
Likewise, if the final is G, we might expect to find and do find that
the most popular cadences involve unstable sonorities on the adjacent
steps of A or F, and so on.
--------------------------------
1.1. A Montpellier manifestation
--------------------------------
Here we'll focus on the F-G-F theme, and some of its documented or
possible expressions. First, I'll quickly recall an example adapted
from the opening of a 13th-century Montpellier motet, #103, _Aimi!
las! vivrai_/_Doucement me tient_/OMNES, which I seem first to have
encountered through an analysis of Richard Crocker in his _A History
1 2 3 | 1 2 3 | 1 ...
F4 E4 D4 E4 F4
C4 D4 C4
F3 G3 F4
(Maj7-5 + Maj3-1) (Maj6-8 + Maj2-4)
Here I've indicated the transient directed progressions introduced by
the seventh sonority F3-C4-E4 at the end of the first unit and the
sixth sonority G3-D4-E4 at the end of the second, each lending impetus
to the musical motion forward into the next unit. The momentary
partitions of M7|5_M3 and M6|5_M2 add a bit of color to the stable
consonances, and the directed resolutions briding from one unit to the
next could be described as _cadentiae_ in a medieval meaning of that
term: apt progressions from more tense to more concordant intervals.
----------------------
1.2. A different style
----------------------
Taking the same framework for the two outer voices, we can also arrive
at a passage from one of the most famous F-G-F pieces of the era, here
1 2
1 2 3 4 5 6 | 1 ...
F4 E4 D4 E4 F4
C4 Bb3 C4
F3 G3 F4
(Maj6-8 + min3-5)
From a conventional Continental point of view, we start at "home" on
the F trine, and move to "away" on a mildly unstable sonority: the
split fifth G3-Bb3-D4, with its two unstable thirds, 5|m3_M3. Then
the E4 in the upper voice gives us the momentary sixth sonority
G3-Bb3-E4 or M6|m3_4, resolving in usual fashion to arrive back at our
trinic "home" on F (Maj6-8 + min3-5).
In fact, however, this is the opening of the English round _Sumer is
icumen in_, if one starts with the entry of the first voice singing
the main canonic melody above the repeated _pes_ in the lower two
voices. (If we elect to sing the pes voices alone first to give a feel
for the "ground bass" pattern, then this passage would be a bit after
the opening.)
While this three-voice passage at the beginning of the canon might
suggest an F-G-F theme of trine-split fifth-trine, as more voices
enter it quickly becomes clear that we have a different vertical style
with pervasive tertian sonorities as the norm, the kind of thing
reported by Anonymous IV for the "Westcountry" of England. This kind > > of writing, where thirds are treated as stable and conclusive,
contrasts with other kinds of styles in England as well as on the
Continent where these intervals are regarded as mildly unstable, and
often participate in directed progressions to stable sonorities such
as trines.
-------------------------------
1.3. A diversion after midnight
-------------------------------
Getting back to the latter kind of style, we could harmonize the
1 2 3 | 1 2 3 | 1 ...
F4 E4 D4 E4 F4
C4 D4 C4 B3 C4
F3 G3 F4
(Maj7-5 + Maj3-1) (Maj6-8 + Maj3-5)
This solution might come out of the same stylistic milieu as our first
example adapted from Montpellier: as in that example, the quick
directed resolutions leading from one rhythmic unit to the next help
move the harmonic rhythm along, and also to provide moments of unity
knitting the voices together in their often diverse motions.
The theme of alternating between F and G can be a taking off point for
lots of ideas. For example, here's something I came up with very early
this morning as a kind of belated midnight discant diversion, with "r"
1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 |
D4 E4 F4 r G4 D4 E4 F4
D4 B3 C4 E4 D4 C4 B3 C4
G3 F3 G3 F3
(Maj6-8 + Maj3-5) (Maj7-5) (Maj6-8 + Maj3-5)
Again I'm showing the directed resolutions because this is an aspect
of technique in lots of motets and the like which it seems to me it
wouldn't hurt to do my part in emphasizing. Certainly I wouldn't want
to suggest this kind of harmonic rhythm -- directed tension at the end
of a unit resolved at the beginning of the next -- as any kind of
"rule"; it's just a common and useful technique.
Other nuances here are the rest in the highest voice, followed by its
entry to supply the octave of a complete trine, and then by a turn of
phrase in this voice yielding a momentary sonority of G3-C4-D4, or
5|4_M2. From any usual standpoint this kind of sonority in the middle
of a unit is quite incidental, and one might well have the voices
proceed in the same way for melodic reasons quite apart from this
vertical detail. However, I must confess to a weakness for 5|4_M2, and
find it a nice touch of color.
-----------------------------------------
1.4. Adam de la Halle: An artful contrast
-----------------------------------------
A complete three-voice rondeau by Adam de la Halle might illustrate
the F-G-F theme in another guise while also demonstrating an artful
use of form to give shape to the "home-away-home" scenario.
Readings of the rhythmic fine points in this rondeau, _He, Diex! quant
verrai_, can vary, so that this version is only one possible solution,
with each of the indicated semibreves dividing a breve taken as having
Musical Form: AB AAAB AB
A | B
1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 + 2 + 3 | 123 ||
C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3 C4
F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4 F4
F3 F3 A3 G3 A3 G3 G3 F3
Here the middle voice has the main melody, and we have a "departure
and return" kind of scenario starting on F and eventually returning
there. Of special interest, and marking a pivotal point in both the
vertical structure and the form, is the unstable split fifth sonority
G3-B3-D4 or 5|M3_m3, strategically situated at the middle of the
piece.
This mildly unstable sonority, which Jacobus as a passionate advocate
for this late 13th-century era will note as a pleasant element of
style when aptly handled, marks a pregnant pause in the form: it
occurs at the end of the "A" section of the rondeau, and signals that
there is more to come.
Moving into the "B" section, we first proceed to another split fifth
sonority on A, the step above G, which leads by a very transient sixth
sonority A3-C4-F4 or m6|m3_4 to a momentary resolution on a G trine
(min6-8 + min3-5), then bringing the music back home with a usual
cadence from a sixth sonority on G to F (Maj6-8 + Maj3-5).
A neat touch of cadential strategy occurs in the portion of the
musical form -- AB AAAB AB -- where the "A" section is thrice
repeated. Here the conclusion of this section is directly followed by
a return to the beginning -- resulting in another standard
D4... F4
B3... C4
G3... F3
(Maj3-5)
In this formula for a G-F cadence, or more generally a cadence where
the lowest voice descends by a step, the lower third of the _quinta
fissa_ (here major) expands to a fifth, while the outer fifth expands
to the octave of a complete trine. While not quite as "efficient" as
cadences where all unstable intervals resolve by stepwise contrary
motion -- here the upper minor third resolves by similar motion to the
upper fourth of the trine, and the highest voice leaps by a third --
this progression is common, and serves as a close in motets.
Here it serves at once to resolve the suspense caused by the
conclusion of the "A" section on an unstable sonority, to reaffirm the
contrast between F as "home" and G as "away," and also to give the
piece a pleasant profile through the minor third motion D4-F4 in the
highest voice of this formula. The actual voice-leading here involves
D4... C4
B3... F4
G3... F3
As a kind of lead-in to Part II, I'll briefly note two possible roles
for the step A in this piece on F.
In the "A" section at the second unit, the trine A3-E4-A4 might be
considered a momentary "home away from home": it is approached by a
transient Maj2-4 resolution between the upper voices. When the A trine
does play this role, it might be considered as something of a
polyphonic equivalent of a confinal -- or, I might say, co-center. For
example, we might have F as center or final, A as co-center, and G as
an active step contrasting with either.
In the "B" section we see another possible role for the step A, by no
means necessarily incompatible with the previous role: a step in
cadential progressions leading to G, which in turn leads to F. Thus if
we try to come up with a simplified version of the "B" section, we
... 3 | 1 2 3 | 1 2 3 ||
E4 F4 G4 E4 F4
C4 D4 B3 C4
A3 G3 F3
Here a sixth sonority on A resolves to a trine on G, and the upper
voices then move to another sixth sonority on G which resolves to F.
One might say that A is to G somewhat as G is to F.
In this piece, we might call F the "ultimate" goal, and G the
"penultimate," since it is the step with the cadential sixth sonority
leading directly to this goal.
Since the step A in this sequence likewise has an unstable sonority
resolving to a trine on the step G, we might if so inclined call it
"the penultimate of the penultimate."
Of course, this simplified version of the "B" section disregards
Adam's elegant ornamentation of the close, and also the variety
brought about by the voice-crossing. As Richard Crocker has well said
in regard to the 13th-century motet, the composers are adept in
finding rich variations on standard passages and progressions.
Influences proposed for these three-voice rondeaux of Adam include the
conductus, the polyphonic rondellus, and improvised accompaniments of
monophonic dance songs. If the last influence were significant,
these masterpieces might record some of what improvising musicians
were doing -- or one version of this, as adapted by a composer skilled
in both the trouvere song and the motet.
At any rate, the F-G-F or more generally "adjacent home and away
steps" theme is a fertile start for improvising or composing: the
dilemma remains, of course, as to which types of improvised polyphonic
techniques, or possibly newly composed arrangements, one considers
appropriate for a given genre in a given performance situation, with
"HAP or HEP" questions[1] likely playing a role in one's choices.
---------------------------------------
1.5. An aside: Fluidity and oscillation
---------------------------------------
Having traced out some of the possibilities of the F-G-F theme, I
should add that in some pieces we have a fluid oscillation or
"see-sawing" between F and G in which either might prove to be "home."
Part of this picture is that just as G is a favorite penultimate for a
center on F, so F is an adjacent degree and common penultimate for a
center on G. Consider this final cadence of a kind often found, for
C4 D4
A3 G3
F3 G3
(Maj3-1 + min3-5)
Here a split fifth on F, 5|M3_m3, resolves to a stable fifth on G;
thus G is the ultimate, and F the cadential penultimate.
In some pieces, there's a charming fluidity, moving back and forth
between F and G and eventually settling on one or the other at the
final cadence. This happens in a most elegant motet, _On parole/A
Paris/FRESE NOUVELE, Montpellier #319.
The piece opens with a trine on F, and soon displays a felicitous
point of form facilitated by the structure of the French tenor,
apparently a street cry advertising "Fresh strawberries, wild
blackberries" -- or, it has been suggested by one commentator,
possibly recording some kind of political slogan.
To see (and hear) this point of form, let us consider the progression
at the conclusion of the first statement of the tenor melody, measures
1 2 3 + | 1 2 3 | 1 2 3 |
A4 A4 G4 F4 G4 D4 E4 F4
E4 D4 C4 D4 r C4
A3 G3 r F3
Here we start with a trine on A, with the upper voices moving by the
end of the unit to a very quick sixth sonority resolving to a trine on
G (min6-8 + min3-5). While the lower two voices pause at the end of
the measure, the note E4 in the highest voice exerts a very satisfying
pull to the full trine on F.
This formula thus might resemble the "B" section of the rondeau by
Adam de la Halle (Section 1.4): there is again a descent in the lowest
voice of A-G-F, with A leading to a momentary resolution to G, and G
to a trine on F.
However, the second and third rhythmic units of this example actually
splice together the conclusion of the first statement of the tenor,
ending on G, as marked by the rest, and the commencement of the next
statement starting on F. At the conclusion of this delightful motet,
one of the most beautiful pieces of music I have heard, we settle
1 + 2 3 + | 1 2 3 ||
G4 A4 A4 G4 F4 G4
A3 B3 C4 D4
A3 G3
In addition to illustrating the fluid interplay between F and G, this
piece has a feature making it appropriate to quote here: in the first
excerpt, the melodic turn in the highest line of G4-D4-E4-F4 provides
one not unlikely source for my own use of this figure (Section 1.3).
----
Note
----
1. "Historically Appropriate Performance" (HAP) aims to do, and do
well, what reasonably _may_ have been done in a given era and genre;
"Historically Educated Performance" (HEP) seeks to canvass period
sources and then do something that "fits the music in an informed
way," quite possibly using new techniques, or techniques of a group
such as the Studio for Early Music which some might hold more typical
of 1970 than 1270.

[Margo Schulter]

Hello, everyone.

Please let me offer a small correction to my transcription of Adam de
la Halle's rondeaux _He Diex! quant verrai_, as posted in my article
inspired by Cait's post quoting Bill Taylor.

---------------------------------------------------------------------
IMPORTANT: Please use a nonproportional font if available for these
examples, e.g. Courier or another typewriter-like font, where all
characters and spaces have the same width.
---------------------------------------------------------------------

Post by Margo Schulter
Musical Form: AB AAAB AB
A | B
1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 + 2 + 3 | 123 ||
C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3 C4
F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4 F4
F3 F3 A3 G3 A3 G3 G3 F3

The correct version, with an impefect long and a breve in the second
measure of the lowest voice rather than a single perfect long -- or a
half/minim and quarter/crotchet rather than a single dotted half/minim
if we read this as 3/4 -- is as follows:

Musical Form: AB AAAB AB

A | B

1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 + 2 + 3 | 123 ||
C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3 C4
F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4 F4
F3 F3 A3 A3 G3 A3 G3 G3 F3

Roger, before responding to your questions, I might want, like you, to
be sure that technical glitches aren't interfering with how we're
seeing and reading the notes.

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Everything's working fine now Margo. And I see the additional A3 in the
lowest voice in the revised version as well.


Now that I have the alignment issue solved, I can say that this _is_
essentially how I saw it on my Mac (sans that new A3). So perhaps it is a
preference issue, my hearing the closing part as odd. It must be in the
rhythm that I'm getting it wrong (still). Anywho, at least we know for sure
that we're looking at the same music now. New fonts are easy, new ears will
be harder for me to come by ;') Let me go over it again. I should say that I
like the ending from the "G3 D4 G4" stack _in and of itself_, it's very
similar to one of the earlier examples you gave, but it's connecting it to
the part that proceeds it that I'm not hearing. Don't mind me though ;') , I
won't give up so easily. In any event that center section is great and the
newest or most unique bit in the example(to me. I'm ok with them as
free-standing units (even though their not supposed to be necessarily).
There's still plenty of treasure there-in for me.

The short begining section though, I'd still like to play with, simplify it
somehow (for my own use at least). After I posted, I stumbled upon a really
pretty pair of leading sonorites that would probably only work easily on my
4 string instrument and tuned as it is (EADG), or singers of course. The two
sonorities add the open high G string as a drone peddled through both trines
F to G. This actually gives a unison G in the second voicing, which pianos
couldn't do but your 2 manual KB could. So it would be F3-C4-F4-G4 to
G3-D4-G4-G4 to proceed the A trine (which commences the center sectiion).
This new opening definately works nice behind the intended melody "C F G A",
the A note being within the A trine when you get to it, and the drone peddle
(high G) would probably be period correct enough, what do you think? In any
event, I would steal that center section as a kernel of a new song in a
minute ;') -- crediting Mr Halle of course.


center section:

. . 1 + 2 3 + + | 1 2 3 + | 1
. . A4 G4 F4 E4 D4 E4 F4 G4 . . .
. . E4 D4 E4 E4 D4 C4 B3 C4 D4 . . .
. . A3 A3 G3 A3 G3 . . .


ending:

. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 D4 E4 F4
. . G3 G3 F3



Thanks
Roger

Post by Margo Schulter
Hello, everyone.
Please let me offer a small correction to my transcription of Adam de
la Halle's rondeaux _He Diex! quant verrai_, as posted in my article
inspired by Cait's post quoting Bill Taylor.
---------------------------------------------------------------------
IMPORTANT: Please use a nonproportional font if available for these
examples, e.g. Courier or another typewriter-like font, where all
characters and spaces have the same width.
---------------------------------------------------------------------

Post by Margo Schulter
Musical Form: AB AAAB AB
A | B
1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 + 2 + 3 | 123 ||
C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3 C4
F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4 F4
F3 F3 A3 G3 A3 G3 G3 F3

The correct version, with an impefect long and a breve in the second
measure of the lowest voice rather than a single perfect long -- or a
half/minim and quarter/crotchet rather than a single dotted half/minim
Musical Form: AB AAAB AB
A | B
1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 + 2 + 3 | 123 ||
C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3 C4
F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4 F4
F3 F3 A3 A3 G3 A3 G3 G3 F3
Roger, before responding to your questions, I might want, like you, to
be sure that technical glitches aren't interfering with how we're
seeing and reading the notes.
Most appreciatively,
Margo Schulter

[Margo Schulter]

Post by Roger E. Blumberg
Everything's working fine now Margo. And I see the additional A3 in the
lowest voice in the revised version as well.

Hi, Roger.

Thank you for confirming that we were dealing with a problem of
proportional and nonproportional fonts, and that the problem now seems
ironed out reasonably well.

One thing I would strongly emphasize is that arranging or adapting a vocal
piece or more generally an ensemble piece of polyphony for any
solo instrument is apt to involve modifications and adjustments, whether
because the instrument is simply unable to do certain things (like
observing voice-crossings), or because the idiomatic style of the
instrument invites elaborations, etc.

In giving examples, I'm hesitant to try an idiomatic arrangement for an
instrument I don't play, because this is better done by people familiar
with the instrument. What I can do is give my own preferences about some
stylistic parameters I might consider in making an arrangement -- which
you or other people doing this would then need to try and see if they fit
the instrument or your taste. It's a process of feedback.

On a single keyboard manual, curiously, I'm content playing a literal
"reduction" of what's written, which I'll show here without taking into
account the crossing of the written voices, etc., and showing a rest where
a written unison means that only two notes at once are actually sounding
on the keyboard:

1 2 3 + | 1...
F4 r G4 A4
C4 F4 F4 E4
F3 F3 F3 A3

Here's there's a momentary partition of the ninth, F3-F4-G4 or M9|8_M2,
less harmonious than M9|5_5, but also catalogued and accepted by Jacobus;
while the melodic effect of the voice crossing obviously can't be
reproduced on a single manual, the tension of that M9|8_M2 might make the
following trine sound sweeter. Again, it might have been done mainly for
melodic reason; and there's that Maj2-4 resolution between the upper
voices. However, if this doesn't fit a plucked instrument so
well, and we're making a free intabulation (a liberty of many centuries),
here's an idea:

1 2 3 + | 1...
F4 F4 G4 A4
C4 C4 E4
F3 F3 A3

This has a momentary M9|5_5; it sounded OK when I played it on a single
keyboard manual, and it keeps some of the melodic nuances that don't
depend on the voice-crossing, as well as the general pattern of
stability/instability.

Of course, in some of the keyboard arrangements of vocal compositions by
Machaut and Landini, for example, much greater liberties occur. Here I'm
trying to go first for a "minimal adjustment" that could make the piece
more easily playable, which isn't necessarily the same as a creative
arrangement for a given instrument.

Again, one of the problems is that we don't have any known 13th-century
intabulations for solo instruments of 13th-century polyphonic pieces --
the arrangements of the Philippe de Vitry motets in the Robertsbridge
Codex (early to middle 14th century) might be the first known. It's a
question of taste (which can vary!), and also of instrumental technique.

On the conclusion of the piece, I should discuss that in another post. For
me, the form is very satisfactory, and one trick might be try playing just
the two lower parts as I noted them in the transcription, the main melodic
and the lowest voice.

By the way, your reaction does illustrate a point that I mentioned in my
post on F-G-F: sometimes either F or G _could_ be a satisfactory
conclusion.

One dramatic example of this is that there's a motet in the Las Huelgas
Codex -- a 13th-century Spanish source -- _In seculum artifex_ -- that was
transcribed and performed for many years in a version ending on G. I have
recordings with instrumental performances. Then, Gordon Anderson published
an edition of Las Huelgas with a version ending on F -- as one would
expect for a piece based on IN SECULUM as the foundation melody or
"tenor." The version ending in G is quite beautiful, and I wouldn't have
suspected that someone would publish a transcription ending on F.

Anyway, thank you for prompting me to analysis of that final cadence in
the Adam de la Halle piece -- and for giving me an opportunity to say that
polyphonic ensemble compositions often get altered when arranged for solo
instruments. The fact that I haven't attempted it in these posts should
been seen mainly as a comment on the limitations of my knowledge of
various instruments, and an invitation for people actually the instruments
to step in. Of course, I can give feedback as to why I might lean toward
one solution rather than another -- but that is also a matter of taste.
You should see how people differ in the "scholarly literature," either
medieval or modern.

Most appreciatively,

Margo Schulter
***@calweb.com

[Margo Schulter]

Post by Margo Schulter
On the conclusion of the piece, I should discuss that in another post. For
me, the form is very satisfactory, and one trick might be try playing just
the two lower parts as I noted them in the transcription, the main melodic
and the lowest voice.

Hi, Roger, and just to clarify: I mean here to try _first_ playing just
the lower two parts of the transcription, which might be easier to do at a
comfortable and pleasing speed so that you can appreciate the flow and the
form. As it happens, these two parts alone pretty much capture the main
outlines of the form, so that if you can get it to the point where it
sounds coherent and comes together in two parts, then you could add the
third part -- or, actually, do some kind of arrangement approximating the
written parts, since obviously the unisons and voice-crossings can't
literally be reproduced, as you and Cait have rightly called to my
attention.

Sometimes, by the way, it can be a very effective performance technique to
start with a single melody from a piece -- here maybe the main melody, or
possibly also the lowest part -- then do a version with two parts (here
the lowest part and main melody together), and finally add the third
voice. I've heard it done for motets where it can really bring out details
of the music and permit a nice build-up.

Also, why don't give you a substitute version of those final two measures
of the "B" section that could avoid unison problems and the like, to give
you a chance to hear the basic form without getting possibly hindered by
the ornamentation with its voice-crossings and unisons. This is _not_ a
proposed arrangement -- although I could picture an intabulator trying out
variations of different kinds -- only a "teaching version" to help you
hear something like what is happening with the general form. Why don't I
actually take it from the start of the "B" section on the third beat of
the previous measure in this transcription:

3 + | 1 + 2 + 3 | 1 ...
E4 F4 G4 F4 E4 D4 E4 F4
C4 D4 C4 B3 C4
A3 G3 F4

I have very mixed feelings about this as an "arrangement," because I've
altered Adam's main melody when maybe I should be doing any adjustments by
preference to accompanying parts, and I'd add that I'm indebted to lots of
motets and the like for that figure in the highest voice. For an ensemble,
at least, I can see how Adam made a beautiful setting that goes with his
main voice; again, this is for what are called "pedagogical purposes," to
see if a simpler version of the close helps in understanding the form.

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Thanks;

and these things I'll try out later and get back to you tommorrow on them.

Thanks
Roger

Post by Margo Schulter

Post by Margo Schulter
On the conclusion of the piece, I should discuss that in another post. For
me, the form is very satisfactory, and one trick might be try playing just
the two lower parts as I noted them in the transcription, the main melodic
and the lowest voice.

Hi, Roger, and just to clarify: I mean here to try _first_ playing just
the lower two parts of the transcription, which might be easier to do at a
comfortable and pleasing speed so that you can appreciate the flow and the
form. As it happens, these two parts alone pretty much capture the main
outlines of the form, so that if you can get it to the point where it
sounds coherent and comes together in two parts, then you could add the
third part -- or, actually, do some kind of arrangement approximating the
written parts, since obviously the unisons and voice-crossings can't
literally be reproduced, as you and Cait have rightly called to my
attention.
Sometimes, by the way, it can be a very effective performance technique to
start with a single melody from a piece -- here maybe the main melody, or
possibly also the lowest part -- then do a version with two parts (here
the lowest part and main melody together), and finally add the third
voice. I've heard it done for motets where it can really bring out details
of the music and permit a nice build-up.
Also, why don't give you a substitute version of those final two measures
of the "B" section that could avoid unison problems and the like, to give
you a chance to hear the basic form without getting possibly hindered by
the ornamentation with its voice-crossings and unisons. This is _not_ a
proposed arrangement -- although I could picture an intabulator trying out
variations of different kinds -- only a "teaching version" to help you
hear something like what is happening with the general form. Why don't I
actually take it from the start of the "B" section on the third beat of
3 + | 1 + 2 + 3 | 1 ...
E4 F4 G4 F4 E4 D4 E4 F4
C4 D4 C4 B3 C4
A3 G3 F4
I have very mixed feelings about this as an "arrangement," because I've
altered Adam's main melody when maybe I should be doing any adjustments by
preference to accompanying parts, and I'd add that I'm indebted to lots of
motets and the like for that figure in the highest voice. For an ensemble,
at least, I can see how Adam made a beautiful setting that goes with his
main voice; again, this is for what are called "pedagogical purposes," to
see if a simpler version of the close helps in understanding the form.
Most appreciatively,
Margo Schulter

[Roger E. Blumberg]

Post by Margo Schulter

Post by Margo Schulter
On the conclusion of the piece, I should discuss that in another post. For
me, the form is very satisfactory, and one trick might be try playing just
the two lower parts as I noted them in the transcription, the main melodic
and the lowest voice.

Hi, Roger, and just to clarify: I mean here to try _first_ playing just
the lower two parts of the transcription, which might be easier to do at a
comfortable and pleasing speed so that you can appreciate the flow and the
form. As it happens, these two parts alone pretty much capture the main
outlines of the form, so that if you can get it to the point where it
sounds coherent and comes together in two parts, then you could add the
third part -- or, actually, do some kind of arrangement approximating the
written parts, since obviously the unisons and voice-crossings can't
literally be reproduced, as you and Cait have rightly called to my
attention.

Hi Margo;
I beleive I've got it right now. It really is all in the rhythm. Amoung
other
things I was jazzing up the middle part and then slowing down and dallying
through the 6 final sonorities, in particular the first four of those last
six.

ending (is 6 sonorites):

. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 D4 E4 F4
. . G3 G3 F3


this is the part I was dallying through (this 4 chord passage):

. . 1 + 2 +
. . G4 F4 E4 D4
. . D4 C4 D4
. . G3



When I played those through as a quick 1234 and then give a little extra
time on the last two (or the last _one_ for sure) then it worked. Also while
jazzing up the center section I neglected to hold the GBD split fifth for
enough counts (I was just flying through it as part of my jazzed-up
rendition of that section).

In the end, if I were actually doing an accoumpaniment, which is what I'm
envisioning (some background support) I would probably just peddle or hold
the GDG trine through that entire four note melody or group of sonorities,
letting the singer(s) supply the melody. This is more what accompaniment
typically is -- one doesn't have to be note for note literal in an
accompaniment. But
of course we do have to start somewhere, we do have to be familiar with the
piece one way or another (and with little or no guesswork involved, or time
spent being way off track without realizing it, etc). Midi renditions of
any/all examples would be wonderful (if not manditory) at some point some
day, I think. There's really no getting around it. One either has to locate
and purchase a recording of each and every piece, or be in a classroom
setting, face to face, where the instructor can play through parts and
passages, _or_ (in this day and age, with all of our high tech gadgetry and
the internet as "global classroom") someone could prepair midi or other
recorded snippets of examples and sample material. Someday, everything will
come togeather at one place and time, with enough someone's pitching in and
providing any nessesary supplimentals. [any takers on the midi renditions
and uploads ;') ? I don't have the tools nor keyboard skills. Or maybe
Sebelius "Scorch" examples. With the Scorch plug-in, as used at
http://www.dolmetsch.com/scorchinfo.htm for the Dolmetsch Recorder Method,
one could include staff notated parts, audio, plus lyric, plus chord charts,
that one could both hear, view, and track on a time-line, measure for
measure, as the passage progressed, and then of course be able to translate
that more faithfully and confidently to any combination of instruments,
singers, or both. And this is in addition to Margo's ASCII renditions. I
think the ASCII is an important tool, one not to be omitted down the line
(there should be more of it generally, not less) because staff notation is
still accessable to only a few.]

Anywho, I'm satisfied that I've got it down better now. The alternate ending
you give below (thank you)is indeed easier to play. As you say though,it
does change the melody line a bit, and for the moment I'm not sure how to
proceed. I can play the original now, as originally posted. I'm still
wondering though about the idea of an accoumpiniment that simply holds the G
trine through that otherwise four sonority passage (letting the singers
carry the melody through). Im also wondering about another possible ending,
wondering if it's too modern sounding, too triadic perhaps. Please tell me
what you think of this arrangement. I think it retains the original melody
pretty faithfully?

original authentic ending:

. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 D4 E4 F4
. . G3 G3 F3


trail balloon ending:

. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 C4 B4 E4 F4
. . G3 G3 F3



so two sonorities, corresponding to the "2 +" in the above, are the changes
in question.

what I'm wondering is (in general and even apart from Halle's piece)if
there's anything _fundamentally_ "non-period" about that trial arrangement?
Is it theoretically legal? Might it have safely have been used by someone
back then, with singers for example? Again, the ultimate purpose of this
whole exercise (for me at least)is to get a better (more authentic or
educated) feel for what kinds of sonorities and progressions _might_ have
been used and might be considered "ok" to employ in either prepared or
improvised accompaniment. My envisaged accompaniment of course is on some
kind of guitarra/lute/guitern,citole using 2, 3, or even 4 voices (strings
or courses plucked or strummed "chords"), and I'm assuming I'd be
accompanying either a singer (even myself) or other instrumentalist who
would largely be carrying the melody with their voice or instrument.


While we're at it, I wonder if I could ask you about a couple of
progressions I came up with last night. Again, I'm wondering how these might
be percieved relative to known practice of vocal part writing. These sprang
from experimenting with a 3 chord passage in Halle's piece and taking it
from there, this part:


. . E4 F4 G4
. . C4 D4
. . A3 G3


first, I added this chord at the end (8|M3_m6):

. . E4 F4 G4 A4
. . C4 D4 C#4
. . A3 G3 A3


then continued, adding more, sliding that same chord up one fret, then a
little alteration, then back down a fret again to the original chord, repeat
that once, and a final.

. . E4 F4 G4 A4 A#4 G4 A4 A#4 G4 A4 A
. . C4 D4 C#4 D4 D4 C#4 D4 D4 C#4 D4
. . A3 G3 A3 A#3 A#3 A3 A#3 A#3 A3 A3


any reason that this wouldn't be legal tender? I could add more from there,
but first I'm wondering about that particular chord (8|M3_m6), and then that
up-a-semitone back-a-semitone kind of progression. This of course has
nothing to do with Halle's piece really, it's just an excursion of mine
(sitting under that tree and experimenting).

Thanks
Roger

Post by Margo Schulter
Sometimes, by the way, it can be a very effective performance technique to
start with a single melody from a piece -- here maybe the main melody, or
possibly also the lowest part -- then do a version with two parts (here
the lowest part and main melody together), and finally add the third
voice. I've heard it done for motets where it can really bring out details
of the music and permit a nice build-up.
Also, why don't give you a substitute version of those final two measures
of the "B" section that could avoid unison problems and the like, to give
you a chance to hear the basic form without getting possibly hindered by
the ornamentation with its voice-crossings and unisons. This is _not_ a
proposed arrangement -- although I could picture an intabulator trying out
variations of different kinds -- only a "teaching version" to help you
hear something like what is happening with the general form. Why don't I
actually take it from the start of the "B" section on the third beat of
3 + | 1 + 2 + 3 | 1 ...
E4 F4 G4 F4 E4 D4 E4 F4
C4 D4 C4 B3 C4
A3 G3 F4
I have very mixed feelings about this as an "arrangement," because I've
altered Adam's main melody when maybe I should be doing any adjustments by
preference to accompanying parts, and I'd add that I'm indebted to lots of
motets and the like for that figure in the highest voice. For an ensemble,
at least, I can see how Adam made a beautiful setting that goes with his
main voice; again, this is for what are called "pedagogical purposes," to
see if a simpler version of the close helps in understanding the form.
Most appreciatively,
Margo Schulter

[Roger E. Blumberg]

The last chord in that excursion of mine is missing the "4" in A4 top voice.
So it should be:

A4
D4
A3

Thanks
Roger

Post by Margo Schulter

Post by Margo Schulter

Post by Margo Schulter
On the conclusion of the piece, I should discuss that in another post.

For

Post by Margo Schulter

Post by Margo Schulter
me, the form is very satisfactory, and one trick might be try playing

just

Post by Margo Schulter

Post by Margo Schulter
the two lower parts as I noted them in the transcription, the main

melodic

Post by Margo Schulter

Post by Margo Schulter
and the lowest voice.

Hi, Roger, and just to clarify: I mean here to try _first_ playing just
the lower two parts of the transcription, which might be easier to do at a
comfortable and pleasing speed so that you can appreciate the flow and the
form. As it happens, these two parts alone pretty much capture the main
outlines of the form, so that if you can get it to the point where it
sounds coherent and comes together in two parts, then you could add the
third part -- or, actually, do some kind of arrangement approximating the
written parts, since obviously the unisons and voice-crossings can't
literally be reproduced, as you and Cait have rightly called to my
attention.

Hi Margo;
I beleive I've got it right now. It really is all in the rhythm. Amoung
other
things I was jazzing up the middle part and then slowing down and dallying
through the 6 final sonorities, in particular the first four of those last
six.
. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 D4 E4 F4
. . G3 G3 F3
. . 1 + 2 +
. . G4 F4 E4 D4
. . D4 C4 D4
. . G3
When I played those through as a quick 1234 and then give a little extra
time on the last two (or the last _one_ for sure) then it worked. Also while
jazzing up the center section I neglected to hold the GBD split fifth for
enough counts (I was just flying through it as part of my jazzed-up
rendition of that section).
In the end, if I were actually doing an accoumpaniment, which is what I'm
envisioning (some background support) I would probably just peddle or hold
the GDG trine through that entire four note melody or group of sonorities,
letting the singer(s) supply the melody. This is more what accompaniment
typically is -- one doesn't have to be note for note literal in an
accompaniment. But
of course we do have to start somewhere, we do have to be familiar with the
piece one way or another (and with little or no guesswork involved, or time
spent being way off track without realizing it, etc). Midi renditions of
any/all examples would be wonderful (if not manditory) at some point some
day, I think. There's really no getting around it. One either has to locate
and purchase a recording of each and every piece, or be in a classroom
setting, face to face, where the instructor can play through parts and
passages, _or_ (in this day and age, with all of our high tech gadgetry and
the internet as "global classroom") someone could prepair midi or other
recorded snippets of examples and sample material. Someday, everything will
come togeather at one place and time, with enough someone's pitching in and
providing any nessesary supplimentals. [any takers on the midi renditions
and uploads ;') ? I don't have the tools nor keyboard skills. Or maybe
Sebelius "Scorch" examples. With the Scorch plug-in, as used at
http://www.dolmetsch.com/scorchinfo.htm for the Dolmetsch Recorder Method,
one could include staff notated parts, audio, plus lyric, plus chord charts,
that one could both hear, view, and track on a time-line, measure for
measure, as the passage progressed, and then of course be able to translate
that more faithfully and confidently to any combination of instruments,
singers, or both. And this is in addition to Margo's ASCII renditions. I
think the ASCII is an important tool, one not to be omitted down the line
(there should be more of it generally, not less) because staff notation is
still accessable to only a few.]
Anywho, I'm satisfied that I've got it down better now. The alternate ending
you give below (thank you)is indeed easier to play. As you say though,it
does change the melody line a bit, and for the moment I'm not sure how to
proceed. I can play the original now, as originally posted. I'm still
wondering though about the idea of an accoumpiniment that simply holds the G
trine through that otherwise four sonority passage (letting the singers
carry the melody through). Im also wondering about another possible ending,
wondering if it's too modern sounding, too triadic perhaps. Please tell me
what you think of this arrangement. I think it retains the original melody
pretty faithfully?
. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 D4 E4 F4
. . G3 G3 F3
. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 C4 B4 E4 F4
. . G3 G3 F3
so two sonorities, corresponding to the "2 +" in the above, are the changes
in question.
what I'm wondering is (in general and even apart from Halle's piece)if
there's anything _fundamentally_ "non-period" about that trial

arrangement?

Post by Margo Schulter
Is it theoretically legal? Might it have safely have been used by someone
back then, with singers for example? Again, the ultimate purpose of this
whole exercise (for me at least)is to get a better (more authentic or
educated) feel for what kinds of sonorities and progressions _might_ have
been used and might be considered "ok" to employ in either prepared or
improvised accompaniment. My envisaged accompaniment of course is on some
kind of guitarra/lute/guitern,citole using 2, 3, or even 4 voices (strings
or courses plucked or strummed "chords"), and I'm assuming I'd be
accompanying either a singer (even myself) or other instrumentalist who
would largely be carrying the melody with their voice or instrument.
While we're at it, I wonder if I could ask you about a couple of
progressions I came up with last night. Again, I'm wondering how these might
be percieved relative to known practice of vocal part writing. These sprang
from experimenting with a 3 chord passage in Halle's piece and taking it
. . E4 F4 G4
. . C4 D4
. . A3 G3
. . E4 F4 G4 A4
. . C4 D4 C#4
. . A3 G3 A3
then continued, adding more, sliding that same chord up one fret, then a
little alteration, then back down a fret again to the original chord, repeat
that once, and a final.
. . E4 F4 G4 A4 A#4 G4 A4 A#4 G4 A4 A
. . C4 D4 C#4 D4 D4 C#4 D4 D4 C#4 D4
. . A3 G3 A3 A#3 A#3 A3 A#3 A#3 A3 A3
any reason that this wouldn't be legal tender? I could add more from there,
but first I'm wondering about that particular chord (8|M3_m6), and then that
up-a-semitone back-a-semitone kind of progression. This of course has
nothing to do with Halle's piece really, it's just an excursion of mine
(sitting under that tree and experimenting).
Thanks
Roger

Post by Margo Schulter
Sometimes, by the way, it can be a very effective performance technique to
start with a single melody from a piece -- here maybe the main melody, or
possibly also the lowest part -- then do a version with two parts (here
the lowest part and main melody together), and finally add the third
voice. I've heard it done for motets where it can really bring out details
of the music and permit a nice build-up.
Also, why don't give you a substitute version of those final two measures
of the "B" section that could avoid unison problems and the like, to give
you a chance to hear the basic form without getting possibly hindered by
the ornamentation with its voice-crossings and unisons. This is _not_ a
proposed arrangement -- although I could picture an intabulator trying out
variations of different kinds -- only a "teaching version" to help you
hear something like what is happening with the general form. Why don't I
actually take it from the start of the "B" section on the third beat of
3 + | 1 + 2 + 3 | 1 ...
E4 F4 G4 F4 E4 D4 E4 F4
C4 D4 C4 B3 C4
A3 G3 F4
I have very mixed feelings about this as an "arrangement," because I've
altered Adam's main melody when maybe I should be doing any adjustments by
preference to accompanying parts, and I'd add that I'm indebted to lots of
motets and the like for that figure in the highest voice. For an ensemble,
at least, I can see how Adam made a beautiful setting that goes with his
main voice; again, this is for what are called "pedagogical purposes," to
see if a simpler version of the close helps in understanding the form.
Most appreciatively,
Margo Schulter

[Roger E. Blumberg]

and this trail balloon ending still had crossed voices on the last chord so
I'll switch them around


was this, trail balloon ending:

. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 C4 B4 E4 F4
. . G3 G3 F3



becomes this, trail balloon ending:

. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 F4
. . D4 C4 C4 B4 E4 C4
. . G3 G3 F3



Thanks
Roger

Post by Margo Schulter

Post by Margo Schulter

Post by Margo Schulter
On the conclusion of the piece, I should discuss that in another post.

For

Post by Margo Schulter

Post by Margo Schulter
me, the form is very satisfactory, and one trick might be try playing

just

Post by Margo Schulter

Post by Margo Schulter
the two lower parts as I noted them in the transcription, the main

melodic

Post by Margo Schulter

Post by Margo Schulter
and the lowest voice.

Hi, Roger, and just to clarify: I mean here to try _first_ playing just
the lower two parts of the transcription, which might be easier to do at a
comfortable and pleasing speed so that you can appreciate the flow and the
form. As it happens, these two parts alone pretty much capture the main
outlines of the form, so that if you can get it to the point where it
sounds coherent and comes together in two parts, then you could add the
third part -- or, actually, do some kind of arrangement approximating the
written parts, since obviously the unisons and voice-crossings can't
literally be reproduced, as you and Cait have rightly called to my
attention.

Hi Margo;
I beleive I've got it right now. It really is all in the rhythm. Amoung
other
things I was jazzing up the middle part and then slowing down and dallying
through the 6 final sonorities, in particular the first four of those last
six.
. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 D4 E4 F4
. . G3 G3 F3
. . 1 + 2 +
. . G4 F4 E4 D4
. . D4 C4 D4
. . G3
When I played those through as a quick 1234 and then give a little extra
time on the last two (or the last _one_ for sure) then it worked. Also while
jazzing up the center section I neglected to hold the GBD split fifth for
enough counts (I was just flying through it as part of my jazzed-up
rendition of that section).
In the end, if I were actually doing an accoumpaniment, which is what I'm
envisioning (some background support) I would probably just peddle or hold
the GDG trine through that entire four note melody or group of sonorities,
letting the singer(s) supply the melody. This is more what accompaniment
typically is -- one doesn't have to be note for note literal in an
accompaniment. But
of course we do have to start somewhere, we do have to be familiar with the
piece one way or another (and with little or no guesswork involved, or time
spent being way off track without realizing it, etc). Midi renditions of
any/all examples would be wonderful (if not manditory) at some point some
day, I think. There's really no getting around it. One either has to locate
and purchase a recording of each and every piece, or be in a classroom
setting, face to face, where the instructor can play through parts and
passages, _or_ (in this day and age, with all of our high tech gadgetry and
the internet as "global classroom") someone could prepair midi or other
recorded snippets of examples and sample material. Someday, everything will
come togeather at one place and time, with enough someone's pitching in and
providing any nessesary supplimentals. [any takers on the midi renditions
and uploads ;') ? I don't have the tools nor keyboard skills. Or maybe
Sebelius "Scorch" examples. With the Scorch plug-in, as used at
http://www.dolmetsch.com/scorchinfo.htm for the Dolmetsch Recorder Method,
one could include staff notated parts, audio, plus lyric, plus chord charts,
that one could both hear, view, and track on a time-line, measure for
measure, as the passage progressed, and then of course be able to translate
that more faithfully and confidently to any combination of instruments,
singers, or both. And this is in addition to Margo's ASCII renditions. I
think the ASCII is an important tool, one not to be omitted down the line
(there should be more of it generally, not less) because staff notation is
still accessable to only a few.]
Anywho, I'm satisfied that I've got it down better now. The alternate ending
you give below (thank you)is indeed easier to play. As you say though,it
does change the melody line a bit, and for the moment I'm not sure how to
proceed. I can play the original now, as originally posted. I'm still
wondering though about the idea of an accoumpiniment that simply holds the G
trine through that otherwise four sonority passage (letting the singers
carry the melody through). Im also wondering about another possible ending,
wondering if it's too modern sounding, too triadic perhaps. Please tell me
what you think of this arrangement. I think it retains the original melody
pretty faithfully?
. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 D4 E4 F4
. . G3 G3 F3
. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 C4
. . D4 C4 C4 B4 E4 F4
. . G3 G3 F3
so two sonorities, corresponding to the "2 +" in the above, are the changes
in question.
what I'm wondering is (in general and even apart from Halle's piece)if
there's anything _fundamentally_ "non-period" about that trial

arrangement?

Post by Margo Schulter
Is it theoretically legal? Might it have safely have been used by someone
back then, with singers for example? Again, the ultimate purpose of this
whole exercise (for me at least)is to get a better (more authentic or
educated) feel for what kinds of sonorities and progressions _might_ have
been used and might be considered "ok" to employ in either prepared or
improvised accompaniment. My envisaged accompaniment of course is on some
kind of guitarra/lute/guitern,citole using 2, 3, or even 4 voices (strings
or courses plucked or strummed "chords"), and I'm assuming I'd be
accompanying either a singer (even myself) or other instrumentalist who
would largely be carrying the melody with their voice or instrument.
While we're at it, I wonder if I could ask you about a couple of
progressions I came up with last night. Again, I'm wondering how these might
be percieved relative to known practice of vocal part writing. These sprang
from experimenting with a 3 chord passage in Halle's piece and taking it
. . E4 F4 G4
. . C4 D4
. . A3 G3
. . E4 F4 G4 A4
. . C4 D4 C#4
. . A3 G3 A3
then continued, adding more, sliding that same chord up one fret, then a
little alteration, then back down a fret again to the original chord, repeat
that once, and a final.
. . E4 F4 G4 A4 A#4 G4 A4 A#4 G4 A4 A
. . C4 D4 C#4 D4 D4 C#4 D4 D4 C#4 D4
. . A3 G3 A3 A#3 A#3 A3 A#3 A#3 A3 A3
any reason that this wouldn't be legal tender? I could add more from there,
but first I'm wondering about that particular chord (8|M3_m6), and then that
up-a-semitone back-a-semitone kind of progression. This of course has
nothing to do with Halle's piece really, it's just an excursion of mine
(sitting under that tree and experimenting).
Thanks
Roger

Post by Margo Schulter
Sometimes, by the way, it can be a very effective performance technique to
start with a single melody from a piece -- here maybe the main melody, or
possibly also the lowest part -- then do a version with two parts (here
the lowest part and main melody together), and finally add the third
voice. I've heard it done for motets where it can really bring out details
of the music and permit a nice build-up.
Also, why don't give you a substitute version of those final two measures
of the "B" section that could avoid unison problems and the like, to give
you a chance to hear the basic form without getting possibly hindered by
the ornamentation with its voice-crossings and unisons. This is _not_ a
proposed arrangement -- although I could picture an intabulator trying out
variations of different kinds -- only a "teaching version" to help you
hear something like what is happening with the general form. Why don't I
actually take it from the start of the "B" section on the third beat of
3 + | 1 + 2 + 3 | 1 ...
E4 F4 G4 F4 E4 D4 E4 F4
C4 D4 C4 B3 C4
A3 G3 F4
I have very mixed feelings about this as an "arrangement," because I've
altered Adam's main melody when maybe I should be doing any adjustments by
preference to accompanying parts, and I'd add that I'm indebted to lots of
motets and the like for that figure in the highest voice. For an ensemble,
at least, I can see how Adam made a beautiful setting that goes with his
main voice; again, this is for what are called "pedagogical purposes," to
see if a simpler version of the close helps in understanding the form.
Most appreciatively,
Margo Schulter

[Margo Schulter]

Post by Roger E. Blumberg
and this trail balloon ending still had crossed voices on the last chord so
I'll switch them around
. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 F4
. . D4 C4 C4 B4 E4 C4
. . G3 G3 F3

Hello, there Roger, and if we disregard all the voice crossings, we could
this version as follows, which looks to me much in keeping with period
style:

. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 E4 F4
. . D4 C4 C4 B4 B3 C4
. . G3 G3 F3

Please note that there's problem at all with having a prominent split
fifth or 5|3_3 (here 5|M3_m3) either as the unstable sonority directly
resolving to the final sonority, or as part of the "build-up" to the
cadence. For example, here's another final cadence from a rondeau of Adam
de la Halle, _Tant con je vivrai_, interestingly showing another way to
set the melodic figure D4-C4-D4-E4-F4 that occurs in the rondeau we've
been discussing also:

1 2 3 + | 1 + 2 3 | 1 2 3 ||
G4 F4 E4 D4 C4 D4 E4 F4
D4 C4 B3 C4
G3 G3 F3

Here we have the split fifth sonority G3-B3-D4 or 5|M3_m3, followed as
often happens by the sixth sonority G3-B3-E4 resolving to F3-C4-F4 (Maj6-8
+ Maj3-5). We could also have the split fifth resolve directly to the
trine (Maj3-5 between lower pair of voices):

D4 F4
B3 C4
G3 F3

In practice, I agree that in accompanying an ensemble, simply playing a
trine on G for the first four sonorities of the original example would be
fine, or in other words:


Ensemble (voice crossings shown):
1 + 2 + 3 | 1 2 3 ||
G4 F4 E4 D4 B3 C4
D4 C4 D4 E4 F4
G3 G3 F3

Plucked string instrument:
G4 E4 F4
D4 B3 C4
G3 G3 F3

This is a dance-song kind of piece, and the rhythm for the plucked string
part might tend to reinforce the flow.

Here's another version of an arrangement of all three voices for a single
string instrument that occurred to me, this one keeping all the notes of
the main melody and accompaniment, albeit breaking a breve of that melody
into two semibreves (or a quarter/crotchet into two eights/quavers in 3/4)
when we write it out without voice crossings:

. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 E4 F4
. . D4 C4 D4 C4 B3 C4
. . G3 G3 F3

This keeps most of the sonorities of Adam's original, including the
momentary G3-D4-E4 or M6|5_2 at the opening of the second beat -- quite
quick and almost "incidental," but hinting at a possible resolution to F
(as a sixth sonority on F often tends to do), confirmed by the following
G3-B3-E4 or M6|M3_4 resolving to the F trine. There are some other touches
of color I'll discuss in a fuller discussion of Adam's original formula.

I need to look at the rest of your examples, and might add one comment for
now. A lot in 13th-century polyphonic style is quite flexible, and in fact
people writing about this music and accustomed to 18th-century style have
complained that there are few "rules," and lots of unpredictable vertical
events. What I can try to say is whether and to what degree something
seems to me "stylish," that is, fitting the patterns of the period as I
hear and improvise them (with the improvisation inevitably bringing into
play my own interpretations).

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Post by Margo Schulter

Post by Roger E. Blumberg
and this trail balloon ending still had crossed voices on the last chord so
I'll switch them around
. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 B3 F4
. . D4 C4 C4 B4 E4 C4
. . G3 G3 F3

Hello, there Roger, and if we disregard all the voice crossings, we could
this version as follows, which looks to me much in keeping with period
. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 E4 F4
. . D4 C4 C4 B4 B3 C4
. . G3 G3 F3

Great. I really am feeling like I can loosen my collar up a bit more every
day, use my "moderns" intuitive ear and a pretty universal form of 4ths
tuned "fretboard logic" and still be within acceptable bounds. I or any
other "modern" player would feel right at home here. Honestly. This really
is so much closer to what we modern fretboard players do now today than even
I would have suspected. That is to say, I'm being very cautious and
respectful and I'm still able to do "what comes natural" (to me) and still
be able to experience and play (hear and enjoy) all manner of color and
texture. Which is to say, I'm wanting for nothing. I'm content. Even by my
modern standards and ears I'm being filled with lovely music, lovely
sonorities (lovely chords) and chord progressions. I feel right at home now,
and would have felt so then. Our chord appreciation genes have not changed
;') and they are not new, polyphony is not new, there _is_ a basic
vocabulary of stuff, that universal appreciation of beauty-in-pattern that
is timeless, classic. We were not singularly incapable, handicapped, or
unsophisticated in our love of and in our creations of musically harmonious
patterns _ever_. I feel vindicated. I had great respect for my ancestors
going in, and it paid off -- the reward is in these pages, the music that I
and we have heard and played these last few days and weeks here.


Thanks Margo (from the bottom of my heart). This has helped me reach back
and touch my heritage and history. I treasure (cherish) being able to
reclaim that heritage as mine, and reclaim my ancestors as me, as kin, cut
from the same cloth. And I really do love music, it was my first love. So
being able to receive this ancestral-communion with music as vehicle makes
it that much more special. It can never get any more "intimate", you can
never get "closer" to them than through their music, to feel and experience
what moved them, what touched their souls. Music has always (first and
foremost)touched my soul. You're allowing to me to touch the soul of my
fellow musicians, those who like me gravitated to music in their youth
because we couldn't help ourselves, we had to have it, had to be near it,
had to learn that craft and become one of those emotion weavers ourselves,
carry on that tradition and pass it on down the line.

Post by Margo Schulter
Please note that there's no problem at all with having a prominent split
fifth or 5|3_3 (here 5|M3_m3) either as the unstable sonority directly
resolving to the final sonority, or as part of the "build-up" to the
cadence.

great, again my collar loosens (within reason of course)



For example, here's another final cadence from a rondeau of Adam

Post by Margo Schulter
de la Halle, _Tant con je vivrai_, interestingly showing another way to
set the melodic figure D4-C4-D4-E4-F4 that occurs in the rondeau we've
1 2 3 + | 1 + 2 3 | 1 2 3 ||
G4 F4 E4 D4 C4 D4 E4 F4
D4 C4 B3 C4
G3 G3 F3
Here we have the split fifth sonority G3-B3-D4 or 5|M3_m3, followed as
often happens by the sixth sonority G3-B3-E4 resolving to F3-C4-F4 (Maj6-8
+ Maj3-5). We could also have the split fifth resolve directly to the
D4 F4
B3 C4
G3 F3
In practice, I agree that in accompanying an ensemble, simply playing a
trine on G for the first four sonorities of the original example would be

great, my intuitions regarding how to approach things are fundamentally
sound I guess.

Post by Margo Schulter
1 + 2 + 3 | 1 2 3 ||
G4 F4 E4 D4 B3 C4
D4 C4 D4 E4 F4
G3 G3 F3
G4 E4 F4
D4 B3 C4
G3 G3 F3
This is a dance-song kind of piece, and the rhythm for the plucked string
part might tend to reinforce the flow.
Here's another version of an arrangement of all three voices for a single
string instrument that occurred to me, this one keeping all the notes of
the main melody and accompaniment, albeit breaking a breve of that melody
into two semibreves (or a quarter/crotchet into two eights/quavers in 3/4)
. . 1 + 2 + 3 | 123 ||
. . G4 F4 E4 D4 E4 F4
. . D4 C4 D4 C4 B3 C4
. . G3 G3 F3
This keeps most of the sonorities of Adam's original, including the
momentary G3-D4-E4 or M6|5_2 at the opening of the second beat -- quite
quick and almost "incidental," but hinting at a possible resolution to F
(as a sixth sonority on F often tends to do), confirmed by the following
G3-B3-E4 or M6|M3_4 resolving to the F trine. There are some other touches
of color I'll discuss in a fuller discussion of Adam's original formula.
I need to look at the rest of your examples, and might add one comment for
now. A lot in 13th-century polyphonic style is quite flexible, and in fact
people writing about this music and accustomed to 18th-century style have
complained that there are few "rules," and lots of unpredictable vertical
events. What I can try to say is whether and to what degree something
seems to me "stylish," that is, fitting the patterns of the period as I
hear and improvise them (with the improvisation inevitably bringing into
play my own interpretations).

Alright, thanks. And I realize that there will come times or specific
examples or trial progressions that I or someone else comes up with that
will in fact be "over the line", e.g. too many accidentals or too odd a
progression or something (un-stylish or fitting), so "I can take it",
whatever your assessment might be. If I like it personally, I can still use
it and play it for my own enjoyment without labeling it as some kind of
medieval approximation or representation. It's just some musical stuff that
I happen to stumble upon, like, or find interesting, that will have no
"lable" (which is fine with me).

Thanks
Roger

Post by Margo Schulter
Most appreciatively,
Margo Schulter

[Roger E. Blumberg]

Thanks Margo;

Your second alternate solution for a revised begining, employing the
momentary M9|5_5, sounds great to me, and it's easy to finger too. I had
actually tried a variation of that earlier (split 9 on F), and liked it.
Your variation is better though. The bit of voice leading or melody line "F4
G4 A4" sounds great. I use my little finger to slide into the G4 from the F4
of the F trine, so it's very expressive. Perfect. ;')

Post by Margo Schulter
1 2 3 + | 1...
F4 F4 G4 A4
C4 C4 E4
F3 F3 A3

Later
Roger

Post by Margo Schulter

Post by Roger E. Blumberg
Everything's working fine now Margo. And I see the additional A3 in the
lowest voice in the revised version as well.

Hi, Roger.
Thank you for confirming that we were dealing with a problem of
proportional and nonproportional fonts, and that the problem now seems
ironed out reasonably well.
One thing I would strongly emphasize is that arranging or adapting a vocal
piece or more generally an ensemble piece of polyphony for any
solo instrument is apt to involve modifications and adjustments, whether
because the instrument is simply unable to do certain things (like
observing voice-crossings), or because the idiomatic style of the
instrument invites elaborations, etc.
In giving examples, I'm hesitant to try an idiomatic arrangement for an
instrument I don't play, because this is better done by people familiar
with the instrument. What I can do is give my own preferences about some
stylistic parameters I might consider in making an arrangement -- which
you or other people doing this would then need to try and see if they fit
the instrument or your taste. It's a process of feedback.
On a single keyboard manual, curiously, I'm content playing a literal
"reduction" of what's written, which I'll show here without taking into
account the crossing of the written voices, etc., and showing a rest where
a written unison means that only two notes at once are actually sounding
1 2 3 + | 1...
F4 r G4 A4
C4 F4 F4 E4
F3 F3 F3 A3
Here's there's a momentary partition of the ninth, F3-F4-G4 or M9|8_M2,
less harmonious than M9|5_5, but also catalogued and accepted by Jacobus;
while the melodic effect of the voice crossing obviously can't be
reproduced on a single manual, the tension of that M9|8_M2 might make the
following trine sound sweeter. Again, it might have been done mainly for
melodic reason; and there's that Maj2-4 resolution between the upper
voices. However, if this doesn't fit a plucked instrument so
well, and we're making a free intabulation (a liberty of many centuries),
1 2 3 + | 1...
F4 F4 G4 A4
C4 C4 E4
F3 F3 A3
This has a momentary M9|5_5; it sounded OK when I played it on a single
keyboard manual, and it keeps some of the melodic nuances that don't
depend on the voice-crossing, as well as the general pattern of
stability/instability.
Of course, in some of the keyboard arrangements of vocal compositions by
Machaut and Landini, for example, much greater liberties occur. Here I'm
trying to go first for a "minimal adjustment" that could make the piece
more easily playable, which isn't necessarily the same as a creative
arrangement for a given instrument.
Again, one of the problems is that we don't have any known 13th-century
intabulations for solo instruments of 13th-century polyphonic pieces --
the arrangements of the Philippe de Vitry motets in the Robertsbridge
Codex (early to middle 14th century) might be the first known. It's a
question of taste (which can vary!), and also of instrumental technique.
On the conclusion of the piece, I should discuss that in another post. For
me, the form is very satisfactory, and one trick might be try playing just
the two lower parts as I noted them in the transcription, the main melodic
and the lowest voice.
By the way, your reaction does illustrate a point that I mentioned in my
post on F-G-F: sometimes either F or G _could_ be a satisfactory
conclusion.
One dramatic example of this is that there's a motet in the Las Huelgas
Codex -- a 13th-century Spanish source -- _In seculum artifex_ -- that was
transcribed and performed for many years in a version ending on G. I have
recordings with instrumental performances. Then, Gordon Anderson published
an edition of Las Huelgas with a version ending on F -- as one would
expect for a piece based on IN SECULUM as the foundation melody or
"tenor." The version ending in G is quite beautiful, and I wouldn't have
suspected that someone would publish a transcription ending on F.
Anyway, thank you for prompting me to analysis of that final cadence in
the Adam de la Halle piece -- and for giving me an opportunity to say that
polyphonic ensemble compositions often get altered when arranged for solo
instruments. The fact that I haven't attempted it in these posts should
been seen mainly as a comment on the limitations of my knowledge of
various instruments, and an invitation for people actually the instruments
to step in. Of course, I can give feedback as to why I might lean toward
one solution rather than another -- but that is also a matter of taste.
You should see how people differ in the "scholarly literature," either
medieval or modern.
Most appreciatively,
Margo Schulter

[Margo Schulter]

Hello, there, Roger and everyone.

Please let give a quick tip, which I might prudently post at the top of
each article using ASCII notation in an age when most people are likely
using GUI operating systems and proportional fonts as the default on
either IBM PC or Mac, and possibly on other platforms such as X-Windows on
UNIX or more generally UNIX-compatible systems. As a user of MS-DOS 6.22
and a text-based UNIX shell account, I take nonproportional display fonts
for granted, but users of such systems might well not do so.

Anyway, my examples in ASCII are meant to be viewed with a nonproportional
font such as Courier where, as on a typical typewriter, all characters and
spaces have the same width.

I don't want to let technical glitches like this get in the way of the
discussion, and would like to thank Roger for alerting me to a problem
which others might be having also.

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Hi Margo;

Thanks. That was it. On my PC, using Outlook Express as the default
newsreader/writer, one has to go under "Tools/Options/Read/Fonts(button)"
and change the "Proportional Font" (which is the default for reading and
write) to "Courier New" even though Courier is a fixed-width or
non-proportional type face (also set it to "smaller" probably). All text in
all mail and all news messages will then always be rendered in Courier.
That's the only way to do it and thus cure any alignment issues. Now, when I
look at your posts again everything lines up as you originally intended it
to (and as it appears on my Mac (which must be defaulting to a fixed-width
front already, even though it's a version of Outlook as well.)Courier looks
fine at a smaller point size so I don't mind leaving this as my new
permanent mail and news font.

Danka
Roger

Post by Margo Schulter
Hello, there, Roger and everyone.
Please let give a quick tip, which I might prudently post at the top of
each article using ASCII notation in an age when most people are likely
using GUI operating systems and proportional fonts as the default on
either IBM PC or Mac, and possibly on other platforms such as X-Windows on
UNIX or more generally UNIX-compatible systems. As a user of MS-DOS 6.22
and a text-based UNIX shell account, I take nonproportional display fonts
for granted, but users of such systems might well not do so.
Anyway, my examples in ASCII are meant to be viewed with a nonproportional
font such as Courier where, as on a typical typewriter, all characters and
spaces have the same width.
I don't want to let technical glitches like this get in the way of the
discussion, and would like to thank Roger for alerting me to a problem
which others might be having also.
Most appreciatively,
Margo Schulter

[Roger E. Blumberg]

Hi Margo;
It's now some days after you first posted this article. I have the fretboard
illustrations done for the complete three-voice rondeau:
1.4. Adam de la Halle: An artful contrast

I'm inserting this post higher in the tree so it doesn't get buried. Figures
are date stamped to coincide with your first posting of the article [January
08, 2004 9:57 PM ]so people can track back to it more easily.

The v2 graphic linked here is a version containing the two changed
sonorities we discussed within this thread on 1-10-2004, the fourth and
third
last chords. I put a gray box around them so they're easy to spot.
So in the v2 version:

these sonorities . . GDE and GDD
become this . . . . GCE and GBD

Loading Image...

Loading Image...


Thanks again
Roger

Post by Margo Schulter
-----------------------------------------
An Essay with Thanks to Cait
Part I: The F-G-F theme
-----------------------------------------
Please let me commence this promised essay by warmly thanking Cait for
an exciting dialogue, and specifically for inspiring this post by
sharing a suggestion of Bill Taylor, an expert in early harp music of
the British Isles, that one typical medieval pattern useful in
accompanying songs is a "home" sonority on F and an "away" sonority on
G -- for example, an alternation between F3-C4-F4 and G3-D4 or
G3-D4-G4.
In looking at this and other characteristic patterns in medieval
music, I'm going to focus on what happens in polyphonic compositions.
This recorded practice could serve as one guide to possible
instrumental accompaniment practices for monophonic songs, albeit a
guide which one might want to use with some caution and with due
artistic judgment.
When I speak of caution and judgment, I have in mind especially some
predilections and at least potential biases of my own to which the
reader should be alerted.
First, for 35 years and a bit more, I've been improvising polyphonic
textures in a medieval vocal kind of style on keyboards. If I produce
something that evokes for me an ensemble organum, clausula, conductus,
motet, or cantilena, etc., then I'm happy. Also, my compositional and
analytical efforts have focused on written polyphony.
Secondly, my responses to improvised accompaniments in performances of
monophonic song might reflect more a delight in familiar textures --
"how neat to have this trouvere song sound like an extempore conductus
or motet" -- rather than a judicious evaluation of likely performance
practices for a particular genre at a particular epoch.
I have taken great pleasure in a rendition of a trobador song by
Marcabru, from around the middle of the 12th century, performed in a
lilting modal rhythm with a plucked string accompaniment, as I recall,
in a nice discant style (as noted in the performance notes) which I
found a bit like a conductus.
Someone looking more critically at likely period style might ask
whether trobador songs in this era were likely to be accompanied at
all (a debatable question, as we've seen in recent threads), and
whether a modal rhythm would prevail rather than a freer declamatory
reading.
Anyway, there are some implicit assumptions in what follows that I'd
like to make a bit more explicit. I tend to assume some kind of modal
or mensural rhythm which could invite something like a composed
polyphonic texture in this type of rhythm, and an approach where
techniques like three-voice sonorities and progressions would not be
out of place. These are the things that I'm accustomed to do, not
necessarily the ones you'd want to do in a given situation.
For more freely declamatory songs, there could be other models. One
could look at polyphonic settings from the 13th century or a bit later
of Psalm recitation tones or the like, or even consider a trinic
equivalent of the "dry recitative" of the 17th century or later.
With these caveats, I'll first consider the F-G-F pattern, and then,
in Part II, another question which you have raised, Cait: the
relationship between steps a third apart, such as F and A.
It's prudent to conclude this preface by saying that the possibilities
suggested below are meant to be illustrative rather than exhaustive.
--------------------
1. The F-G-F pattern
--------------------
In recommending the "F home, G away" pattern, Bill Taylor has called
attention to a theme characteristic of much Continental as well as
English music in the 13th century.
We might actually take this as a theme within a yet more pervasive
theme: the frequent alternation between steps a degree apart, typical
of a style where progressions by stepwise contrary motion define the
ideal for efficient and compelling cadential action. Thus if our final
or trinic center of repose in on F, we'd expect unstable cadential
sonorities on the adjacent steps of G or E, and this is in fact what
tends to happen in standard practice.
Likewise, if the final is G, we might expect to find and do find that
the most popular cadences involve unstable sonorities on the adjacent
steps of A or F, and so on.
--------------------------------
1.1. A Montpellier manifestation
--------------------------------
Here we'll focus on the F-G-F theme, and some of its documented or
possible expressions. First, I'll quickly recall an example adapted
from the opening of a 13th-century Montpellier motet, #103, _Aimi!
las! vivrai_/_Doucement me tient_/OMNES, which I seem first to have
encountered through an analysis of Richard Crocker in his _A History
1 2 3 | 1 2 3 | 1 ...
F4 E4 D4 E4 F4
C4 D4 C4
F3 G3 F4
(Maj7-5 + Maj3-1) (Maj6-8 + Maj2-4)
Here I've indicated the transient directed progressions introduced by
the seventh sonority F3-C4-E4 at the end of the first unit and the
sixth sonority G3-D4-E4 at the end of the second, each lending impetus
to the musical motion forward into the next unit. The momentary
partitions of M7|5_M3 and M6|5_M2 add a bit of color to the stable
consonances, and the directed resolutions briding from one unit to the
next could be described as _cadentiae_ in a medieval meaning of that
term: apt progressions from more tense to more concordant intervals.
----------------------
1.2. A different style
----------------------
Taking the same framework for the two outer voices, we can also arrive
at a passage from one of the most famous F-G-F pieces of the era, here
1 2
1 2 3 4 5 6 | 1 ...
F4 E4 D4 E4 F4
C4 Bb3 C4
F3 G3 F4
(Maj6-8 + min3-5)
From a conventional Continental point of view, we start at "home" on
the F trine, and move to "away" on a mildly unstable sonority: the
split fifth G3-Bb3-D4, with its two unstable thirds, 5|m3_M3. Then
the E4 in the upper voice gives us the momentary sixth sonority
G3-Bb3-E4 or M6|m3_4, resolving in usual fashion to arrive back at our
trinic "home" on F (Maj6-8 + min3-5).
In fact, however, this is the opening of the English round _Sumer is
icumen in_, if one starts with the entry of the first voice singing
the main canonic melody above the repeated _pes_ in the lower two
voices. (If we elect to sing the pes voices alone first to give a feel
for the "ground bass" pattern, then this passage would be a bit after
the opening.)
While this three-voice passage at the beginning of the canon might
suggest an F-G-F theme of trine-split fifth-trine, as more voices
enter it quickly becomes clear that we have a different vertical style
with pervasive tertian sonorities as the norm, the kind of thing
reported by Anonymous IV for the "Westcountry" of England. This kind
of writing, where thirds are treated as stable and conclusive,
contrasts with other kinds of styles in England as well as on the
Continent where these intervals are regarded as mildly unstable, and
often participate in directed progressions to stable sonorities such
as trines.
-------------------------------
1.3. A diversion after midnight
-------------------------------
Getting back to the latter kind of style, we could harmonize the
1 2 3 | 1 2 3 | 1 ...
F4 E4 D4 E4 F4
C4 D4 C4 B3 C4
F3 G3 F4
(Maj7-5 + Maj3-1) (Maj6-8 + Maj3-5)
This solution might come out of the same stylistic milieu as our first
example adapted from Montpellier: as in that example, the quick
directed resolutions leading from one rhythmic unit to the next help
move the harmonic rhythm along, and also to provide moments of unity
knitting the voices together in their often diverse motions.
The theme of alternating between F and G can be a taking off point for
lots of ideas. For example, here's something I came up with very early
this morning as a kind of belated midnight discant diversion, with "r"
1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 |
D4 E4 F4 r G4 D4 E4 F4
D4 B3 C4 E4 D4 C4 B3 C4
G3 F3 G3 F3
(Maj6-8 + Maj3-5) (Maj7-5) (Maj6-8 + Maj3-5)
Again I'm showing the directed resolutions because this is an aspect
of technique in lots of motets and the like which it seems to me it
wouldn't hurt to do my part in emphasizing. Certainly I wouldn't want
to suggest this kind of harmonic rhythm -- directed t nsion at the end
of a unit resolved at the beginning of the next -- as any kind of
"rule"; it's just a common and useful technique.
Other nuances here are the rest in the highest voice, followed by its
entry to supply the octave of a complete trine, and then by a turn of
phrase in this voice yielding a momentary sonority of G3-C4-D4, or
5|4_M2. From any usual standpoint this kind of sonority in the middle
of a unit is quite incidental, and one might well have the voices
proceed in the same way for melodic reasons quite apart from this
vertical detail. However, I must confess to a weakness for 5|4_M2, and
find it a nice touch of color.
-----------------------------------------
1.4. Adam de la Halle: An artful contrast
-----------------------------------------
A complete three-voice rondeau by Adam de la Halle might illustrate
the F-G-F theme in another guise while also demonstrating an artful
use of form to give shape to the "home-away-home" scenario.
Readings of the rhythmic fine points in this rondeau, _He, Diex! quant
verrai_, can vary, so that this version is only one possible solution,
with each of the indicated semibreves dividing a breve taken as having
Musical Form: AB AAAB AB
A | B
1 2 3 + | 1 + 2 3 + + | 1 2 3 + | 1 + 2 + 3 | 123 ||
C4 F4 G4 A4 G4 F4 E4 D4 E4 F4 G4 F4 E4 D4 B3 C4
F4 F4 E4 D4 E4 E4 D4 C4 B3 C4 D4 C4 D4 E4 F4
F3 F3 A3 G3 A3 G3 G3 F3
Here the middle voice has the main melody, and we have a "departure
and return" kind of scenario starting on F and eventually returning
there. Of special interest, and marking a pivotal point in both the
vertical structure and the form, is the unstable split fifth sonority
G3-B3-D4 or 5|M3_m3, strategically situated at the middle of the
piece.
This mildly unstable sonority, which Jacobus as a passionate advocate
for this late 13th-century era will note as a pleasant element of
style when aptly handled, marks a pregnant pause in the form: it
occurs at the end of the "A" section of the rondeau, and signals that
there is more to come.
Moving into the "B" section, we first proceed to another split fifth
sonority on A, the step above G, which leads by a very transient sixth
sonority A3-C4-F4 or m6|m3_4 to a momentary resolution on a G trine
(min6-8 + min3-5), then bringing the music back home with a usual
cadence from a sixth sonority on G to F (Maj6-8 + Maj3-5).
A neat touch of cadential strategy occurs in the portion of the
musical form -- AB AAAB AB -- where the "A" section is thrice
repeated. Here the conclusion of this section is directly followed by
a return to the beginning -- resulting in another standard
D4... F4
B3... C4
G3... F3
(Maj3-5)
In this formula for a G-F cadence, or more generally a cadence where
the lowest voice descends by a step, the lower third of the _quinta
fissa_ (here major) expands to a fifth, while the outer fifth expands
to the octave of a complete trine. While not quite as "efficient" as
cadences where all unstable intervals resolve by stepwise contrary
motion -- here the upper minor third resolves by similar motion to the
upper fourth of the trine, and the highest voice leaps by a third --
this progression is common, and serves as a close in motets.
Here it serves at once to resolve the suspense caused by the
conclusion of the "A" section on an unstable sonority, to reaffirm the
contrast between F as "home" and G as "away," and also to give the
piece a pleasant profile through the minor third motion D4-F4 in the
highest voice of this formula. The actual voice-leading here involves
D4... C4
B3... F4
G3... F3
As a kind of lead-in to Part II, I'll briefly note two possible roles
for the step A in this piece on F.
In the "A" section at the second unit, the trine A3-E4-A4 might be
considered a momentary "home away from home": it is approached by a
transient Maj2-4 resolution between the upper voices. When the A trine
does play this role, it might be considered as something of a
polyphonic equivalent of a confinal -- or, I might say, co-center. For
example, we might have F as center or final, A as co-center, and G as
an active step contrasting with either.
In the "B" section we see another possible role for the step A, by no
means necessarily incompatible with the previous role: a step in
cadential progressions leading to G, which in turn leads to F. Thus if
we try to come up with a simplified version of the "B" section, we
... 3 | 1 2 3 | 1 2 3 ||
E4 F4 G4 E4 F4
C4 D4 B3 C4
A3 G3 F3
Here a sixth sonority on A resolves to a trine on G, and the upper
voices then move to another sixth sonority on G which resolves to F.
One might say that A is to G somewhat as G is to F.
In this piece, we might call F the "ultimate" goal, and G the
"penultimate," since it is the step with the cadential sixth sonority
leading directly to this goal.
Since the step A in this sequence likewise has an unstable sonority
resolving to a trine on the step G, we might if so inclined call it
"the penultimate of the penultimate."
Of course, this simplified version of the "B" section disregards
Adam's elegant ornamentation of the close, and also the variety
brought about by the voice-crossing. As Richard Crocker has well said
in regard to the 13th-century motet, the composers are adept in
finding rich variations on standard passages and progressions.
Influences proposed for these three-voice rondeaux of Adam include the
conductus, the polyphonic rondellus, and improvised accompaniments of
monophonic dance songs. If the last influence were significant,
these masterpieces might record some of what improvising musicians
were doing -- or one version of this, as adapted by a composer skilled
in both the trouvere song and the motet.
At any rate, the F-G-F or more generally "adjacent home and away
steps" theme is a fertile start for improvising or composing: the
dilemma remains, of course, as to which types of improvised polyphonic
techniques, or possibly newly composed arrangements, one considers
appropriate for a given genre in a given performance situation, with
"HAP or HEP" questions[1] likely playing a role in one's choices.
---------------------------------------
1.5. An aside: Fluidity and oscillation
---------------------------------------
Having traced out some of the possibilities of the F-G-F theme, I
should add that in some pieces we have a fluid oscillation or
"see-sawing" between F and G in which either might prove to be "home."
Part of this picture is that just as G is a favorite penultimate for a
center on F, so F is an adjacent degree and common penultimate for a
center on G. Consider this final cadence of a kind often found, for
C4 D4
A3 G3
F3 G3
(Maj3-1 + min3-5)
Here a split fifth on F, 5|M3_m3, resolves to a stable fifth on G;
thus G is the ultimate, and F the cadential penultimate.
In some pieces, there's a charming fluidity, moving back and forth
between F and G and eventually settling on one or the other at the
final cadence. This happens in a most elegant motet, _On parole/A
Paris/FRESE NOUVELE, Montpellier #319.
The piece opens with a trine on F, and soon displays a felicitous
point of form facilitated by the structure of the French tenor,
apparently a street cry advertising "Fresh strawberries, wild
blackberries" -- or, it has been suggested by one commentator,
possibly recording some kind of political slogan.
To see (and hear) this point of form, let us consider the progression
at the conclusion of the first statement of the tenor melody, measures
1 2 3 + | 1 2 3 | 1 2 3 |
A4 A4 G4 F4 G4 D4 E4 F4
E4 D4 C4 D4 r C4
A3 G3 r F3
Here we start with a trine on A, with the upper voices moving by the
end of the unit to a very quick sixth sonority resolving to a trine on
G (min6-8 + min3-5). While the lower two voices pause at the end of
the measure, the note E4 in the highest voice exerts a very satisfying
pull to the full trine on F.
This formula thus might resemble the "B" section of the rondeau by
Adam de la Halle (Section 1.4): there is again a descent in the lowest
voice of A-G-F, with A leading to a momentary resolution to G, and G
to a trine on F.
However, the second and third rhythmic units of this example actually
splice together the conclusion of the first statement of the tenor,
ending on G, as marked by the rest, and the commencement of the next
statement starting on F. At the conclusion of this delightful motet,
one of the most beautiful pieces of music I have heard, we settle
1 + 2 3 + | 1 2 3 ||
G4 A4 A4 G4 F4 G4
A3 B3 C4 D4
A3 G3
In addition to illustrating the fluid interplay between F and G, this
piece has a feature making it appropriate to quote here: in the first
excerpt, the melodic turn in the highest line of G4-D4-E4-F4 provides
one not unlikely source for my own use of this figure (Section 1.3).
----
Note
----
1. "Historically Appropriate Performance" (HAP) aims to do, and do
well, what reasonably _may_ have been done in a given era and genre;
"Historically Educated Performance" (HEP) seeks to canvass period
sources and then do something that "fits the music in an informed
way," quite possibly using new techniques, or techniques of a group
such as the Studio for Early Music which some might hold more typical
of 1970 than 1270.

[Margo Schulter]

Dear Roger and All,

Please let me apologize because I'm a bit tired, and might wisely give
myself a bit more time on completing that article on the F-G-F and F-A
relationships, and also in responding to some of your examples of
improvisation.

For now, however, I do want to say how exciting it is that you're
enjoying the richness of this music and the variety of vertical
structures and progressions that it offers. Again, when people other
than "medievalists" become advocates, that's a good sign.

Above all, I wouldn't want to make comments that could come between
you and a good improvisation. What I can do is say what I might do in
a particular situation in cadencing on a given degree, or in tending
to read an accidental inflection as pointing toward a certain directed
progression, etc. -- or what I'm familiar with in 13th-14th century
sources, to say the least a very partial and selective "survey."

Most appreciatively,

Margo Schulter
***@calweb.com

[Margo Schulter]

-----------------------------------------
Medieval Polyphonic Patterns:
An Essay with Thanks to Cait
Part IIA: The F-G-A question (1)
-----------------------------------------

Please let me again express my thanks to Cait for raising an important
question prompting this portion of my essay: the role or possible
treatment of the degree A in a piece centered on F, especially in a
style of accompaniment where F is taken as "home" and G as "away."

Before getting into some patterns of 13th-century polyphony that might
be relevant for certain accompanied monophonic songs also, I would
offer some general observations applying to simpler and possibly often
more appropriate textures than the conductus-like or motet-like
three-voice progressions I shall be describing.

One option with a piece centered on F, of course, is simply to
maintain a single drone, for example one on the fifth F3-C4 or the
complete trine F3-C4-F4. Here the prominent note A in the melody will
form a "split fifth" sonority F3-A3-C4 with the outer fifth of the
drone divided into two thirds, here the major third below and the
minor third above; this sonority will eventually resolve to stability
when the melody moves to the final F, or possibly to its fifth C.

If one is using a moveable drone, however, or simply adding fifths or
trines at points where they seem to have a pleasing effect and aptly
decorate the melody, then to a "home" of F3-C4-F4 and an "away" of
G3-D4 or G3-D4-G4 one might add a "home away from home" of A3-E4 or
A3-E4-A4. In this way A, like G and F, may have a stable and richly
concordant sonority for its accompaniment, especially when it occurs
prominently.

I use the term "home away from home" because in Gregorian chant,
melodies with a final of F often use A as a prominent tone, for
example a reciting tone in Psalm settings. When secular monophonic
songs follow a similar pattern, then an accompaniment including some
fifths or trines on A to complement those on F (the final or note of
repose) and G (often a note of motion and contrast) can reinforce this
structure.

To this point, my remarks might apply to wide range of monophonic
genres, once we cross the threshold of deciding that _some_
instrumental accompaniment is appropriate. The technique of using a
simple drone, or adding fifths or trines here and there where they
seem to fit, could apply to a melody in a free declamatory style as
well as to one in a measured rhythm like that of a dance song.

What follows might be most relevant to songs following or approaching
a measured rhythm, since the three-voice progressions I discuss are
those of measured polyphony, albeit sometimes _flexibly_ measured
polyphony, as in the conductus (where a modern edition like that of
Gordon Anderson can show _one_ possible rhythmic interpretation).

However, the patterns I am about to discuss as resources for a
deliberate strategy of accompaniment modelled on composed three-voice
textures can also arise when a melody is accompanied in a simpler
style, providing as it were an unplanned adornment. As a compromise
between these simpler and more elaborate approaches, one might
follow a more "modest" technique such as accompanying some principal
notes of a song with fifths -- but strategically disposed so that the
vertical-melodic interactions sometimes pleasantly but unobtrusively
produce three-voice sonorities and progressions like those described
below.


-----------------------------------------------------------
1. F-G-A and alternation: Fifthing and mediating sonorities
-----------------------------------------------------------

A basic question in polyphonic textures, composed or improvised, is
how to move from point A to point B -- or from point F to point A, as
in the following melody:

F3 G3 A3

An attractive three-voice technique is to alternate stable and
unstable sonorities, as in this idiom which seems to me typical of the
conductus:

C4 D4 E4
C4 B3 A3
F3 G3 A3

(Maj3-1 + min3-5)

A characteristic of this figure is that the outer voices engage in
"fifthing," moving together in concordant fifths, while the middle
voice proceeds in contrary motion. We start on a stable fifth F3-C4,
move to an unstable split fifth G3-B3-D4, and then resolve the
relatively concordant but unstable thirds by progressing to another
stable fifth, A3-E4.

There's thus an alternation of stable-unstable-stable, with F and A as
stable and the contrasting degree of G as unstable. This kind of
pattern, composed or improvised, might play into a kind of tendency
that some modern scholars have proposed for 13th-century melodies in
monophonic or polyphonic styles: degrees a third apart often seem to
be "allied," and degrees a second apart to be "contrasting."

This kind of texture with two voices moving in fifths, and a third
moving in contrary motion, has lots of possibilities, and we'll
develop more of them shortly. First, however, let's look at (and hear)
what's happening to some of the two-voice progressions in this
example, thereby encountering one manifestation of a pleasant figure
noted by the writer of a treatise from around the late 13th century.

Considering first the lower pair of voices, we have:

C4 B3 A3
F3 G3 A3

5 Maj3 1

Here we might say that in proceeding from the fifth to the unison, the
unstable third "mediates" between these stable concords, making
possible stepwise contrary motion throughout and also providing an
element of vertical contrast through its instability and tension.

We might refer to this general two-voice pattern as 5-3-1. Now let us
consider the upper pair of voices:

C4 D4 E4
C4 B3 A3

1 min3 5

Here we move from unison to fifth via the unstable third B3-D4 which
"mediates" between these stable concords, or 1-3-5. Again, we have the
pleasing contrast and alternation of a "stable-unstable-stable"
pattern featuring stepwise contrary motion.

Our medieval author remarks that a third is useful for moving from
unison to fifth or from fifth to unison, and indeed this is one
favorite way of proceeding either in two-voice writing or between two
voices of a multi-voice texture, as here.

Another three-voice solution for the F-G-A theme involves descending
motion of the outer voices, which again engage in fifthing, while the
middle voice ascends in contrary motion, treating A as the upper note
of the fifth D3-A4:

C4 B3 A4
F4 G3 A3
F3 E3 D3

(min3-5 + Maj3-1)

Here we have 1-3-5 between the lower voices and 5-3-1 between the
upper voices, with the resolution of the split fifth again involving a
major third contracting to a unison while a minor third expands to a
fifth.

While the two examples are similar, there is a distinction in vertical
color: the split fifth sonority in the first example, G3-B3-D4, has
the major third below and minor third above or 5|M3_m3, while here in
E3-G3-B3 they are arranged conversely (5|m3_M3). Jacobus, writing
around 1325, prefers the first arrangement but notes that the second
is also acceptable, citing a motet known to us from the Bamberg and
Montpellier Codices opening with the sonority A3-C4-E4.

The theme of unstable mediating intervals or sonorities facilitating
smoother motion between stable concords, and also providing the
element of directed resolutions by contrary motion, is a fertile one.
For example, let us consider a variation on our last progression:

1 2 3 | 1 2 3 | 1
C4 B3 C4 D4
F4 G3 A3
F3 E3 D3

(min6-8 + min3-5)

Here the second fifth between the outer voices, E3-B3, expands to the
octave of a complete trine D3-A3-D4 by way of the mediating minor
sixth E3-C4, a figure we might call "5-6-8." The result is a sixth
sonority of m6|m3_4. While the outer minor sixth expands to the
octave, the lower minor third expands to the fifth.


-----------------------------------------------------------
2. Stepping up and down: Opposing and connecting sonorities
-----------------------------------------------------------

Looking again at our three-voice examples so far, we might note a
pattern when the lowest voice participates in the directed resolution
of an unstable interval by contrary motion. When the unstable interval
contracts, the lower voice moves _up_; when the unstable interval
_expands_, the lower voice moves _down_.


C4 D4 E4 C4 B3 A3 C4 B3 C4 D4
C4 B3 A3 F3 G3 A3 F3 G3 A3
F3 G3 A3 F3 E3 D3 F3 E3 D3

(Maj3-1) (min3-5) (min6-8 + min3-5)

In the first example, the lowest voice takes part in a contracting
resolution (Maj3-1) and moves up; in the second, it moves down as part
of an expanding resolution (min3-5); and in the third, it likewise
moves down while participating in two expanding resolutions: min3-5
with the middle voice and min6-8 with the upper voice.

Accordingly, the lowest voice can "step up" with contracting
resolutions (e.g. 3-1, 7-5, 6-4), and "step down" with expanding ones
(e.g. 2-4, 3-5, 6-8).

For one method of "stepping up" from one stable fifth to another,
let's consider this F-G situation:

1 2 3 | 1 ...
C4 D4
F3 A3 G3
F3 G3

(Maj3-1 + min3-5)

Here the two outer voices move in fifths, with the middle voice
momentarily leaping a third to form an unstable split fifth sonority
which resolves in usual fashion, the lower major third contracting to
a unison and the upper minor third expanding to a fifth.

Let us now focus on the lower pair of voices:

1 2 3 | 1 ...

F3 A3 G3
F3 G3

1 Maj3 1

The upper of these voices starts at a unison with the lower voice,
ascends by leap to the unstable third F3-A3, and then descends by step
to complete the Maj3-1 resolution by which our lower voice "steps up."
Since the upper voice approaches and leaves the note A3 in opposite
directions, by a kind of "zigzag" motion, we might call this note an
_opposing_ tone, and the third F3-A3 an "opposing interval." We could
describe this two-voice pattern as motion from one unison to another
decorated by the opposing interval of a third, or 1-3-1.

The upper pair of voices show (and sound) another common pattern:

1 2 3 | 1 ...

C4 D4
F3 A3 G3

5 min3 5

These voices move from one stable fifth (F3-C4) to another (G3-D4),
with the lower voice of the pair introducing the opposing tone of A3
and the opposing interval of the minor third A3-C4, resolving min3-5.
We could describe this as motion in fifth decorated by the intervening
third and its resolution, or 5-3-5. Our medieval theorist who notes
that thirds are useful in moving from unison to fifth or vice versa
also recommends them in moving "from fifth to fifth," very likely
meaning this kind of pattern.

Looking again at all three voices, we could describe the split fifth
F3-A3-C4 or 5|M3_m3 as an "opposing sonority" resolving with the lower
major third contracting to a unison and the upper minor third
expanding to a fifth, as the middle voice completes its 1-3-1 pattern
with the lowest voice and 5-3-5 pattern with the highest voice.

1 2 3 | 1 ...
C4 D4
F3 A3 G3
F3 G3

The situation of "stepping up" in the lower voice from F to G offers
an opportunity to show another useful opposing pattern, 5-7-5:

C4 E4 D4 C4 E4 D4
C4 D4 F3 A3 G3
F3 G3 or F3 G3

(Maj7-5 + Maj3-1) (Maj7-5 + Maj3-1)

In the first progression, the lower two voices move in fifths while
the highest voice decorates the progression with the opposing tone E4,
forming a momentary opposing sonority of F3-C4-E4 or M7|5_M3 and
weaving a 5-7-5 pattern with the lowest voice and a 1-3-1 pattern with
the middle voice. In the second progression, both upper voices have
opposing tones, moving in patterns of 1-3-1 and 5-7-5 with the lowest
voice and producing an opposing sonority of F3-A3-E4 or M7|M3_5.

To illustrate the difference between mediating and opposing tones, and
how these two categories can nicely combine in a three-voice texture,
let us consider an attractive way of "stepping down" in the lowest
voice from G to F:

1 2 3 | 1 ...
D4 E4 F4
D4 B3 C4
G3 F3

(Maj6-8 + Maj3-5)

Here the outer voices move by contrary motion from fifth to octave
with a mediating major sixth (5-M6-8), while the lower voices move in
fifths with an opposing major third (5-M3-5). Together, these figures
produce the sixth sonority G3-B3-E4 or M6|M3_4 with its standard
directed resolution.

The highest voice with its mediating tone moves in a "straight line,"
ascending by step (D4-E4-F4), while the middle voice with its opposing
tone moves in a zigzag pattern, down a third and up a step (D4-B3-C4).
Two-voice figures like the mediating 5-6-8 or opposing 5-3-5 are like
basic "stitches" which can be deliciously interwoven in the tapestry
of a three-voice texture.

This example also shows how the lowest voice can "step down" through
expanding resolutions with one or more upper voices, here Maj3-5 with
the middle voice and Maj6-8 with the upper voice.

Now let's consider the situation of "stepping down" from a trine on G
to another on F, with two variations bringing into play other very
useful opposing figures:

G4 E4 F4 G4 E4 F4
D4 C4 D3 B3 C4
G3 F3 or G3 F3

(Maj6-8 + Maj2-4) (Maj6-8 + Maj3-5)

In the first example, the opposing tone E4 in the highest voice weaves
an 8-M6-8 pattern with the lowest voice, and also a 4-M2-4 pattern
with the middle voice, producing the sixth sonority G3-D4-E4 or
M6|5_M2 and its directed resolution with the outer major sixth
moving to the octave and the upper major second to the upper fourth of
the trine on F.

In the second example, the two upper voices both have opposing tones
forming patterns of 8-M6-8 and 5-M3-5 with the lowest voice, producing
a sixth sonority of G3-B3-E4 or M6|M3_4 and its standard resolution.

Now that we've done a bit of "stepping up" and "stepping down" with
mediating or opposing intervals, let's consider a third kind of
intervening interval in another version of the last G-F progression:

1 2 3 | 1
G4 F4 E4 F4
D3 C4 B3 C4
G3 F3

(Maj6-8 + Maj3-5)

This time, in each upper voice, the leap of a third in approaching the
opposing tone is "filled in" with the connecting step, so that our
8-6-8 and 5-3-5 patterns become 8-7-6-8 and 5-4-3-5, with the upper
voices moving in fourths. These "connecting tones" C4 in the middle
voice and F4 in the highest voice facilitate smoother melodic motion,
and also result in the mildly unstable "connecting sonority" of
G3-C4-F4 or m7|4_4, an outer minor seventh "split" into two concordant
fourths. In a discussion of the minor seventh, Jacobus recommends this
agreeable sonority.

While connecting sonorities often play a rather unassuming role in the
middle of a rhythmic unit, they can sometimes make a much more
prominent and dramatic appearance, as with the beautiful m7|4_4 in
this formula for an internal or final cadence.

1 2 3 | 1 2 3 | 1 2 3 ||
G4 F4 F4 E4 F4
D3 C4 C4 B3 C4
G3 F3

(Maj6-8 + Maj3-5)

Apart from the changes in rhythm, this progression is identical to the
last, combining figures of 5-4-M3-4 and 8-m7-M6-8.

In stepping up and down, we can "mix and match" these figures in
varied ways to weave a polyphonic fabric, as in the following example
which illustrates one optional nuance regarding 13th-century
accidentals:

1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 ||
F4 E4 D4 F4 E4 E4 F4 G4 F4 E4 F4
C4 A3 G3 B(b)3 A3 E4 D4 C4 B3 C4
F3 G3 A3 A3 G3 F3

We start with a trine on F, and "step up" to a fifth on G through
mediating intervals of the major seventh (8-M7-5) and major third
(5-M3-1) in the two upper voices with respect to the lowest voice,
producing a mediating sonority of F3-A3-E4 or M7|M3_5, with standard
resolutions of (Maj7-5 + Maj3-1).

Next we "step up" again from our fifth on G to another on A, using an
optional Bb in the middle voice, with opposing intervals of a minor
seventh (5-m7-5) and minor third (5-m3-1) above the lowest voice, and
a mediating sonority of G3-B(b)3-F4 (min7-5 + min3-1).

After pausing on A, which might have the effect of a "home away from
home," we "step down" from this fifth to a trine on G by way of a
mediating tone in the highest voice, forming mediating intervals of a
minor sixth (5-m6-8) with the lowest voice and a minor second (1-m2-4)
with the middle voice, and a mediating sonority of m6|5_m2 resolving
(min6-8 + min2-4).

Finally, we "step down" from our a G trine to an F trine via
connecting and opposing intervals formed by both upper voices with the
lowest voice, 8-m7-M6-8 and 5-4-M3-5, producing the momentary color of
a connecting m7|4_4 sonority and an opposing sonority of M6|M3_4,
resolving (Maj6-8 + Maj3-5).

The optional nuance of accidental usage favored in some 13th-century
styles and pieces with a final or "home" on F is a tendency to use Bb
in cadences on A (descending semitone Bb-A) and B-natural in cadences
on F (ascending semitone B-C). However, this is only one 13th-century
approach suggested by manuscript accidentals: some pieces might use a
consistent Bb or B-natural, and indicated accidentals sometimes vary
in different sources for the same piece.

(Continued in Part IIB)

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Hi Margo;

Thanks for these. I'm going through Part IIa now.

Roger

Post by Margo Schulter
-----------------------------------------
An Essay with Thanks to Cait
Part IIA: The F-G-A question (1)
-----------------------------------------
Please let me again express my thanks to Cait for raising an important
question prompting this portion of my essay: the role or possible
treatment of the degree A in a piece centered on F, especially in a
style of accompaniment where F is taken as "home" and G as "away."
Before getting into some patterns of 13th-century polyphony that might
be relevant for certain accompanied monophonic songs also, I would
offer some general observations applying to simpler and possibly often
more appropriate textures than the conductus-like or motet-like
three-voice progressions I shall be describing.
One option with a piece centered on F, of course, is simply to
maintain a single drone, for example one on the fifth F3-C4 or the
complete trine F3-C4-F4. Here the prominent note A in the melody will
form a "split fifth" sonority F3-A3-C4 with the outer fifth of the
drone divided into two thirds, here the major third below and the
minor third above; this sonority will eventually resolve to stability
when the melody moves to the final F, or possibly to its fifth C.
If one is using a moveable drone, however, or simply adding fifths or
trines at points where they seem to have a pleasing effect and aptly
decorate the melody, then to a "home" of F3-C4-F4 and an "away" of
G3-D4 or G3-D4-G4 one might add a "home away from home" of A3-E4 or
A3-E4-A4. In this way A, like G and F, may have a stable and richly
concordant sonority for its accompaniment, especially when it occurs
prominently.
I use the term "home away from home" because in Gregorian chant,
melodies with a final of F often use A as a prominent tone, for
example a reciting tone in Psalm settings. When secular monophonic
songs follow a similar pattern, then an accompaniment including some
fifths or trines on A to complement those on F (the final or note of
repose) and G (often a note of motion and contrast) can reinforce this
structure.
To this point, my remarks might apply to wide range of monophonic
genres, once we cross the threshold of deciding that _some_
instrumental accompaniment is appropriate. The technique of using a
simple drone, or adding fifths or trines here and there where they
seem to fit, could apply to a melody in a free declamatory style as
well as to one in a measured rhythm like that of a dance song.
What follows might be most relevant to songs following or approaching
a measured rhythm, since the three-voice progressions I discuss are
those of measured polyphony, albeit sometimes _flexibly_ measured
polyphony, as in the conductus (where a modern edition like that of
Gordon Anderson can show _one_ possible rhythmic interpretation).
However, the patterns I am about to discuss as resources for a
deliberate strategy of accompaniment modelled on composed three-voice
textures can also arise when a melody is accompanied in a simpler
style, providing as it were an unplanned adornment. As a compromise
between these simpler and more elaborate approaches, one might
follow a more "modest" technique such as accompanying some principal
notes of a song with fifths -- but strategically disposed so that the
vertical-melodic interactions sometimes pleasantly but unobtrusively
produce three-voice sonorities and progressions like those described
below.
-----------------------------------------------------------
1. F-G-A and alternation: Fifthing and mediating sonorities
-----------------------------------------------------------
A basic question in polyphonic textures, composed or improvised, is
how to move from point A to point B -- or from point F to point A, as
F3 G3 A3
An attractive three-voice technique is to alternate stable and
unstable sonorities, as in this idiom which seems to me typical of the
C4 D4 E4
C4 B3 A3
F3 G3 A3
(Maj3-1 + min3-5)
A characteristic of this figure is that the outer voices engage in
"fifthing," moving together in concordant fifths, while the middle
voice proceeds in contrary motion. We start on a stable fifth F3-C4,
move to an unstable split fifth G3-B3-D4, and then resolve the
relatively concordant but unstable thirds by progressing to another
stable fifth, A3-E4.
There's thus an alternation of stable-unstable-stable, with F and A as
stable and the contrasting degree of G as unstable. This kind of
pattern, composed or improvised, might play into a kind of tendency
that some modern scholars have proposed for 13th-century melodies in
monophonic or polyphonic styles: degrees a third apart often seem to
be "allied," and degrees a second apart to be "contrasting."
This kind of texture with two voices moving in fifths, and a third
moving in contrary motion, has lots of possibilities, and we'll
develop more of them shortly. First, however, let's look at (and hear)
what's happening to some of the two-voice progressions in this
example, thereby encountering one manifestation of a pleasant figure
noted by the writer of a treatise from around the late 13th century.
C4 B3 A3
F3 G3 A3
5 Maj3 1
Here we might say that in proceeding from the fifth to the unison, the
unstable third "mediates" between these stable concords, making
possible stepwise contrary motion throughout and also providing an
element of vertical contrast through its instability and tension.
We might refer to this general two-voice pattern as 5-3-1. Now let us
C4 D4 E4
C4 B3 A3
1 min3 5
Here we move from unison to fifth via the unstable third B3-D4 which
"mediates" between these stable concords, or 1-3-5. Again, we have the
pleasing contrast and alternation of a "stable-unstable-stable"
pattern featuring stepwise contrary motion.
Our medieval author remarks that a third is useful for moving from
unison to fifth or from fifth to unison, and indeed this is one
favorite way of proceeding either in two-voice writing or between two
voices of a multi-voice texture, as here.
Another three-voice solution for the F-G-A theme involves descending
motion of the outer voices, which again engage in fifthing, while the
middle voice ascends in contrary motion, treating A as the upper note
C4 B3 A4
F4 G3 A3
F3 E3 D3
(min3-5 + Maj3-1)
Here we have 1-3-5 between the lower voices and 5-3-1 between the
upper voices, with the resolution of the split fifth again involving a
major third contracting to a unison while a minor third expands to a
fifth.
While the two examples are similar, there is a distinction in vertical
color: the split fifth sonority in the first example, G3-B3-D4, has
the major third below and minor third above or 5|M3_m3, while here in
E3-G3-B3 they are arranged conversely (5|m3_M3). Jacobus, writing
around 1325, prefers the first arrangement but notes that the second
is also acceptable, citing a motet known to us from the Bamberg and
Montpellier Codices opening with the sonority A3-C4-E4.
The theme of unstable mediating intervals or sonorities facilitating
smoother motion between stable concords, and also providing the
element of directed resolutions by contrary motion, is a fertile one.
1 2 3 | 1 2 3 | 1
C4 B3 C4 D4
F4 G3 A3
F3 E3 D3
(min6-8 + min3-5)
Here the second fifth between the outer voices, E3-B3, expands to the
octave of a complete trine D3-A3-D4 by way of the mediating minor
sixth E3-C4, a figure we might call "5-6-8." The result is a sixth
sonority of m6|m3_4. While the outer minor sixth expands to the
octave, the lower minor third expands to the fifth.
-----------------------------------------------------------
2. Stepping up and down: Opposing and connecting sonorities
-----------------------------------------------------------
Looking again at our three-voice examples so far, we might note a
pattern when the lowest voice participates in the directed resolution
of an unstable interval by contrary motion. When the unstable interval
contracts, the lower voice moves _up_; when the unstable interval
_expands_, the lower voice moves _down_.
C4 D4 E4 C4 B3 A3 C4 B3 C4 D4
C4 B3 A3 F3 G3 A3 F3 G3 A3
F3 G3 A3 F3 E3 D3 F3 E3 D3
(Maj3-1) (min3-5) (min6-8 + min3-5)
In the first example, the lowest voice takes part in a contracting
resolution (Maj3-1) and moves up; in the second, it moves down as part
of an expanding resolution (min3-5); and in the third, it likewise
moves down while participating in two expanding resolutions: min3-5
with the middle voice and min6-8 with the upper voice.
Accordingly, the lowest voice can "step up" with contracting
resolutions (e.g. 3-1, 7-5, 6-4), and "step down" with expanding ones
(e.g. 2-4, 3-5, 6-8).
For one method of "stepping up" from one stable fifth to another,
1 2 3 | 1 ...
C4 D4
F3 A3 G3
F3 G3
(Maj3-1 + min3-5)
Here the two outer voices move in fifths, with the middle voice
momentarily leaping a third to form an unstable split fifth sonority
which resolves in usual fashion, the lower major third contracting to
a unison and the upper minor third expanding to a fifth.
1 2 3 | 1 ...
F3 A3 G3
F3 G3
1 Maj3 1
The upper of these voices starts at a unison with the lower voice,
ascends by leap to the unstable third F3-A3, and then descends by step
to complete the Maj3-1 resolution by which our lower voice "steps up."
Since the upper voice approaches and leaves the note A3 in opposite
directions, by a kind of "zigzag" motion, we might call this note an
_opposing_ tone, and the third F3-A3 an "opposing interval." We could
describe this two-voice pattern as motion from one unison to another
decorated by the opposing interval of a third, or 1-3-1.
1 2 3 | 1 ...
C4 D4
F3 A3 G3
5 min3 5
These voices move from one stable fifth (F3-C4) to another (G3-D4),
with the lower voice of the pair introducing the opposing tone of A3
and the opposing interval of the minor third A3-C4, resolving min3-5.
We could describe this as motion in fifth decorated by the intervening
third and its resolution, or 5-3-5. Our medieval theorist who notes
that thirds are useful in moving from unison to fifth or vice versa
also recommends them in moving "from fifth to fifth," very likely
meaning this kind of pattern.
Looking again at all three voices, we could describe the split fifth
F3-A3-C4 or 5|M3_m3 as an "opposing sonority" resolving with the lower
major third contracting to a unison and the upper minor third
expanding to a fifth, as the middle voice completes its 1-3-1 pattern
with the lowest voice and 5-3-5 pattern with the highest voice.
1 2 3 | 1 ...
C4 D4
F3 A3 G3
F3 G3
The situation of "stepping up" in the lower voice from F to G offers
C4 E4 D4 C4 E4 D4
C4 D4 F3 A3 G3
F3 G3 or F3 G3
(Maj7-5 + Maj3-1) (Maj7-5 + Maj3-1)
In the first progression, the lower two voices move in fifths while
the highest voice decorates the progression with the opposing tone E4,
forming a momentary opposing sonority of F3-C4-E4 or M7|5_M3 and
weaving a 5-7-5 pattern with the lowest voice and a 1-3-1 pattern with
the middle voice. In the second progression, both upper voices have
opposing tones, moving in patterns of 1-3-1 and 5-7-5 with the lowest
voice and producing an opposing sonority of F3-A3-E4 or M7|M3_5.
To illustrate the difference between mediating and opposing tones, and
how these two categories can nicely combine in a three-voice texture,
let us consider an attractive way of "stepping down" in the lowest
1 2 3 | 1 ...
D4 E4 F4
D4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)
Here the outer voices move by contrary motion from fifth to octave
with a mediating major sixth (5-M6-8), while the lower voices move in
fifths with an opposing major third (5-M3-5). Together, these figures
produce the sixth sonority G3-B3-E4 or M6|M3_4 with its standard
directed resolution.
The highest voice with its mediating tone moves in a "straight line,"
ascending by step (D4-E4-F4), while the middle voice with its opposing
tone moves in a zigzag pattern, down a third and up a step (D4-B3-C4).
Two-voice figures like the mediating 5-6-8 or opposing 5-3-5 are like
basic "stitches" which can be deliciously interwoven in the tapestry
of a three-voice texture.
This example also shows how the lowest voice can "step down" through
expanding resolutions with one or more upper voices, here Maj3-5 with
the middle voice and Maj6-8 with the upper voice.
Now let's consider the situation of "stepping down" from a trine on G
to another on F, with two variations bringing into play other very
G4 E4 F4 G4 E4 F4
D4 C4 D3 B3 C4
G3 F3 or G3 F3
(Maj6-8 + Maj2-4) (Maj6-8 + Maj3-5)
In the first example, the opposing tone E4 in the highest voice weaves
an 8-M6-8 pattern with the lowest voice, and also a 4-M2-4 pattern
with the middle voice, producing the sixth sonority G3-D4-E4 or
M6|5_M2 and its directed resolution with the outer major sixth
moving to the octave and the upper major second to the upper fourth of
the trine on F.
In the second example, the two upper voices both have opposing tones
forming patterns of 8-M6-8 and 5-M3-5 with the lowest voice, producing
a sixth sonority of G3-B3-E4 or M6|M3_4 and its standard resolution.
Now that we've done a bit of "stepping up" and "stepping down" with
mediating or opposing intervals, let's consider a third kind of
1 2 3 | 1
G4 F4 E4 F4
D3 C4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)
This time, in each upper voice, the leap of a third in approaching the
opposing tone is "filled in" with the connecting step, so that our
8-6-8 and 5-3-5 patterns become 8-7-6-8 and 5-4-3-5, with the upper
voices moving in fourths. These "connecting tones" C4 in the middle
voice and F4 in the highest voice facilitate smoother melodic motion,
and also result in the mildly unstable "connecting sonority" of
G3-C4-F4 or m7|4_4, an outer minor seventh "split" into two concordant
fourths. In a discussion of the minor seventh, Jacobus recommends this
agreeable sonority.
While connecting sonorities often play a rather unassuming role in the
middle of a rhythmic unit, they can sometimes make a much more
prominent and dramatic appearance, as with the beautiful m7|4_4 in
this formula for an internal or final cadence.
1 2 3 | 1 2 3 | 1 2 3 ||
G4 F4 F4 E4 F4
D3 C4 C4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)
Apart from the changes in rhythm, this progression is identical to the
last, combining figures of 5-4-M3-4 and 8-m7-M6-8.
In stepping up and down, we can "mix and match" these figures in
varied ways to weave a polyphonic fabric, as in the following example
which illustrates one optional nuance regarding 13th-century
1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 ||
F4 E4 D4 F4 E4 E4 F4 G4 F4 E4 F4
C4 A3 G3 B(b)3 A3 E4 D4 C4 B3 C4
F3 G3 A3 A3 G3 F3
We start with a trine on F, and "step up" to a fifth on G through
mediating intervals of the major seventh (8-M7-5) and major third
(5-M3-1) in the two upper voices with respect to the lowest voice,
producing a mediating sonority of F3-A3-E4 or M7|M3_5, with standard
resolutions of (Maj7-5 + Maj3-1).
Next we "step up" again from our fifth on G to another on A, using an
optional Bb in the middle voice, with opposing intervals of a minor
seventh (5-m7-5) and minor third (5-m3-1) above the lowest voice, and
a mediating sonority of G3-B(b)3-F4 (min7-5 + min3-1).
After pausing on A, which might have the effect of a "home away from
home," we "step down" from this fifth to a trine on G by way of a
mediating tone in the highest voice, forming mediating intervals of a
minor sixth (5-m6-8) with the lowest voice and a minor second (1-m2-4)
with the middle voice, and a mediating sonority of m6|5_m2 resolving
(min6-8 + min2-4).
Finally, we "step down" from our a G trine to an F trine via
connecting and opposing intervals formed by both upper voices with the
lowest voice, 8-m7-M6-8 and 5-4-M3-5, producing the momentary color of
a connecting m7|4_4 sonority and an opposing sonority of M6|M3_4,
resolving (Maj6-8 + Maj3-5).
The optional nuance of accidental usage favored in some 13th-century
styles and pieces with a final or "home" on F is a tendency to use Bb
in cadences on A (descending semitone Bb-A) and B-natural in cadences
on F (ascending semitone B-C). However, this is only one 13th-century
approach suggested by manuscript accidentals: some pieces might use a
consistent Bb or B-natural, and indicated accidentals sometimes vary
in different sources for the same piece.
(Continued in Part IIB)
Most appreciatively,
Margo Schulter

[Roger E. Blumberg]

Hi Margo;

Here's the figures to accompany Part IIA.

Again, these are for 4 course 4ths-tuned chromatic fretted string
instruments: lute, citole, guitarra latina, etc. [note; common lute tuning
would be 4-3-4 across four courses rather than the 4-4-4 used here.] Tuning
used is mostly EADG (4ths tuning)like the lowest pitched 4 strings of
guitar, but a few are rendered a whole-step down, DGCF (is also 4ths
tuning). This later tuning was simply to allow showing (and hearing) a
couple Unison tones that were otherwise off the fretboard (beyond the nut)in
EADG tuning. Two fretboard note spellers are at the top of the following URL
list: EADG, and DGCF.

Figures having "v2" in their file-names are slightly modified simplified
voicings and fingerings, typically changing a sonority that contains a
Unison into a Trine, e.g. an F3-F3-C4 vertical stack might become F3-C4-F4.
Figures with no v2 are verbatim, exactly as given in the essay, including
Unisons (octave range is changed in some figures however). Also, any
previously identified errors in Octave notations have been corrected here.

Thanks
Roger


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Post by Margo Schulter
-----------------------------------------
An Essay with Thanks to Cait
Part IIA: The F-G-A question (1)
-----------------------------------------
(Continued in Part IIB)
Most appreciatively,
Margo Schulter

[Roger E. Blumberg]

Hi Margo;

Ok, a few comments and questions on Part IIA. . .

as a reminder of why we're here; a few paragraphs in, Margo says . . .

. . the patterns I am about to discuss as resources for a
deliberate strategy of accompaniment modeled on composed three-voice
textures . . .

so now, on with the show.

. . a kind of tendency
that some modern scholars have proposed for 13th-century melodies in
monophonic or polyphonic styles: degrees a third apart often seem to
be "allied," and degrees a second apart to be "contrasting."
. . Here we might say that in proceeding from the fifth to the unison, the
unstable third "mediates" between these stable concords, making
possible stepwise contrary motion throughout and also providing an
element of vertical contrast through its instability and tension.
. . Our medieval author remarks that a third is useful for moving from
unison to fifth or from fifth to unison, and indeed this is one
favorite way of proceeding either in two-voice writing or between two
voices of a multi-voice texture, as here.

in two of the early figures . . .
Loading Image...
. . . we see both species of "split fifth" (analogous to Major and minor
triads) each used to "mediate" between two "trines", resulting an a pattern
of stable-unstable-stable, the split-fifths are the "mediating instability".
Both examples are very pretty by the way, and if I understand correctly they
were a staple bit of musical vocabulary, meat and potatoes almost -- hence a
good "resource for a deliberate strategy of accompaniment".

The theme of unstable mediating intervals or sonorities facilitating
smoother motion between stable concords, and also providing the
element of directed resolutions by contrary motion, is a fertile one.
1 2 3 | 1 2 3 | 1
C4 B3 C4 D4
F4 G3 A3
F3 E3 D3
(min6-8 + min3-5)

This one (above) is really fabulous Margo!
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig1.06v2.gif
Fertile indeed (this bit B3 C4 D4 and the progression of chords used to
express it) for ideas in constructing accompaniment using three voice
sonorities, a kind of voice leading or "melody chord" playing.



This next example (below) might be more interesting than I originally
thought . .

For one method of "stepping up" from one stable fifth to another,
1 2 3 | 1 ...
C4 D4
F3 A3 G3
F3 G3
(Maj3-1 + min3-5)

can this principle be extended further or applied more generally in a kind
of "split time" fashion?. That is, (first, if I could I'll convert the
Unison sonorities into trines) splitting a time alotment for a given trine
between itself and a split-fifth on the same degree? For example, continuing
the above progression something like this?:

1 2 3 | 1
C4 D4 E4
F3 A3 G3 B3 A3
F3 G3 A3


so we're moving from F to G to A (I'm using all trines there but we can keep
it to all Unison sonorities if you like just to establish whether or not the
idea is sound) but between each we're inserting a split-fifth to add some
interest and perhaps help drive the progression along more smoothly as well.
And we're still alternating between stable and unstable sonorities
throughout.



These next two are insanely great!

http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.06abV2.gif
These are my absolute favorites of this PartIIA. These are out of this
world.

The situation of "stepping up" in the lower voice from F to G offers
C4 E4 D4 C4 E4 D4
C4 D4 F3 A3 G3
F3 G3 or F3 G3
(Maj7-5 + Maj3-1) (Maj7-5 + Maj3-1)

These again are a kind of "split time" the way I conceptualize things
(Unison or Trine to Major 7th on the same degree), the unstable mediating
sonorities are most definately driving the progressions forward in these two
examples. This time the Major 7th intervals are providing the tension
(instability) where in the previous examples it was the 3rds in the
split-fifths. I like the second example best, and it has both M3rd and M7th
intervals in it's mediating sonority.

Speaking of that second example, what would you say of this progression?
I'll start with two trines on F and G, insert your F A E sonority between
them and add a fourth sonority (G3 B3 G4) to mediate back to an F trine,
creating a pretty cycle I could repeat indefinately (and play easily):

F4 E4 G4 F4
C4 A3 D3 B3 C4
F3 G3 F3




the next one too is beautiful . .

1 2 3 | 1 ...
D4 E4 F4
D4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)

we heard this earlier (In PartI) but now we can group it together with these
other mediating sonorities
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.07.gif



the next two are also gorgeous and again sonorities we've come across
previously:
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.08a-b.gif

Now let's consider the situation of "stepping down" from a trine on G
to another on F, with two variations bringing into play other very
G4 E4 F4 G4 E4 F4
D4 C4 D3 B3 C4
G3 F3 or G3 F3
(Maj6-8 + Maj2-4) (Maj6-8 + Maj3-5)

and another pretty one from earlier
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.09.gif

1 2 3 | 1
G4 F4 E4 F4
D3 C4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)

and last but not least:
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.11.gif
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.11v2.gif

In stepping up and down, we can "mix and match" these figures in
varied ways to weave a polyphonic fabric, as in the following example
which illustrates one optional nuance regarding 13th-century
1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 ||
F4 E4 D4 F4 E4 E4 F4 G4 F4 E4 F4
C4 A3 G3 B(b)3 A3 E4 D4 C4 B3 C4
F3 G3 A3 A3 G3 F3

Well, this opens with my favorite chord of the day (that second sonority),
and then it gets better. That whole initial string is very nice (so is the
ending but we're already familiar with it, the begining part here is the new
stuff). The string of first 5 chords taken as a phrase, then chords 6 7 and
8 taken as a phrase, then the all 8 initial chords taken together are great
(and new to us).

The fourth chord, with the Bb was definitely the most surprising to hear,
and pleasantly so, very nice.

In the phrase of chords 6, 7, and 8, the sonority A3 E4 F4 was also
surprising. It's more dissonant than I would have expected to hear, but I
like it a lot. I keep thinking of how moody and jazzy much of this sounds,
perhaps "Gothic" is the correct and appropriate word for the mood of it. It
suits me fine in any event, I love it. I almost said "dark" but it's really
not. Even it's somewhat dark tones (painterly tones and hues) are gentle,
pure, honest, and quickly enough "run home" to consonance, so it isn't a
darkness that's wallowed in for long, certainly not nurtured. It's a
sophisticated way of doing it. Even the consonances aren't too pretty nor
overly sweet because the final has no Major third to it (no "happy face"
Major triad). It's just a point of "strength", rest and power, neutral, calm
repose, contrasted with the mild darkness and mild sweetness (of a split
fifth lets say). "Subtle and sophisticated, "understated and pure", that's
probably the closest I can come to describing my impressions of these
examples so far.

[P.S. To my recollection we've yet to use a G B F (no flat on the B) and at
some point I hope we can work in some of that in too.]


alrighty, thanks Margo, that was good, I appreciate it. On to Part IIB in a
day or two (I hope).

Roger

[Margo Schulter]

Post by Roger E. Blumberg
Hi Margo;
Ok, a few comments and questions on Part IIA. . .

Hi, Roger, and my apologies for the delay in answering this: last week
I was involved with a music project, and I much appreciate your
patience as well this helpful response with some excellent
observations and questions, a real treat.

Post by Roger E. Blumberg
in two of the early figures . . .
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig1.02n05v2.gif
. . . we see both species of "split fifth" (analogous to Major and
minor triads) each used to "mediate" between two "trines", resulting
an a pattern of stable-unstable-stable, the split-fifths are the
"mediating instability". Both examples are very pretty by the way,
and if I understand correctly they were a staple bit of musical
vocabulary, meat and potatoes almost -- hence a good "resource for a
deliberate strategy of accompaniment".

To take your last sentence first, I'd much agree, both on the beauty
of these progressions, and their use as a "staple bit of musical
vocabulary" -- this is the kind of thing we see and hear all the time
in 13th-century conductus and motets, etc. While it's often debated
just what a style of instrumental accompaniment might have been like,
and whether and how often such improvised accompaniments might have
taken on a style like that of composed three-voice polyphony, I'd say
at least that they're a "resource for a deliberate strategy of
accompaniment" if one accepts such compositions as a valid model.

Now for the more delicate question: whether and how the 13th-century
"split fifth" with major third placed below minor (e.g. F3-A3-C4), or
the converse (e.g. A3-C4-E4), might be taken as "analogous to major
and minor triads."

Obviously there's some analogy, because the interval categories in a
medieval split fifth (_quinta fissa_ in Latin) or a 17th-19th century
triad are the same -- fifth, major third, and minor third.

At the same time, I'd want to emphasize that the musical usage and
context are often quite different: the musical expectation that such a
sonority invites resolution to something more blending in a medieval
setting, but itself defines the essence of full and stable concord in
a 17th-19th century setting. This can effect things like intonation
and, especially on a keyboard, temperament: Pythagorean just
intonation is apt for the medieval usage, but not for a 16th-19th
century style based on stable thirds and sixths (at least in usual
harmonic timbres).

Similarly, a dominant seventh chord as tuned in a usual 18th-century
style (say in meantone or an unequal well-temperament on keyboard) has
the same categories of intervals as a stable 4:5:6:7 tetrad -- an
outer minor seventh, and adjacent intervals in ascending order of
major third, minor third, and minor third. Yet these are quite
different in practice: the tendency of V7 to resolve to a tonic triad
is basic to tonal harmony, while in a tetradic style of that like Paul
Erlich, 4:5:6:7 defines the standard of full and stable concord.

This is a bit of an aside, but I wanted to explain some possible
contrasts in practice as well as theory between the uses in different
styles of sonorities with the same interval categories.

Post by Roger E. Blumberg

Post by Margo Schulter
1 2 3 | 1 2 3 | 1
C4 B3 C4 D4
F4 G3 A3
F3 E3 D3
(min6-8 + min3-5)

This one (above) is really fabulous Margo!
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig1.06v2.gif
Fertile indeed (this bit B3 C4 D4 and the progression of chords used to
express it) for ideas in constructing accompaniment using three voice
sonorities, a kind of voice leading or "melody chord" playing.

Again, this is a commonplace in 13th-century motets and the like, with
a quick cadential sixth in the highest voice "decorating" a
progression from fifth to octave between the outer voices.

Post by Roger E. Blumberg
This next example (below) might be more interesting than I
originally thought . .

Post by Margo Schulter
1 2 3 | 1 ...
C4 D4
F3 A3 G3
F3 G3
(Maj3-1 + min3-5)

can this principle be extended further or applied more generally in
a kind of "split time" fashion?. That is, (first, if I could I'll
convert the Unison sonorities into trines) splitting a time alotment
for a given trine between itself and a split-fifth on the same
degree? For example, continuing the above progression something like
1 2 3 | 1
C4 D4 E4
F3 A3 G3 B3 A3
F3 G3 A3
so we're moving from F to G to A (I'm using all trines there but we
can keep it to all Unison sonorities if you like just to establish
whether or not the idea is sound) but between each we're inserting a
split-fifth to add some interest and perhaps help drive the
progression along more smoothly as well. And we're still
alternating between stable and unstable sonorities throughout.

This is exactly the idea that I mean to present here, and thank you
for stating it so clearly with an example of your own which so nicely
shows how these progressions can be "chained" or sequenced, as happens
in written compositions.

Your term "split time" also suggests an aspect of this kind of
technique of alternation between stable and unstable sonorities. As
one treatise typically dated to the early 13th century explains, the
"odd-numbered" notes (main beats) should generally be more consonant
or less dissonant than the "even-numbered" notes (secondary beats).
Actually this holds more specifically in the common rhythmic patterns
(often called rhythmic modes) with two notes to a metrical unit or
foot, either long-short (Mode 1) or short-long (Mode 2).

Post by Roger E. Blumberg
These next two are insanely great!
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.06abV2.gif
These are my absolute favorites of this PartIIA. These are out of this
world.

Post by Margo Schulter
The situation of "stepping up" in the lower voice from F to G offers
C4 E4 D4 C4 E4 D4
C4 D4 F3 A3 G3
F3 G3 or F3 G3
(Maj7-5 + Maj3-1) (Maj7-5 + Maj3-1)

These again are a kind of "split time" the way I conceptualize
things (Unison or Trine to Major 7th on the same degree), the
unstable mediating sonorities are most definately driving the
progressions forward in these two examples. This time the Major 7th
intervals are providing the tension (instability) where in the
previous examples it was the 3rds in the split-fifths. I like the
second example best, and it has both M3rd and M7th intervals in it's
mediating sonority.

Yes, I love this kind of progression also! Again, we have the "split
time" theme as you have called it, or alternation between stability
and instability. What I'd want to emphasize is that recognizing
patterns like this can, in my view, much enhance the enjoyment of
13th-century polyphony.

A technical point about my usage. While the sonorities with major
sevenths in this example do indeed "mediate" in a general sense
between stable sonorities, I use the concept of a "mediating" sonority
more narrowly to mean one where an unstable interval is approached and
left in the same direction by one of the voices forming it, for
example:

F4 E4 D4
C4 A3 G3
F3 G3

Here the highest voice moves 8-M7-5 with respect to the lowest voice,
descending F4-E4-D4, while the middle voice moves 5-M3-1, descending
C4-A3-G3. The unstable intervals of the major seventh and major third
are thus approached and left in the same direction in these upper
voices, making them mediating intervals in my narrower definition.

Compare now the second progression above:

C4 E4 D4
F3 A3 G3
F3 G3

The unstable sonority F3-A3-E4 with its major third and seventh is the
same, but this time the upper voices approach these unstable intervals
by ascent but leave them by descent: F3-A3-G3 and C4-E4-D4. These are
what I term "opposing" intervals, because of these opposite directions
of motion.

This is a fine point, and logically the unstable intervals could be
said in either case to "mediate" between two stable sonorities; I just
wanted to explain my own usage.

Post by Roger E. Blumberg
Speaking of that second example, what would you say of this
progression? I'll start with two trines on F and G, insert your F A
E sonority between them and add a fourth sonority (G3 B3 G4) to
mediate back to an F trine, creating a pretty cycle I could repeat
F4 E4 G4 F4
C4 A3 D3 B3 C4
F3 G3 F3

This is indeed the kind of idea I'm getting at, and if I were doing
this I might tend generally to let the highest voice also take part
with an opposing tone in that second progression, for example:

F4 E4 G4 E4 F4
C4 A3 D3 B3 C4
F3 G3 F3

With this kind of cycle you can repeat it with various touches of
ornamentation or the like.

Post by Roger E. Blumberg
the next one too is beautiful . .

Post by Margo Schulter
1 2 3 | 1 ...
D4 E4 F4
D4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)

we heard this earlier (In PartI) but now we can group it together with these
other mediating sonorities
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.07.gif

I might note a complication of my nomenclature: here the highest voice
has a mediating tone (D4-E4-F4) giving the mediating interval of major
sixth between fifth and octave (5-M6-8), while the middle voice has an
opposing tone (D4-B3-C4) giving the opposing interval of a major third
between two fifths (5-M3-5). There are many combinations or
permutations for these patterns, and your general usage of "mediating
sonority" certainly applies.

Post by Roger E. Blumberg
the next two are also gorgeous and again sonorities we've come across
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.08a-b.gif

Post by Margo Schulter
G4 E4 F4 G4 E4 F4
D4 C4 D3 B3 C4
G3 F3 or G3 F3
(Maj6-8 + Maj2-4) (Maj6-8 + Maj3-5)

What I'd want to emphasize, again, is how often these figures occur in
13th-century motets, for example. Recognizing how all three voices can
move together in directed progressions can help not only in analyzing
the music, but in intuitively "grasping" the musical language, so to
speak, getting a more fluent understanding of some of the common
phrases.

Post by Roger E. Blumberg
and another pretty one from earlier
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.09.gif

Post by Margo Schulter
1 2 3 | 1
G4 F4 E4 F4
D3 C4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)

It can be fun to look for all the ways that a composer like Adam de la
Halle varies this kind of progression with different ornaments or
voice crossings.

Post by Roger E. Blumberg
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.11.gif
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.11v2.gif

Post by Margo Schulter
1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 ||
F4 E4 D4 F4 E4 E4 F4 G4 F4 E4 F4
C4 A3 G3 B(b)3 A3 E4 D4 C4 B3 C4
F3 G3 A3 A3 G3 F3

Well, this opens with my favorite chord of the day (that second
sonority), and then it gets better. That whole initial string is
very nice (so is the ending but we're already familiar with it, the
begining part here is the new stuff). The string of first 5 chords
taken as a phrase, then chords 6 7 and 8 taken as a phrase, then the
all 8 initial chords taken together are great (and new to us).
The fourth chord, with the Bb was definitely the most surprising to hear,
and pleasantly so, very nice.

Jacobus of Liege describes this kind of sonority as an outer minor
seventh "split" into fifth and minor third -- here with the minor
third below the fifth. In the 14th century, I'd say that Guillaume de
Machaut has a certain leaning for it.

Post by Roger E. Blumberg
In the phrase of chords 6, 7, and 8, the sonority A3 E4 F4 was also
surprising. It's more dissonant than I would have expected to hear,
but I like it a lot. I keep thinking of how moody and jazzy much of
this sounds, perhaps "Gothic" is the correct and appropriate word
for the mood of it.

You've hit on one important point: a contrast between stable concords
and tensely unstable intervals is one characteristic of 13th-century
technique not always positively appreciated by some 19th-20th century
critics, who complain of "inexplicable discords" and the like. You can
read complaints about the "toleration of cacophony" in this music,
which might translate, "very different textures than those we learned
in our 18th-19th century harmony textbooks."

To give another example with A3-E4-F4, where the outer minor sixth as
well as the upper minor second is quite discordant by 13th-century
standards, by the way:

1 2 3 | 1
E4 F4 G4
D4 E4 D4
A3 G3

Here the opening A3-D4-E4, a fifth divided into lower fourth and upper
major second, is unstable but relatively concordant -- the effect is
somewhat like that of a stable fifth or trine, but with the tension of
the major second adding energy and moving things forward. Then the
tension mounts with that A3-E4-F4, beautifully resolving to the trine
G3-D4-G4, with minor sixth expanding to octave and minor second to
fourth.

I suspect that the labels of "inexplicable discord" might apply in
part to figures like this. One might ask: "Is this really more
discordant or acoustically complex than Wagner?" Rather, I'd suggest,
it's an example of musical patterns, very beautiful, which differ from
those of the 19th century.

By the way, while the above version might be easier to play on a
one-manual keyboard or fretted instrument, the original part-writing
is like this:

1 2 3 | 1
D4 E4 F4 G4
E4 F4 E4 D4
A3 G3

Post by Roger E. Blumberg
It suits me fine in any event, I love it. I almost said "dark" but
it's really not. Even it's somewhat dark tones (painterly tones and
hues) are gentle, pure, honest, and quickly enough "run home" to
consonance, so it isn't a darkness that's wallowed in for long,
certainly not nurtured. It's a sophisticated way of doing it.

Different people might have different impressions of these hues, but
I'd strongly agree that getting to know the hues or patterns of a
given style is very important. There is a "painterly" element of
contrast or alternation -- I like that adjective!

Post by Roger E. Blumberg
Even the consonances aren't too pretty nor overly sweet because the
final has no Major third to it (no "happy face" Major triad). It's
just a point of "strength", rest and power, neutral, calm repose,
contrasted with the mild darkness and mild sweetness (of a split
fifth lets say). "Subtle and sophisticated, "understated and pure",
that's probably the closest I can come to describing my impressions
of these examples so far.

As I said above, on some of these observations different people can
have different impressions: I find a complete trine or fifth very
sweet in this context, but can understand how people accustomed to
ending on a major triad might find this a bit different. Similarly, I
might guess that in the context of some contemporary jazz styles where
a seventh or ninth chord might be the usual stable concord, a triad
might sound rather "simple" if not "incomplete." The alternation
between repose and tension or active motion is something we both feel
in this music, and my examples are designed to bring out this theme.

Post by Roger E. Blumberg
[P.S. To my recollection we've yet to use a G B F (no flat on the B)
and at some point I hope we can work in some of that in too.]

For now, why don't I make just a quick point about this: a sonority
like G3-B3-F4 might resolve with the unstable major third and minor
seventh progressing by stepwise contrary motion, and the upper
diminished fifth acting much like a stable fifth in terms of the way
it progresses (although it's unstable, of course). Let's compare these
progressions:

F4 E4 F4 E4
B3 A3 Bb3 A3
G3 A3 G3 A3

(min7-5 + Maj3-1) (min7-5 + min3-1)

Note that in both progressions the lower two voices have a 3-1, the
outer voices a 7-5, and the upper voices move together in fifths --
diminished and perfect in the first version, and both perfect in the
second version.

We get more into the role of diminished fifths or tritones in further
posts -- this reply is already quite long -- but I wanted at least to
give a quick example for now.

Post by Roger E. Blumberg
alrighty, thanks Margo, that was good, I appreciate it. On to Part IIB in a
day or two (I hope).

Thank you for your helpful comments, and also for your patience in
waiting for my reply.

Post by Roger E. Blumberg
Roger

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Post by Margo Schulter

Post by Roger E. Blumberg
Hi Margo;
Ok, a few comments and questions on Part IIA. . .

Hi, Roger, and my apologies for the delay in answering this: last week
I was involved with a music project, and I much appreciate your
patience as well this helpful response with some excellent
observations and questions, a real treat.

Hi Margo;

no problem, I hope it went well, and I'm happy to participate (learn).

Post by Margo Schulter

Post by Roger E. Blumberg
in two of the early figures . . .
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig1.02n05v2.gif
. . . we see both species of "split fifth" (analogous to Major and
minor triads) each used to "mediate" between two "trines", resulting
an a pattern of stable-unstable-stable, the split-fifths are the
"mediating instability". Both examples are very pretty by the way,
and if I understand correctly they were a staple bit of musical
vocabulary, meat and potatoes almost -- hence a good "resource for a
deliberate strategy of accompaniment".

To take your last sentence first, I'd much agree, both on the beauty
of these progressions, and their use as a "staple bit of musical
vocabulary" -- this is the kind of thing we see and hear all the time
in 13th-century conductus and motets, etc. While it's often debated
just what a style of instrumental accompaniment might have been like,
and whether and how often such improvised accompaniments might have
taken on a style like that of composed three-voice polyphony, I'd say
at least that they're a "resource for a deliberate strategy of
accompaniment" if one accepts such compositions as a valid model.

alrighty, I'm glad to be more clear on that now. It'll still take a little
more "re-programing" I suspect, made firm by putting it into practice, to
counter-act the long ingrained misconceptions surrounding those sonorities
in relation to medieval music, but I think I'm getting it burned in now.

[And my saying "analogous to Major and minor triads" was more for the
benefit of a reader who might be jumping in cold, that they'd at least know
which sonorities were being referred to ]

Post by Margo Schulter
Now for the more delicate question: whether and how the 13th-century
"split fifth" with major third placed below minor (e.g. F3-A3-C4), or
the converse (e.g. A3-C4-E4), might be taken as "analogous to major
and minor triads."
Obviously there's some analogy, because the interval categories in a
medieval split fifth (_quinta fissa_ in Latin) or a 17th-19th century
triad are the same -- fifth, major third, and minor third.
At the same time, I'd want to emphasize that the musical usage and
context are often quite different: the musical expectation that such a
sonority invites resolution to something more blending in a medieval
setting, but itself defines the essence of full and stable concord in
a 17th-19th century setting. This can effect things like intonation
and, especially on a keyboard, temperament: Pythagorean just
intonation is apt for the medieval usage, but not for a 16th-19th
century style based on stable thirds and sixths (at least in usual
harmonic timbres).
Similarly, a dominant seventh chord as tuned in a usual 18th-century
style (say in meantone or an unequal well-temperament on keyboard) has
the same categories of intervals as a stable 4:5:6:7 tetrad -- an
outer minor seventh, and adjacent intervals in ascending order of
major third, minor third, and minor third. Yet these are quite
different in practice: the tendency of V7 to resolve to a tonic triad
is basic to tonal harmony, while in a tetradic style of that like Paul
Erlich, 4:5:6:7 defines the standard of full and stable concord.
This is a bit of an aside, but I wanted to explain some possible
contrasts in practice as well as theory between the uses in different
styles of sonorities with the same interval categories.

Post by Roger E. Blumberg

Post by Margo Schulter
1 2 3 | 1 2 3 | 1
C4 B3 C4 D4
F4 G3 A3
F3 E3 D3
(min6-8 + min3-5)

This one (above) is really fabulous Margo!
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig1.06v2.gif
Fertile indeed (this bit B3 C4 D4 and the progression of chords used to
express it) for ideas in constructing accompaniment using three voice
sonorities, a kind of voice leading or "melody chord" playing.

Again, this is a commonplace in 13th-century motets and the like, with
a quick cadential sixth in the highest voice "decorating" a
progression from fifth to octave between the outer voices.

ornaments and decorations, inter-mediating unstable sonorities -- the
growing pallet.

Post by Margo Schulter

Post by Roger E. Blumberg
This next example (below) might be more interesting than I
originally thought . .

Post by Margo Schulter
1 2 3 | 1 ...
C4 D4
F3 A3 G3
F3 G3
(Maj3-1 + min3-5)

can this principle be extended further or applied more generally in
a kind of "split time" fashion?. That is, (first, if I could I'll
convert the Unison sonorities into trines) splitting a time alotment
for a given trine between itself and a split-fifth on the same
degree? For example, continuing the above progression something like
1 2 3 | 1
C4 D4 E4
F3 A3 G3 B3 A3
F3 G3 A3
so we're moving from F to G to A (I'm using all trines there but we
can keep it to all Unison sonorities if you like just to establish
whether or not the idea is sound) but between each we're inserting a
split-fifth to add some interest and perhaps help drive the
progression along more smoothly as well. And we're still
alternating between stable and unstable sonorities throughout.

This is exactly the idea that I mean to present here, and thank you
for stating it so clearly with an example of your own which so nicely
shows how these progressions can be "chained" or sequenced, as happens
in written compositions.

oh, good. That helps alot. Much accompaniment really is about taking a
skeletal motif and filling time in and around it in interesting and tasteful
ways, with variety, ornament and decoration, etc. So anything that adds to
that basic vocabulary of techniques, the ways and means of doing it, adds
up. And again, this is one of those "universal logics" or approaches, it
seems to me, as is the split-time concept generally, i.e. the little tricks
one uses over and over to create the musical interest woven in and around a
basic framework.

Post by Margo Schulter
Your term "split time" also suggests an aspect of this kind of
technique of alternation between stable and unstable sonorities. As
one treatise typically dated to the early 13th century explains, the
"odd-numbered" notes (main beats) should generally be more consonant
or less dissonant than the "even-numbered" notes (secondary beats).
Actually this holds more specifically in the common rhythmic patterns
(often called rhythmic modes) with two notes to a metrical unit or
foot, either long-short (Mode 1) or short-long (Mode 2).

Post by Roger E. Blumberg
These next two are insanely great!
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.06abV2.gif
These are my absolute favorites of this PartIIA. These are out of this
world.

Post by Margo Schulter
The situation of "stepping up" in the lower voice from F to G offers
C4 E4 D4 C4 E4 D4
C4 D4 F3 A3 G3
F3 G3 or F3 G3
(Maj7-5 + Maj3-1) (Maj7-5 + Maj3-1)

These again are a kind of "split time" the way I conceptualize
things (Unison or Trine to Major 7th on the same degree), the
unstable mediating sonorities are most definately driving the
progressions forward in these two examples. This time the Major 7th
intervals are providing the tension (instability) where in the
previous examples it was the 3rds in the split-fifths. I like the
second example best, and it has both M3rd and M7th intervals in it's
mediating sonority.

Yes, I love this kind of progression also! Again, we have the "split
time" theme as you have called it, or alternation between stability
and instability. What I'd want to emphasize is that recognizing
patterns like this can, in my view, much enhance the enjoyment of
13th-century polyphony.

yep, they really are beautiful. And it seems to be coming true and apparent
that these alternations between stable and unstable, or maybe
repose-energetic-repose (because they certainly energize me when I hear them
;') really is key. i.e. they are a "definer" of this music and actually
provide and embody the enjoyment, that's where the pleasure lies. Remove
that, and you no longer have the music. So it's beyond enhancement, it's
really the _is_ of it.

Post by Margo Schulter
A technical point about my usage. While the sonorities with major
sevenths in this example do indeed "mediate" in a general sense
between stable sonorities, I use the concept of a "mediating" sonority
more narrowly to mean one where an unstable interval is approached and
left in the same direction by one of the voices forming it, for
F4 E4 D4
C4 A3 G3
F3 G3
Here the highest voice moves 8-M7-5 with respect to the lowest voice,
descending F4-E4-D4, while the middle voice moves 5-M3-1, descending
C4-A3-G3. The unstable intervals of the major seventh and major third
are thus approached and left in the same direction in these upper
voices, making them mediating intervals in my narrower definition.
C4 E4 D4
F3 A3 G3
F3 G3
The unstable sonority F3-A3-E4 with its major third and seventh is the
same, but this time the upper voices approach these unstable intervals
by ascent but leave them by descent: F3-A3-G3 and C4-E4-D4. These are
what I term "opposing" intervals, because of these opposite directions
of motion.
This is a fine point, and logically the unstable intervals could be
said in either case to "mediate" between two stable sonorities; I just
wanted to explain my own usage.

ok. So one can "inter-mediate" between intervals, stable-unstable-stable, by
using either mediating or opposing _directional_ motion. (how's that?)

Post by Margo Schulter

Post by Roger E. Blumberg
Speaking of that second example, what would you say of this
progression? I'll start with two trines on F and G, insert your F A
E sonority between them and add a fourth sonority (G3 B3 G4) to
mediate back to an F trine, creating a pretty cycle I could repeat
F4 E4 G4 F4
C4 A3 D3 B3 C4
F3 G3 F3

This is indeed the kind of idea I'm getting at, and if I were doing
this I might tend generally to let the highest voice also take part
F4 E4 G4 E4 F4
C4 A3 D3 B3 C4
F3 G3 F3

cool.

Post by Margo Schulter
With this kind of cycle you can repeat it with various touches of
ornamentation or the like.

more ornamentation, ornamentation is good ;')

Post by Margo Schulter

Post by Roger E. Blumberg
the next one too is beautiful . .

Post by Margo Schulter
1 2 3 | 1 ...
D4 E4 F4
D4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)

we heard this earlier (In PartI) but now we can group it together with these
other mediating sonorities
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.07.gif

I might note a complication of my nomenclature: here the highest voice
has a mediating tone (D4-E4-F4) giving the mediating interval of major
sixth between fifth and octave (5-M6-8), while the middle voice has an
opposing tone (D4-B3-C4) giving the opposing interval of a major third
between two fifths (5-M3-5). There are many combinations or
permutations for these patterns, and your general usage of "mediating
sonority" certainly applies.

"inter-mediating" sonorties (got it)

Post by Margo Schulter

Post by Roger E. Blumberg
the next two are also gorgeous and again sonorities we've come across
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.08a-b.gif

Post by Margo Schulter
G4 E4 F4 G4 E4 F4
D4 C4 D3 B3 C4
G3 F3 or G3 F3
(Maj6-8 + Maj2-4) (Maj6-8 + Maj3-5)

What I'd want to emphasize, again, is how often these figures occur in
13th-century motets, for example. Recognizing how all three voices can
move together in directed progressions can help not only in analyzing
the music, but in intuitively "grasping" the musical language, so to
speak, getting a more fluent understanding of some of the common
phrases.

got it

Post by Margo Schulter

Post by Roger E. Blumberg
and another pretty one from earlier
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.09.gif

Post by Margo Schulter
1 2 3 | 1
G4 F4 E4 F4
D3 C4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)

It can be fun to look for all the ways that a composer like Adam de la
Halle varies this kind of progression with different ornaments or
voice crossings.

Post by Roger E. Blumberg
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.11.gif
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.11v2.gif

Post by Margo Schulter
1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 ||
F4 E4 D4 F4 E4 E4 F4 G4 F4 E4 F4
C4 A3 G3 B(b)3 A3 E4 D4 C4 B3 C4
F3 G3 A3 A3 G3 F3

Well, this opens with my favorite chord of the day (that second
sonority), and then it gets better. That whole initial string is
very nice (so is the ending but we're already familiar with it, the
begining part here is the new stuff). The string of first 5 chords
taken as a phrase, then chords 6 7 and 8 taken as a phrase, then the
all 8 initial chords taken together are great (and new to us).
The fourth chord, with the Bb was definitely the most surprising to hear,
and pleasantly so, very nice.

Jacobus of Liege describes this kind of sonority as an outer minor
seventh "split" into fifth and minor third -- here with the minor
third below the fifth. In the 14th century, I'd say that Guillaume de
Machaut has a certain leaning for it.

great, so it is common enough, definately in the mix

Post by Margo Schulter

Post by Roger E. Blumberg
In the phrase of chords 6, 7, and 8, the sonority A3 E4 F4 was also
surprising. It's more dissonant than I would have expected to hear,
but I like it a lot. I keep thinking of how moody and jazzy much of
this sounds, perhaps "Gothic" is the correct and appropriate word
for the mood of it.

You've hit on one important point: a contrast between stable concords
and tensely unstable intervals is one characteristic of 13th-century
technique not always positively appreciated by some 19th-20th century
critics, who complain of "inexplicable discords" and the like. You can
read complaints about the "toleration of cacophony" in this music,
which might translate, "very different textures than those we learned
in our 18th-19th century harmony textbooks."
To give another example with A3-E4-F4, where the outer minor sixth as
well as the upper minor second is quite discordant by 13th-century
1 2 3 | 1
E4 F4 G4
D4 E4 D4
A3 G3
Here the opening A3-D4-E4, a fifth divided into lower fourth and upper
major second, is unstable but relatively concordant -- the effect is
somewhat like that of a stable fifth or trine, but with the tension of
the major second adding energy and moving things forward. Then the
tension mounts with that A3-E4-F4, beautifully resolving to the trine
G3-D4-G4, with minor sixth expanding to octave and minor second to
fourth.
I suspect that the labels of "inexplicable discord" might apply in
part to figures like this. One might ask: "Is this really more
discordant or acoustically complex than Wagner?" Rather, I'd suggest,
it's an example of musical patterns, very beautiful, which differ from
those of the 19th century.

that variation is beautiful too, and complex, and even discordant, but
hardly "inexplicable" i.e. if one "gets it".
This kind of sound is what I'm coming to expect and the thing that I _like_
about it, this rich and sophisticated pallet, and accomplished in a "less is
more" fashion, a purity, where you can really _feel_ and hear and appreciate
and distinguish what's in the mix. I might use an analogy of a deceptively
"simple" inked or etched line drawing that captures an "essence", expresses
it more purely, than a full-out oil painting might. The analogy might extend
to a Renaissance master's figure drawing or a 19th century Japanese print,
purity of line, and the fewer lines the better. It's really the definition
of sophisticated classic design, in all things and ages. Again, we know what
humans were producing in all other art forms, their level of sophistication
and capacity, so we can extrapolate what they might have been striving for
in their music. i.e. if one is known to have appreciated "fine" art and
craftsmanship you know it applied to _all_ things. If you assume and expect
sophistication and you look for it, it's there. If you go in expecting and
presuming infantile or somehow adolescent and under-developed capacity,
taste, and practice, then that's probably what you'll see -- and we would
dis-honor them and ourselves if we did that.

Post by Margo Schulter
By the way, while the above version might be easier to play on a
one-manual keyboard or fretted instrument, the original part-writing
1 2 3 | 1
D4 E4 F4 G4
E4 F4 E4 D4
A3 G3

Post by Roger E. Blumberg
It suits me fine in any event, I love it. I almost said "dark" but
it's really not. Even it's somewhat dark tones (painterly tones and
hues) are gentle, pure, honest, and quickly enough "run home" to
consonance, so it isn't a darkness that's wallowed in for long,
certainly not nurtured. It's a sophisticated way of doing it.

Different people might have different impressions of these hues, but
I'd strongly agree that getting to know the hues or patterns of a
given style is very important. There is a "painterly" element of
contrast or alternation -- I like that adjective!

Post by Roger E. Blumberg
Even the consonances aren't too pretty nor overly sweet because the
final has no Major third to it (no "happy face" Major triad). It's
just a point of "strength", rest and power, neutral, calm repose,
contrasted with the mild darkness and mild sweetness (of a split
fifth lets say). "Subtle and sophisticated, "understated and pure",
that's probably the closest I can come to describing my impressions
of these examples so far.

As I said above, on some of these observations different people can
have different impressions: I find a complete trine or fifth very
sweet in this context, but can understand how people accustomed to
ending on a major triad might find this a bit different. Similarly, I
might guess that in the context of some contemporary jazz styles where
a seventh or ninth chord might be the usual stable concord, a triad
might sound rather "simple" if not "incomplete." The alternation
between repose and tension or active motion is something we both feel
in this music, and my examples are designed to bring out this theme.

and you've suceeded ;')

Post by Margo Schulter

Post by Roger E. Blumberg
[P.S. To my recollection we've yet to use a G B F (no flat on the B)
and at some point I hope we can work in some of that in too.]

For now, why don't I make just a quick point about this: a sonority
like G3-B3-F4 might resolve with the unstable major third and minor
seventh progressing by stepwise contrary motion, and the upper
diminished fifth acting much like a stable fifth in terms of the way
it progresses (although it's unstable, of course). Let's compare these
F4 E4 F4 E4
B3 A3 Bb3 A3
G3 A3 G3 A3
(min7-5 + Maj3-1) (min7-5 + min3-1)
Note that in both progressions the lower two voices have a 3-1, the
outer voices a 7-5, and the upper voices move together in fifths --
diminished and perfect in the first version, and both perfect in the
second version.

alrighty, and I can hear a lot of potential in that second progression -- a
"droney minor" (as it were).


before I go, I wonder if I could explore that "chaining" idea a little
further. Using that same F-G-A progression kernel (and I'll use trines and
uncross some voices),

here's the one I inquired about, which got an "ok"

1 2 3 | 1
F4 C4 G4 D4 A4
C4 A3 D4 B3 E4
F3 G3 A3




so how about these next two?


F4 G4 A4
C4 D4 E4
F3 A3 G3 B3 A3


and below, using 9th sonorities . .


G4 F4 A4 G4 A4
C4 D4 E4
F3 A3 G3 B3 A3


in other words, these are three possible solutions from which I might
mix-n-match pieces of to add variety and spice to my "fill" accompaniment in
and around a basic F-G-A progression.


here's two more that are just excursions I'm curious about and I don't know
where else to insert them.
The first progression might be in the midst of something else or even a
concluding three chord phrase (slow and deliberate).
The second progression is just combining some ideas suggested by earlier
progressions. The center voice is carrying the melody for the most part,
effecting a kind of voice-led melody-chording similar to what we heard
earlier and even intentionally moving to Unison (which I've previously
avoided due to fingering issues), and also including some "rich" sonorities
(e.g. FCD to FCE) of the kind I'm beginning to sense might be "period
appreciated". The first chord, call it a "suspended quinta fissa" which I
already know was "appreciated" (not to mention all of the other rich
progressions you've shown us), pretty much sets the tone and stage for those
later rich sonorities, they seem to fit the definition of appropriate (or at
least plausible) taste by now (to me)



D4 F4 A4
C4 D4 E4
F3 A3




E4 D4 E4 G4 F4 ...
D4 C4 A3 C4 D4 B3 C4
A3 F3 G3 F3 A3


and I know that in the seventh (from the beginning) sonority above (GBG) you
might like to see an additional voice move, but I like it this way, call it
a "signature sonority" as long as it passes muster generally I'd prefer to
use it, it has a bell-like clearity that I like and keep returning to, I
resonate to it I guess.

Thanks Margo

Roger

Post by Margo Schulter
We get more into the role of diminished fifths or tritones in further
posts -- this reply is already quite long -- but I wanted at least to
give a quick example for now.

Post by Roger E. Blumberg
alrighty, thanks Margo, that was good, I appreciate it. On to Part IIB in a
day or two (I hope).

Thank you for your helpful comments, and also for your patience in
waiting for my reply.

Post by Roger E. Blumberg
Roger

Most appreciatively,
Margo Schulter

[Stephen Fryer]

To Margo, Roger, et alii, greetings!

I have found this discussion very interesting and enlightening, although I am
having to catch up to it because I lost my news server for a while,
immediately after Margo started this thread. (By the way, it would be much
easier to catch up and to read your comments if you could trim the quoted
parts of yur messages to just what you are immediately commenting on - over
600 lines, of which maybe 10% really needed to be there slows things down,
including understanding what you are saying.)

Being interested in 13th c. music, I was trying to find something about the
implications of counterpoint with 3rds treated as unstable intervals - and
this discussion has given me considerable insight. It also presents me with a
new and most pleasurable way of listening to 13th c. motets (In mari miserie -
Gemma pudicicie - MANERE seems a particularly apt example).

I do have a few questions (of course - see tag line below).

Margo: I was a little confused at first by your ocatve designations, being
used to counting from A to a, etc. For instance, in your example
1 2 3 | 1 2 3 | 1
C4 B3 C4 D4
F4 G3 A3
F3 E3 D3
the sequence C4-B3-C4 looked two consecutive skips of a ninth, which would
have been rather odd. I did eventually realize that you were counting C to c,
etc. Perhaps you could tell me why you prefer this?

Roger: You explained your preference for a tuning in all fourths across four
strings (4-4-4), such as the lower four strings of a guitar (in standard
E-A-D-G tuning), which seemed reasonable. However, you also commented that a
lute would give 4-3-4, which puzzled me somewhat, since the lower four courses
of a lute in "standard" (vieil acord) tuning would give 4-4-3 and the upper
four 3-4-4 (by the way I have been playing the examples in this tuning and
they mostly result in quite reasonable fingerings). I presume I must have
misunderstood something in what you said. Perhaps you could help clear up
this confusion (on a rather unimportant and peripheral point)?

On the idea of stable-unstable-stable sequences, it has been said that this is
the driving force of all music, and that the history of polyphonic music has
been the defining of ever more unstable combinations as stable and the search
for more unstable combinations to keep the music driving forward.

Here is the opening of a motet (O Maria virgo-O Maria maris-IN VERITATE) from
the La Clayette manuscript (I posted a notation [Noteworthy Composer]file at
http://home.prcn.org/~sfryer/temp/MOTET.nwc ):

1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |
F4-E4-D4-C4-D4-E4-G4-A5-F4-G4----r--E4-C4-D4-E4-D4-E4-F4-E4-D4-C4----r-
C4----D4-F4----E4-D4----C4-C4----B4-A4----G3-A4----B4-C4-------r-------
F3-------F3-------G3-------r--------A4-------A4-------F3-------r-------

You can hear it as played on guitar or lute at
http://home.prcn.org/~sfryer/temp/MOTET%20V2.mid

There are some features here which haven't been discussed, such as the tenor
part being broken into repeated rhythmic figures (in this case separated by
rests). The differing phrase lengths of the triplum and motetus help keep the
music going throuhg cadences (as at measure 4).

While the vertical aspect of the music is important, it is dependent on the
horizontal melodies which comprise it, unlike what we are used to hearing in
more recent music. Listening to a double motet is truly wonderful because it
requires attention to both vertical and horizontal aspects of the music to
fully appreciate.

You have mentioned the idea of using these vertical sonorities to build
accompaniments. One strategy which was probably used at the time, and
certainly a little later was to use the accompanying instrument to carry
whichever voices were not being sung. To give an idea of what this might
sound like I posted a version of the motet with the triplum played by recorder
accompanied by lute at http://home.prcn.org/~sfryer/temp/MOTET%20V1.mid .

Here is the final phrase of a tune of which the words would imply that it was
written in 1193. All seems reasonably conventional until the suspension at
the beginning of the last bar forces the final cadential resolution to be
delayed until the weak second beat. Are there other songs which do this? Up
until this point, devising a suitable accompaniment embodying the ideas you
have been discussing works quite easily. I haven't come up with a solution
for the last two bars that I really like yet - perhaps you would like to see
what you can do with it.

1--+--2--+--3--+--|1--+--2--+--3---+---|1--+--2--+--3--+--||
F4----G4----F4-E4--D4----------E4-D4-C4-C4----D4----------

Again, thank you both for this fascinating discussion!

[Roger E. Blumberg]

Hi Stephen;

I'm glad to hear someone else out there is interested and playing along as
well ;')

About the tuning; As I understand it, 4 course 434 is early "lute kernel"
tuning to which additional courses, both high and low, were added over time.
If one begins with 344 kernel and just adds lower courses that could make
enough sense too. Ultimately, this family of tunings encompasses early
Vihuela/Guitar as well (so if you start with 344 you'd be both adding lower
courses and eliminating one higher course eventually). It's all the same
animal as far as I'm concerned though, and there probably were any number of
possible variations used, nevertheless I'd be happy to be corrected
regarding the 434 kernel if I'm wrong. The whole topic _is_ rather central
to me (actually). I believe there is documentation of a mid-1500's Vihuelist
saying that Guitarra Latina tuning (for example) was the same as the 4
center courses of 6 course lute/vihuela (i.e. 434)

[Roman, (or anyone else) what's your take on early 4 course lute tuning?]

Thanks for the midi files Stephen. I'm a student here, so I'll leave it
Margo and others to comment on the pieces and techniques you mention. There
was some mention of accompanying a melody by "fifthing" (adds two more
voices to the mix) thereby giving you a total of three voices, parts, or
lines.

As you say, the horizontal rhythms and phrasing of lines was no doubt a
large factor within this (or any) music. I'm thinking that perhaps the
vertical sonority components present, their existence and cataloguing, have
gotten less attention generally, and my particular hope was in trying to get
a handle on them -- a rare opportunity for me. The potential of designing
period plausible three voice accompaniment (rather that just two) and on a
single instrument, e.g. fretted strings or harp, is the challenge I find
most interesting. To me, one or more singers or recorders could still add
any necessary melodic (horizontal) phrasing on top of and in addition to the
rhythms, phrasing, and sonorities contributed by an accompanist, so those
necessary melodic considerations would not be lost in the end. I'm also
attracted to the idea of using a single instrument as a composition tool,
composing songs, and for that I (at least) find three voice sonorities get
my juices flowing better, even to help design some intricately phrased
melody to be sung (or played on recorder) on top of the accompaniment
foundation. I find a richer foundation more musically inspiring (both
melodically and rhythmically), so blocking out actual or peroid plausable
three voice vertical sonorities (phrasing and melodic components assumed)
has been a real treat for me. If we were to now split the voices off between
multiple instruments or singers, or sit down and try to compose some
multi-part piece, I'd at least have some clue regarding the possible colors,
textures, progressions, an ensemble might collectively affect. None of this
contrary to any of your points and examples by the way, I guess I'm just
commenting on my own chord-appreciation leanings with respect to the overall
appreciation of medieval-period musical taste and practice. That's the part
of this that lit my fire in the first place.

So, do you imagine there was polyphony in ancient Egypt too? ;') [I Googled
you last night]

Thanks
Roger

Post by Stephen Fryer
To Margo, Roger, et alii, greetings!
I have found this discussion very interesting and enlightening, although I am
having to catch up to it because I lost my news server for a while,
immediately after Margo started this thread. (By the way, it would be much
easier to catch up and to read your comments if you could trim the quoted
parts of yur messages to just what you are immediately commenting on - over
600 lines, of which maybe 10% really needed to be there slows things down,
including understanding what you are saying.)
Being interested in 13th c. music, I was trying to find something about the
implications of counterpoint with 3rds treated as unstable intervals - and
this discussion has given me considerable insight. It also presents me with a
new and most pleasurable way of listening to 13th c. motets (In mari miserie -
Gemma pudicicie - MANERE seems a particularly apt example).
I do have a few questions (of course - see tag line below).
Margo: I was a little confused at first by your ocatve designations, being
used to counting from A to a, etc. For instance, in your example
1 2 3 | 1 2 3 | 1
C4 B3 C4 D4
F4 G3 A3
F3 E3 D3
the sequence C4-B3-C4 looked two consecutive skips of a ninth, which would
have been rather odd. I did eventually realize that you were counting C to c,
etc. Perhaps you could tell me why you prefer this?
Roger: You explained your preference for a tuning in all fourths across four
strings (4-4-4), such as the lower four strings of a guitar (in standard
E-A-D-G tuning), which seemed reasonable. However, you also commented that a
lute would give 4-3-4, which puzzled me somewhat, since the lower four courses
of a lute in "standard" (vieil acord) tuning would give 4-4-3 and the upper
four 3-4-4 (by the way I have been playing the examples in this tuning and
they mostly result in quite reasonable fingerings). I presume I must have
misunderstood something in what you said. Perhaps you could help clear up
this confusion (on a rather unimportant and peripheral point)?
On the idea of stable-unstable-stable sequences, it has been said that this is
the driving force of all music, and that the history of polyphonic music has
been the defining of ever more unstable combinations as stable and the search
for more unstable combinations to keep the music driving forward.
Here is the opening of a motet (O Maria virgo-O Maria maris-IN VERITATE) from
the La Clayette manuscript (I posted a notation [Noteworthy Composer]file at
1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |
F4-E4-D4-C4-D4-E4-G4-A5-F4-G4----r--E4-C4-D4-E4-D4-E4-F4-E4-D4-C4----r-
C4----D4-F4----E4-D4----C4-C4----B4-A4----G3-A4----B4-C4-------r-------
F3-------F3-------G3-------r--------A4-------A4-------F3-------r-------
You can hear it as played on guitar or lute at
http://home.prcn.org/~sfryer/temp/MOTET%20V2.mid
There are some features here which haven't been discussed, such as the tenor
part being broken into repeated rhythmic figures (in this case separated by
rests). The differing phrase lengths of the triplum and motetus help keep the
music going throuhg cadences (as at measure 4).
While the vertical aspect of the music is important, it is dependent on the
horizontal melodies which comprise it, unlike what we are used to hearing in
more recent music. Listening to a double motet is truly wonderful because it
requires attention to both vertical and horizontal aspects of the music to
fully appreciate.
You have mentioned the idea of using these vertical sonorities to build
accompaniments. One strategy which was probably used at the time, and
certainly a little later was to use the accompanying instrument to carry
whichever voices were not being sung. To give an idea of what this might
sound like I posted a version of the motet with the triplum played by recorder
accompanied by lute at http://home.prcn.org/~sfryer/temp/MOTET%20V1.mid .
Here is the final phrase of a tune of which the words would imply that it was
written in 1193. All seems reasonably conventional until the suspension at
the beginning of the last bar forces the final cadential resolution to be
delayed until the weak second beat. Are there other songs which do this?

Up

Post by Stephen Fryer
until this point, devising a suitable accompaniment embodying the ideas you
have been discussing works quite easily. I haven't come up with a solution
for the last two bars that I really like yet - perhaps you would like to see
what you can do with it.
1--+--2--+--3--+--|1--+--2--+--3---+---|1--+--2--+--3--+--||
F4----G4----F4-E4--D4----------E4-D4-C4-C4----D4----------
Again, thank you both for this fascinating discussion!
--
Stephen Fryer
Lund Computer Services
**************************************************
The more answers I find, the more questions I have
**************************************************

[Stephen Fryer]

Hi Roger

Post by Roger E. Blumberg
About the tuning; As I understand it, 4 course 434 is early "lute kernel"
tuning to which additional courses, both high and low, were added over
time. If one begins with 344 kernel and just adds lower courses that could
make enough sense too. Ultimately, this family of tunings encompasses early
Vihuela/Guitar as well (so if you start with 344 you'd be both adding
lower courses and eliminating one higher course eventually). It's all the
same animal as far as I'm concerned though, and there probably were any
number of possible variations used, nevertheless I'd be happy to be
corrected regarding the 434 kernel if I'm wrong. The whole topic _is_
rather central to me (actually). I believe there is documentation of a
mid-1500's Vihuelist saying that Guitarra Latina tuning (for example) was
the same as the 4 center courses of 6 course lute/vihuela (i.e. 434)

It was Fray Juan Bermudo who wrote that, around 1540 (I've seen various dates
ascribed to this). The lute already had six courses by the beginning of the
16th century, tuned in the standard 44344, and as far as I know there isn't
any information about the tuning of lutes before that. It is interesting
though that strings were added to the bottom of the guitar's range to bring it
up to its current six strings. Amat, at the end of the 16th c. gives tuning
instructions for the 5-course guitar which give the intervals 4434 (like the
upper 5 strings of a guitar). He also gives slightly ambiguous instructions
for the 4-course guitar, which appears to be tuned 434. And that is all the
information I am aware of that might bear on the subject - beyond that is only
speculation.

Post by Roger E. Blumberg
Thanks for the midi files Stephen. I'm a student here, so I'll leave it
Margo and others to comment on the pieces and techniques you mention.

You had mentioned that MIDI would be nice for hearing examples, so I thought
that since there weren't very many I'd provide them. As for the rest, well
I'm sure you are quite able to look at things and draw conclusions, or to
experiment with things and see what sounds "right."

Of course "right" is rather dependent on the situation. I was reviewing some
music history, and they mentioned the "standard cadence" for 13th c. motets,
etc., so I compared it to their "standard cadence" for later music, after 3rds
were taken as stable intervals. And you know it was really obvious WHY they
worked the way they did, but if I hadn't put them side by side I probably
wouldn't have got it. Here they are:
E4 - F4 E4 - F4
B4 - C4 B4 - A4
G3 - F3 G3 - F3
13th c. 16th c.
In the first we have no third in the final chord because it is unstable; in
the second we do have a third because, not only is it a stable interval, but
also we need it to define the mode (major/minor). Of course as often as not
they insisted on it being a major third even in a minor key, just to mess
things up.

Post by Roger E. Blumberg
There was some mention of accompanying a melody by "fifthing" (adds two
more voices to the mix) thereby giving you a total of three voices, parts,
or lines.

One of the 13th c. theorists (I forget who; Margo probably knows) talks about
accompaniments using fourths and fifths, but it is rather unclear exactly how
this was done. One idea is to play a suitable open fifth to make a consonance
with the first melody note of each "bar" - sort of like a pair of drones a
fifth apart, except that the pitch of the drones changes to suit the melody
line. The melody notes in between these can form any consonance or dissonance
with the accompaniment since they are on weaker beats. And shazzam! there are
our alternations of stability and instability that drives us forward (someone,
I forget who, claimed that musical composition was the art of avoiding a final
cadence as long as possible).

Post by Roger E. Blumberg
None of this contrary to any of your points and examples by the
way, I guess I'm just commenting on my own chord-appreciation leanings with
respect to the overall appreciation of medieval-period musical taste and
practice. That's the part of this that lit my fire in the first place.

If we only look at music from one angle, I think we lose a lot. I'd been so
busy trying to train my ear to follow the separate voices in double motets,
that I was missing the the "breathing" effect created by the vertical
combinations. This discussion has helped with that part of it a lot.

Post by Roger E. Blumberg
So, do you imagine there was polyphony in ancient Egypt too? ;') [I Googled
you last night]

Well, for the Google-y eyed among you: I strongly doubt it, at least in the
sense of interweaving melodies. Of course, in spite of speculations I have
seen, we really have no evidence other than pictures for their music, though
it quite obviously changed over time. In the Old Kingdom before 2000BC we
typically see a bunch of people clapping and/or dancing while one person is
singing or playing a wind instrument, sometimes both the singer and the wind
player. In the New Kingdom (after 1500 BC) we get trios singing and playing,
with typically a lute-family instrument and a wind instrument together.
Unfortunately that is about all we can say.

Best regards

[Margo Schulter]

Post by Stephen Fryer
Of course "right" is rather dependent on the situation. I was reviewing some
music history, and they mentioned the "standard cadence" for 13th c. motets,
etc., so I compared it to their "standard cadence" for later music, after 3rds
were taken as stable intervals. And you know it was really obvious WHY they
worked the way they did, but if I hadn't put them side by side I probably
E4 - F4 E4 - F4
B4 - C4 B4 - A4
G3 - F3 G3 - F3
13th c. 16th c.
In the first we have no third in the final chord because it is unstable; in
the second we do have a third because, not only is it a stable interval, but
also we need it to define the mode (major/minor). Of course as often as not
they insisted on it being a major third even in a minor key, just to mess
things up.

Hello, there, and maybe I could comment a bit on the 16th-century usage.
As you recognize, consistently having a third above the bass in a closing
sonority be major -- with accidental inflections if required -- is hardly
apt if one's goal is to distinguish closes for modes naturally with a
major third above the final (Mixolydian, Ionian, Lydian) from those with a
minor third (Dorian, Aeolian, Phrygian). Rather, while Zarlino for example
recognizes this distinction between two families of modes, as we might
say, based on the natural quality of the third above the final, the idea
of altering minor thirds to major in closing sonorities is to obtain a
more smooth and conclusive harmony.

Around 1500, interestingly, when the practice of closing sonorities
including thirds is coming into vogue, unaltered minor thirds seem to have
been acceptable, for example in Josquin's _Mille Regretz_ in E Phrygian.
One indication that an unaltered G above the final E was acceptable is
that Schlick's irregular temperament for organ in 1511 has an Ab adjusted
so that it could also serve as a tolerable G# for ornamented cadences to
A, but an unlikely note to use in a stable and conclusive sonority calling
for the major third E-G#.

By the 1520's, however, Pietro Aaron is reporting a preference for major
thirds or tenths above the bass at certain locations, and his treatise on
the modes of 1525 shows such alterations in closes on D and E.

Anyway, Vicentino in 1555 finds closing on a major third above the bass
much preferable to the minor third, and in 1558, Zarlino offers a
mathematical explanation for this preference. The division of the 3:2
fifth with the major third below and minor above is a harmonic division
with a string ratio of 15:12:10 -- a 5:4 major third below a 6:5 minor
third -- with the ratio of differences between adjacent terms (15-12,
12-10) at 3:2, the same as the ratio of the fifth being divided. In
contrast, the string ratio for the arrangement with the minor third below
the major is 6:5:4, an arithmetic division with equal differences between
terms, which Zarlino generally finds less harmonious.

He offers another explanation based on the _senario_, the series of
natural numbers from one to six (1-2-3-4-5-6) from which the consonances
of 16th-century music are derived in their pure or just ratios (actually
the minor sixth or 8:5 requires adding the term 8).

Zarlino suggests as guide to the ideal arrangement and spacing of voices
and intervals that ratios should if possible have the same order and
placement as in the scenario. Thus a 4:5 major third comes before a 5:6
minor third in this natural series, and therefore the major third is most
harmoniously placed below the minor, rather than the converse. Also, in
the natural series, the octave (1:2) and even double octave (1:4) precede
the major third (4:5), so ideally one prefers the tenth to the simple
third, and indeed where possible might favor the major seventeenth (1:5).

The ideal for both Vicentino and Zarlino is "richness of harmony" or
"perfect harmony" as measured by 16th-century tastes: a sonority including
a third and fifth above the bass, or sometimes in place of the fifth, the
sixth. Part of this ideal, especially at a close, is that the voices
should be arranged as sonorously as possible: thus the placement of the
major third below the minor, with accidental inflections if necessary to
achieve this arrangement.

By the way, there's a lot of discussion by Zarlino and other 16th-century
theorists about how to define the mode of a piece: tradition, for example,
often focuses mainly on the mode of the tenor voice, but Vicentino
suggests looking to the bass, and often the closing note in that voice is
taken as one guide. In some styles (e.g. Spanish organ settings by a
composer such as Antonio Cabezon), there are some standard "procedures"
for different modes or Psalm tones, for example the placement of the
cadences on characteristic steps.

Also, Phrygian is often distinctive because its final cadences involve
descending semitones, as in these formulae, which I'll give both in MIDI
C-c MIDI notation and A-a notation:

MIDI notation (C4 as middle C, C-c octaves)

A4 G#4 A4 G#4
D4 E4 E4 E4
A3 B3 C4 B3
F3 E3 A2 E3

A-a notation (C2 as middle C, A-a octaves)

A3 G#2 A3 G#2
D2 E2 E2 E2
A2 B2 C2 B2
F1 E1 A1 E1

More specifically, in the first formula, we have a major third expanding
to a fifth between the two lower voices, and a a major sixth to an octave
in the lowest and third lowest voices, with a descending semitone in the
lowest voice and ascending whole-tone steps in these upper voices. This is
a "remissive" cadence, or in Spanish _remissa_, as defined by Tomas de
Santa Maria (1565).

The second formula, while common in Phrygian, can apply to some other
modes also.

Anyway, 16th-century cadences are a bit of a digression, but I did want to
address the interesting point you raise. I'm not sure how clear my
response is, and would welcome more comments or discussion.

Most appreciatively,

Margo Schulter
***@calweb.com

[Stephen Fryer]

Post by Margo Schulter

Post by Stephen Fryer
In the first we have no third in the final chord because it is unstable; in
the second we do have a third because, not only is it a stable interval, but
also we need it to define the mode (major/minor). Of course as often as not
they insisted on it being a major third even in a minor key, just to mess
things up.

Hello, there, and maybe I could comment a bit on the 16th-century usage.
As you recognize, consistently having a third above the bass in a closing
sonority be major -- with accidental inflections if required -- is hardly
apt if one's goal is to distinguish closes for modes naturally with a
major third above the final (Mixolydian, Ionian, Lydian) from those with a
minor third (Dorian, Aeolian, Phrygian). Rather, while Zarlino for example
recognizes this distinction between two families of modes, as we might
say, based on the natural quality of the third above the final, the idea
of altering minor thirds to major in closing sonorities is to obtain a
more smooth and conclusive harmony.

Actually, that explanation did occur to me as most likely - after I sent the
message of course. It is nice to have some documentation from contemporary
theorists supporting it. I have an annoying habit of asking people awkward
questions like "how do you know?" and "Where's your documentation for that?" ;-)

[Roger E. Blumberg]

Post by Stephen Fryer
Hi Roger

Post by Roger E. Blumberg
I believe there is documentation of a
mid-1500's Vihuelist saying that Guitarra Latina tuning (for example) was
the same as the 4 center courses of 6 course lute/vihuela (i.e. 434)

It was Fray Juan Bermudo who wrote that, around 1540 (I've seen various dates
ascribed to this).

great, thanks

Post by Stephen Fryer
The lute already had six courses by the beginning of the
16th century, tuned in the standard 44344,

right, so it's the earlier 5 course tuning that's the question. Perhaps it
was straight 4ths across all 5, 4444, or even 4434, but 4344 seems less
likely to me, the "need" for a 3rd doesn't seem to arise so early in the
pattern.

Post by Stephen Fryer
and as far as I know there isn't
any information about the tuning of lutes before that. It is interesting
though that strings were added to the bottom of the guitar's range to bring it
up to its current six strings. Amat, at the end of the 16th c. gives tuning
instructions for the 5-course guitar which give the intervals 4434 (like the
upper 5 strings of a guitar). He also gives slightly ambiguous instructions
for the 4-course guitar, which appears to be tuned 434. And that is all the
information I am aware of that might bear on the subject - beyond that is only
speculation.

By the way, I tried your 344 tuning across 4 courses, and I'm having doubts
about it, that 4 fret stretch to play an Octave, 5th, or trine, on the lower
3 strings/courses is my biggest question mark. Of your two suggested
tunings, 443 would make more sense to me. As time goes by, all 4ths, 444, is
making the most sence (as it turns out).

Post by Stephen Fryer

Post by Roger E. Blumberg
Thanks for the midi files Stephen. I'm a student here, so I'll leave it
Margo and others to comment on the pieces and techniques you mention.

You had mentioned that MIDI would be nice for hearing examples, so I thought
that since there weren't very many I'd provide them.

right, I suspected you picked up on that, and I and everyone else appreciate
it and thank you for it. That said, I hope people remember that midi is just
another tool and that it's important to hear the peices in real voices and
instruments because midi is notoriously "cheesy" no matter what the music
is. And I know you won't take offence at that. I just want to make sure
folks get the most enjoyment and pleasure from the examples as possible. I'm
extremely greatful to be able to play (hear and appreciate) all of the
examples given so far on a real string instrument. If I had had only midi
examples to hear this whole time I don't think it would have had the nearly
same impact upon me. By the way, the recorder voiceing in midi _is_ nice.

Post by Stephen Fryer
As for the rest, well
I'm sure you are quite able to look at things and draw conclusions, or to
experiment with things and see what sounds "right."

ok, I'll chime in as I feel able

Post by Stephen Fryer
Of course "right" is rather dependent on the situation. I was reviewing some
music history, and they mentioned the "standard cadence" for 13th c. motets,
etc., so I compared it to their "standard cadence" for later music, after 3rds
were taken as stable intervals. And you know it was really obvious WHY they
worked the way they did, but if I hadn't put them side by side I probably
E4 - F4 E4 - F4
B4 - C4 B4 - A4
G3 - F3 G3 - F3
13th c. 16th c.
In the first we have no third in the final chord because it is unstable; in
the second we do have a third because, not only is it a stable interval, but
also we need it to define the mode (major/minor). Of course as often as not
they insisted on it being a major third even in a minor key, just to mess
things up.

that is interesting. I didn't realize an FAF (R3R) sonority was concidered
"standard" later (rather than full triad final). And I guess I'm still
wondering just how "unstable" our 3rds really have been (all along) and on
_which_ instruments. On Lutes (and then Viols), which have varriable
temperament (tied and movable frets), I still wonder if 3rds were ever such
a big issue, same with singers. What I'm saying is that while 3rds were a
recognized temperament trouble-spot, they were "solvable" on lutes (and
never a problem with singers), you just tweak your fret placements a little.
And if I'm not mistaken, minor thirds were never an issue at all, it was
just Major 3rds. Keyboards are the biggest issue, or perhaps ensembles of
fixed-hole recorders and other woodwinds. But, for example, with solo lute
accompaniing a voice (singer), the 3rds should never have been such a big
deal, ever, and as far back as we see fretted lute-like and guitarra-like
instruments, e.g. in the Cantigas, 1260 AD. This is to say, we could have
had, might have had, should have had, stable thirds as far back as 1260 and
earlier if we wanted them (300 years before the mid 1500s). So the "reasons"
and timing for the acceptance of Major 3rds as "stable" might have less to
do with there general availability, they had been "available" to us for a
very long time.

Post by Stephen Fryer

Post by Roger E. Blumberg
There was some mention of accompanying a melody by "fifthing" (adds two
more voices to the mix) thereby giving you a total of three voices, parts,
or lines.

One of the 13th c. theorists (I forget who; Margo probably knows) talks about
accompaniments using fourths and fifths, but it is rather unclear exactly how
this was done. One idea is to play a suitable open fifth to make a consonance
with the first melody note of each "bar" - sort of like a pair of drones a
fifth apart, except that the pitch of the drones changes to suit the melody
line. The melody notes in between these can form any consonance or dissonance
with the accompaniment since they are on weaker beats. And shazzam! there are
our alternations of stability and instability that drives us forward (someone,
I forget who, claimed that musical composition was the art of avoiding a final
cadence as long as possible).

Post by Roger E. Blumberg
None of this contrary to any of your points and examples by the
way, I guess I'm just commenting on my own chord-appreciation leanings with
respect to the overall appreciation of medieval-period musical taste and
practice. That's the part of this that lit my fire in the first place.

If we only look at music from one angle, I think we lose a lot. I'd been so
busy trying to train my ear to follow the separate voices in double motets,
that I was missing the the "breathing" effect created by the vertical
combinations. This discussion has helped with that part of it a lot.

that's an interesting way of putting it. I guess that's part of what I mean
regarding using a single instrument to help compose a song. The "breathing"
time lets you play around with possible melodies in your head while you're
playing (blocking out the sonorities). That's what I mean about 3 voice
sonorities played as a foundation getting the "melody composing" juices
going. You can "idle" (breath) on any chord or two chord progression and
test melody lines on top of it, also implicit in this is the idea of things
"writing themselves", where possible "next chords" are automatically
suggested, melody line resolutions in and among the sonorities are suggested
the minute you hear them. Experimentation, accident, and reproducibility,
and are also in the mix, the facilitating factors that such an instrument
provides.

Post by Stephen Fryer

Post by Roger E. Blumberg
So, do you imagine there was polyphony in ancient Egypt too? ;') [I Googled
you last night]

Well, for the Google-y eyed among you: I strongly doubt it, at least in the
sense of interweaving melodies. Of course, in spite of speculations I have
seen, we really have no evidence other than pictures for their music, though
it quite obviously changed over time. In the Old Kingdom before 2000BC we
typically see a bunch of people clapping and/or dancing while one person is
singing or playing a wind instrument, sometimes both the singer and the wind
player. In the New Kingdom (after 1500 BC) we get trios singing and playing,
with typically a lute-family instrument and a wind instrument together.
Unfortunately that is about all we can say.

I guess I depends on how we define polyphony. With two hands at the harp,
harmonic intervals are a certainty. Add just one singer or any other
instrument to that mix and we've already got polyphony (chords), by my
definition. I believe humans have been exploring chords for many thousands
of years. Even on solo harp, if we grant two tones at once, one in each
hand, the leap to 3 at once is not hard to make, we had plenty of fingers
still available, plenty of appreciation capacity left, and lots of reason to
try, to experiment, to pleasure ourselves. Documentation would be nice, but
I don't really think we need it. We just need to recognize human nature.
Once we got to the point of purposely setting out to construct multi-toned
music making machines, plus playing with arithmetic (string division ratios,
etc) experimenting with tunings, etc, the hunt for chords is already on.
That is to say, once you come to recognize 2 tones at once (harmonic
interval), the hunt is on, the stage is set, the conditions are in place,
the pleasure is known, the race is on. That's my take anyway. I really think
harmonic intervals (2 tones at once) is the definer, and immediately
thereafter you will go further, if you can, and on a harp you can. So as
early as humans had harps (not to mention multiple singers) the race has
been on, chords have been known experienced and enjoyed, I think.


Thanks
Roger

Post by Stephen Fryer
Best regards
--
Stephen Fryer
Lund Computer Services
**************************************************
The more answers I find, the more questions I have
**************************************************

[Stephen Fryer]

Post by Roger E. Blumberg
By the way, I tried your 344 tuning across 4 courses, and I'm having doubts
about it, that 4 fret stretch to play an Octave, 5th, or trine, on the lower
3 strings/courses is my biggest question mark. Of your two suggested
tunings, 443 would make more sense to me. As time goes by, all 4ths, 444, is
making the most sence (as it turns out).

I'm not sure I understand what you're saying here. Having the third in there
reduces a lot of the stretches - at least that's the way it looks to me.

Post by Roger E. Blumberg
That said, I hope people remember that midi is just
another tool and that it's important to hear the peices in real voices and
instruments because midi is notoriously "cheesy" no matter what the music
is. And I know you won't take offence at that. I just want to make sure
folks get the most enjoyment and pleasure from the examples as possible. I'm
extremely greatful to be able to play (hear and appreciate) all of the
examples given so far on a real string instrument. If I had had only midi
examples to hear this whole time I don't think it would have had the nearly
same impact upon me. By the way, the recorder voiceing in midi _is_ nice.

The guitar (nylon string) voicing is absolutely horrible. And there is
nothing usable for a singing voice either.

Post by Roger E. Blumberg
And I guess I'm still
wondering just how "unstable" our 3rds really have been (all along) and on
_which_ instruments. On Lutes (and then Viols), which have varriable
temperament (tied and movable frets), I still wonder if 3rds were ever such
a big issue, same with singers. What I'm saying is that while 3rds were a
recognized temperament trouble-spot, they were "solvable" on lutes (and
never a problem with singers), you just tweak your fret placements a little.
And if I'm not mistaken, minor thirds were never an issue at all, it was
just Major 3rds. Keyboards are the biggest issue, or perhaps ensembles of
fixed-hole recorders and other woodwinds. But, for example, with solo lute
accompaniing a voice (singer), the 3rds should never have been such a big
deal, ever, and as far back as we see fretted lute-like and guitarra-like
instruments, e.g. in the Cantigas, 1260 AD. This is to say, we could have
had, might have had, should have had, stable thirds as far back as 1260 and
earlier if we wanted them (300 years before the mid 1500s). So the "reasons"
and timing for the acceptance of Major 3rds as "stable" might have less to
do with there general availability, they had been "available" to us for a
very long time.

The instability is at least partly in how you "hear" them- to us they sound
stable, to them they were somewhat unstable. As for the lute etc. making them
more stable, remember that the lute is related to the favourite instrument of
the medieval theorists, the monochord, which determined where people expected
to put their frets. As for the frets being movable - well sort of. As far as
I know they were of rawhide or gut, tied on wet so that they tightened as they
dried to prevent problems of loose frets. That doesn't make it very easy to
move them in practice. John Dowland (1610) gave a method of calculating fret
positions which gives results considerably different that what you would find
on a lute or guitar using current calculation methods (see
http://www.shipbrook.com/jeff/frets.html )

Post by Roger E. Blumberg
that's an interesting way of putting it. I guess that's part of what I mean
regarding using a single instrument to help compose a song. The "breathing"
time lets you play around with possible melodies in your head while you're
playing (blocking out the sonorities).

Actually I was referring to the alternation of stable - unstable - stable,
breathing out - in - out.

[Roger E. Blumberg]

Post by Stephen Fryer

Post by Roger E. Blumberg
By the way, I tried your 344 tuning across 4 courses, and I'm having doubts
about it, that 4 fret stretch to play an Octave, 5th, or trine, on the lower
3 strings/courses is my biggest question mark. Of your two suggested
tunings, 443 would make more sense to me. As time goes by, all 4ths, 444, is
making the most sence (as it turns out).

I'm not sure I understand what you're saying here. Having the third in there
reduces a lot of the stretches - at least that's the way it looks to me.

you'll need courier fonts here . .

well, here's Octave, 5th, and Trine, in 344 tuning,
lowest 3 strings. Notice that all are a 4 fret stretch or span


Octave P5th Trine

X X
+---+---+ +---+---+ +---+---+
| | | | | | | | |
+---+---+ +---+---+ +---+---+
| | | | | | | | |
+---+---+ +---+---+ +---+---+
3fr R | | R | | R | |
+---+---+ +---+---+ +---+---+
| | | | | | | | |
+---+---+ +---+---+ +---+---+
| | | | | | | | |
+---+---+ +---+---+ +---+---+
6fr | | R | 5 | | 5 R
+---+---+ +---+---+ +---+---+



now, here's octave, 5th, and trine, in 444 tuning, lowest 3 strings.
Notice all are a 3 fret stretch


Octave P5th Trine

X X
+---+---+ +---+---+ +---+---+
| | | | | | | | |
+---+---+ +---+---+ +---+---+
| | | | | | | | |
+---+---+ +---+---+ +---+---+
3fr R | | R | | R | |
+---+---+ +---+---+ +---+---+
| | | | | | | | |
+---+---+ +---+---+ +---+---+
5fr | | R | 5 | | 5 R
+---+---+ +---+---+ +---+---+
| | | | | | | | |
+---+---+ +---+---+ +---+---+

Post by Stephen Fryer

Post by Roger E. Blumberg
That said, I hope people remember that midi is just
another tool and that it's important to hear the peices in real voices and
instruments because midi is notoriously "cheesy" no matter what the music
is. And I know you won't take offence at that. I just want to make sure
folks get the most enjoyment and pleasure from the examples as possible. I'm
extremely greatful to be able to play (hear and appreciate) all of the
examples given so far on a real string instrument. If I had had only midi
examples to hear this whole time I don't think it would have had the nearly
same impact upon me. By the way, the recorder voiceing in midi _is_ nice.

The guitar (nylon string) voicing is absolutely horrible. And there is
nothing usable for a singing voice either.

I'm sorry, I meant all previous examples were very nice on fetboard, but/and
the midi versions (if they had existed) might not have done them justice
compared to a real instrument or real singers.

Post by Stephen Fryer

Post by Roger E. Blumberg
And I guess I'm still
wondering just how "unstable" our 3rds really have been (all along) and on
_which_ instruments. On Lutes (and then Viols), which have varriable
temperament (tied and movable frets), I still wonder if 3rds were ever such
a big issue, same with singers. What I'm saying is that while 3rds were a
recognized temperament trouble-spot, they were "solvable" on lutes (and
never a problem with singers), you just tweak your fret placements a little.
And if I'm not mistaken, minor thirds were never an issue at all, it was
just Major 3rds. Keyboards are the biggest issue, or perhaps ensembles of
fixed-hole recorders and other woodwinds. But, for example, with solo lute
accompaniing a voice (singer), the 3rds should never have been such a big
deal, ever, and as far back as we see fretted lute-like and

guitarra-like

Post by Stephen Fryer

Post by Roger E. Blumberg
instruments, e.g. in the Cantigas, 1260 AD. This is to say, we could have
had, might have had, should have had, stable thirds as far back as 1260 and
earlier if we wanted them (300 years before the mid 1500s). So the "reasons"
and timing for the acceptance of Major 3rds as "stable" might have less to
do with there general availability, they had been "available" to us for a
very long time.

The instability is at least partly in how you "hear" them- to us they sound
stable, to them they were somewhat unstable.

I'm not so sure. I believe it had to do more with Pythagorean tuning (to
pure 5ths) that left us with Major 3rd intervals that were "unrestfull" and
unstable, they were some cents off from what we might consider stable. It
was a temperament and tuning issue (and on some instruments more than
others). I don't think our ears have changed so much.

Post by Stephen Fryer
As for the lute etc. making them
more stable, remember that the lute is related to the favourite instrument of
the medieval theorists, the monochord, which determined where people expected
to put their frets.

I really don't think they're much related. One might use a monochord for
research, but the one did not lead to the other.

Post by Stephen Fryer
As for the frets being movable - well sort of. As far as
I know they were of rawhide or gut, tied on wet so that they tightened as they
dried to prevent problems of loose frets. That doesn't make it very easy to
move them in practice.

I was under the impression that Lute and Viol players adjusted their frets
regularly (within reason), a hair of adjustment, a nudge, can go long way.
They were tight, but not so tight you couldn't do some fine tuning.

Post by Stephen Fryer
John Dowland (1610) gave a method of calculating fret
positions which gives results considerably different that what you would find
on a lute or guitar using current calculation methods (see
http://www.shipbrook.com/jeff/frets.html )

thanks, I'll check that out later

Post by Stephen Fryer

Post by Roger E. Blumberg
that's an interesting way of putting it. I guess that's part of what I mean
regarding using a single instrument to help compose a song. The "breathing"
time lets you play around with possible melodies in your head while you're
playing (blocking out the sonorities).

Actually I was referring to the alternation of stable - unstable - stable,
breathing out - in - out.

I see, I misunderstood your particular meaning.

Thanks
Roger

Post by Stephen Fryer
--
Stephen Fryer
Lund Computer Services
**************************************************
The more answers I find, the more questions I have
**************************************************

[Margo Schulter]

Post by Stephen Fryer
The instability is at least partly in how you "hear" them- to us they sound
stable, to them they were somewhat unstable.

Hello, there, Stephen, and I'd like briefly to support a point that this
statement might imply: that what's "stable" is a matter of style or of
listener expectations, although a given tuning scheme might tend to
reinforce or rather decidedly compromise such expectations.

For example, on a keyboard tempered with 12 equal semitones, I hear a
major third as unstable in a 13th-14th century context of the kind we're
mostly discussing in this thread, but as stable in a 16th-century context.
The size of the interval, 400 cents, is the same in either setting.

What I might propose is using "stable/unstable" to describe this kind of
difference between musical styles or listener expectations for a given
interval or sonority, and maybe using something like "blending/tense" or
"simple/complex" to compare tunings of an interval or sonority.

As you nicely mentioned in an earlier post, there's a general tendency in
Western European polyphony, at any rate, for certain unstable sonorities
gradually to be treated as increasingly stable or even conclusive; this
tendency might influence tuning and temperament at different points, as
well as vice versa.

Just how these factors interact is an interesting question.

Most appreciatively,

Margo Schulter
***@calweb.com

[Roman Turovsky]

Post by Roger E. Blumberg
[Roman, (or anyone else) what's your take on early 4 course lute tuning?]

It is a bit outside my area of expertise (mine is 1650's+), sorry. But I'd
post this question to medieval-***@cs.dartmouth.edu (posting now requires
being a subscriber[medieval-lute-request @cs.dartmouth.edu]).
I would only venture to say that the 3rds between strings make a lute A LOT
easier to play.
RT
______________
Roman M. Turovsky
http://turovsky.org
http://polyhymnion.org

[Roger E. Blumberg]

Post by Roman Turovsky

Post by Roger E. Blumberg
[Roman, (or anyone else) what's your take on early 4 course lute tuning?]

It is a bit outside my area of expertise (mine is 1650's+), sorry. But I'd
I would only venture to say that the 3rds between strings make a lute A LOT
easier to play.
RT

thanks Roman. There are a number of Lute and Vihuela history books around
that I can't afford to buy, so folks having access to those books, plus the
collected research among those on the lute list could yield some interesting
info.

On a six course machine, having a 3rd somewhere near the middle does help
alot, for chord fingerings specifically (plus syncing the 2-octave note on a
single fretline, strings 1 and 6). I actually prefer many 6 string voicings
in lute tuning rather than guitar tuning (meaning 44344 rather than 44434),
but I've got too many years of muscle memory invested in guitar tuning to
switch now. With five courses or less, the mid 3rd seems less nesessary,
although I do like 5 course Vihuela/Guitar in 4434.
http://www.thecipher.com/basic_vihuela-5_chords_1.html
Actually, I think we went overboard generally, 5 courses seems just right. 6
and over, in any tuning, was pushing it, perhaps.

Roger

Post by Roman Turovsky
______________
Roman M. Turovsky
http://turovsky.org
http://polyhymnion.org

[Roman Turovsky]

Post by Roger E. Blumberg
On a six course machine, having a 3rd somewhere near the middle does help
alot, for chord fingerings specifically (plus syncing the 2-octave note on a
single fretline, strings 1 and 6). I actually prefer many 6 string voicings
in lute tuning rather than guitar tuning (meaning 44344 rather than 44434),

Do note that major triad tuning (such as so so-called Russian Guitar tuning,
which actually is an import from Kobza, a Ukrainian Lute) makes things even
easier both vertically and horizontally, but I cannot state in all fairness
that it was implemented before 1600.
RT

[Roman Turovsky]

Post by Roger E. Blumberg
Actually, I think we went overboard generally, 5 courses seems just right. 6
and over, in any tuning, was pushing it, perhaps.

What do you mean? There is nothing sexier than 13 courses (with 3rds
outnumbering the 4ths), and there is no greater aphrodisiac than a juicy
minor 10th chord with added 9th.
RT

[Roger E. Blumberg]

Post by Roman Turovsky

Post by Roger E. Blumberg
Actually, I think we went overboard generally, 5 courses seems just right. 6
and over, in any tuning, was pushing it, perhaps.

What do you mean? There is nothing sexier than 13 courses (with 3rds
outnumbering the 4ths), and there is no greater aphrodisiac than a juicy
minor 10th chord with added 9th.
RT

I just mean the complication factors, ease of leaning and playing. 5 seems a
comfortable place to stop, a comfortable amount to "get your head around"
(for anyone). There's nothing wrong with more courses per say, I'm just
saying 5 is "just right". Also then, if you throw in some re-entrant bits
(tune some courses up or down an octave from normal) on a 5 course machine
you get a lot of bang for the buck. This was apparently pretty common on 5
course Vihuela/Guitar and still is the case on Mexican 5 course Mariachi
Vihuela/Guitar (Guitarra de Golpe).

Post by Roman Turovsky
minor 10th chord with added 9th.

but you can do that in far less tham 13 coures! In fact with only 4 courses
in 4ths you can easily do R,5,9,b10 on 4 adjacent strings. What is your
formula for minor 10th chord, by the way?

Roger

[Roman Turovsky]

Post by Roger E. Blumberg

Post by Roman Turovsky

Post by Roger E. Blumberg
Actually, I think we went overboard generally, 5 courses seems just

right. 6

Post by Roman Turovsky

Post by Roger E. Blumberg
and over, in any tuning, was pushing it, perhaps.

What do you mean? There is nothing sexier than 13 courses (with 3rds
outnumbering the 4ths), and there is no greater aphrodisiac than a juicy
minor 10th chord with added 9th.
RT

I just mean the complication factors, ease of leaning and playing. 5 seems a
comfortable place to stop, a comfortable amount to "get your head around"
(for anyone). There's nothing wrong with more courses per say, I'm just
saying 5 is "just right". Also then, if you throw in some re-entrant bits
(tune some courses up or down an octave from normal) on a 5 course machine
you get a lot of bang for the buck. This was apparently pretty common on 5
course Vihuela/Guitar and still is the case on Mexican 5 course Mariachi
Vihuela/Guitar (Guitarra de Golpe).

Ahhh, OK.

Post by Roger E. Blumberg

Post by Roman Turovsky
minor 10th chord with added 9th.

but you can do that in far less tham 13 coures! In fact with only 4 courses
in 4ths you can easily do R,5,9,b10 on 4 adjacent strings. What is your
formula for minor 10th chord, by the way?

in d:
_a_
_c_
_a_
___
___
___
///a

or in g:
_f_
_h_
_f_
___
___
___
a

Actually the first is 18 with added 17. Even better.
RT

[Roger E. Blumberg]

Post by Roman Turovsky

Post by Roger E. Blumberg

Post by Roman Turovsky

Post by Roger E. Blumberg
Actually, I think we went overboard generally, 5 courses seems just

right. 6

Post by Roman Turovsky

Post by Roger E. Blumberg
and over, in any tuning, was pushing it, perhaps.

What do you mean? There is nothing sexier than 13 courses (with 3rds
outnumbering the 4ths), and there is no greater aphrodisiac than a juicy
minor 10th chord with added 9th.
RT

I just mean the complication factors, ease of leaning and playing. 5 seems a
comfortable place to stop, a comfortable amount to "get your head around"
(for anyone). There's nothing wrong with more courses per say, I'm just
saying 5 is "just right". Also then, if you throw in some re-entrant bits
(tune some courses up or down an octave from normal) on a 5 course machine
you get a lot of bang for the buck. This was apparently pretty common on 5
course Vihuela/Guitar and still is the case on Mexican 5 course Mariachi
Vihuela/Guitar (Guitarra de Golpe).

Ahhh, OK.

Post by Roger E. Blumberg

Post by Roman Turovsky
minor 10th chord with added 9th.

but you can do that in far less tham 13 coures! In fact with only 4 courses
in 4ths you can easily do R,5,9,b10 on 4 adjacent strings. What is your
formula for minor 10th chord, by the way?

_a_
_c_
_a_
___
___
___
///a
_f_
_h_
_f_
___
___
___
a
Actually the first is 18 with added 17. Even better.
RT

no comprendo your notation. What would it be in this kind of notation
R,5,9,b10

Roger

[David Kilpatrick]

Post by Roger E. Blumberg
Hi Stephen;
I'm glad to hear someone else out there is interested and playing along as
well ;')
About the tuning; As I understand it, 4 course 434 is early "lute kernel"
tuning to which additional courses, both high and low, were added over time.
If one begins with 344 kernel and just adds lower courses that could make
enough sense too. Ultimately, this family of tunings encompasses early
Vihuela/Guitar as well (so if you start with 344 you'd be both adding lower
courses and eliminating one higher course eventually). It's all the same
animal as far as I'm concerned though, and there probably were any number of
possible variations used, nevertheless I'd be happy to be corrected
regarding the 434 kernel if I'm wrong. The whole topic _is_ rather central
to me (actually). I believe there is documentation of a mid-1500's Vihuelist
saying that Guitarra Latina tuning (for example) was the same as the 4
center courses of 6 course lute/vihuela (i.e. 434)
[Roman, (or anyone else) what's your take on early 4 course lute tuning?]

I've always understood that the Arabic ud tuning in straight fourths for
four or five courses was the tuning carried back to Europe with the
lute (ud) in its unfretted form. The problem with introducing a major
third interval is that it fixes a kind of 'temperament' when different
regions of Europe probably used a slightly different third. Both the
3rds and 7ths of monophonic instruments, like pipes/gaita, have retained
their peculiar sharpening or flattening relative to modern 3rds even
today, and tuning in fourths on an unfretted (or movable tied fret)
stringed polyphonic instrument allows the required pitch variations in
these intervals, relative to open strings which were used a great deal
on early short necked instruments (and continued to be, more so than on
modern guitar).

The 4434 4344 choice, on a fretted four-course instrument, might be
convenient but might not be sonorous in all the required keys.

Fourth-interval tuning is excellent on a four-courser and I have small
single-string four course instrument which works very well this way.

Fourth interval tuning also works on five courses, as with the later
Turkish ud, but is less convenient for any kind of chordal playing once
you reach six courses. The Spanish laud retains a full six double
courses in fourths all the way, and is supposed be tuned this way
because the six-course ud of Moorish Spain was in fourths. Following the
expulsion of the Moors, the lute became unfashionable socially (though I
don't believe the myth that it was banned). So did the characteristic
sound produced by the one-semitone difference in pitch (plus two
octaves) created in the 1st and 6th courses by 4th interval tuning, and
the laud went underground as a purely folk instrument, keeping this. The
guitar and northern European lute had an entirely different sonority,
due to the use of a fixed third interval (eventually, in a modern equal
temperament) between one pair of open strings - and the benefit of 1st
and 6th strings exactly two octaves apart, removing the odd
'unsympathetic' ring of the laud.

Once you go beyond six strings, 4th interval tuning simply isn't fun at
all as each successive open string ends up a semitone different in pitch
(plus octaves) from another.If you had a big enough instrument, fourth
intervals would eventually cover the entire chromatic scale.

The same can be said of any fixed interval, but there is another
technical reason why fourth intervals are used - string tension and
instrument design. Early three-string instruments typically used 1-5-8,
root fifth octave. This was essentially a fourth interval between the
mean and treble, and the bourdon might not be a particularly wonderful
sound but only had to act as a drone much of the time. They were already
at the limit of the string technology. Four strings in fourth intervals
could be achieved too, but string making had to be improved before the
modern violin (etc) tuning of four strings in fifths was possible. This
is a wide pitch range and even today cheaper strings rarely manage it
nicely.

Today we can manage five strings in fifth intervals (and Robert Fripp
tunes his six-string guitar in fifths all the way, aided by a special
string set - steel/PB - made by John Pearse and sold as 'New Standard
Tuning'). I've tried this and found that while it's wonderful for easily
transposed melody playing, it is not so great for chords or polyphonic
'moving parts' - at which the standard 444344 guitar or 443444 lute
tunings really excel.

Unfortunately, cross-Atlantic and 19th century influences make it
impossible to guess whether the 43444 tuning of a Venezuelan or Canarian
five-string ukelele/tiple (miniature vihuela), or the odd tunings of
things Portuguese guitarra, have any connection with historic
'pre-Columbus' tunings. Ditto all South and Central American stringed
instruments. My instruction books tell me that both the Portuguese
guitarra and the Spanish laud (six course wire strung instruments) had
'old tunings' - i.e. Victorian era tunings - which were different from
the modern ones, in the case of Portugal that seems to be open major
triad chord (totally 18th c influenced) and in Spain, I am unsure -
maybe they used a 3rd interval at some past date, because it's certainly
easier to play the laud with chords that way.

The modern Turkish lavta (a four-course, double strung courses, long
neck, fretted lute) is in 5th intervals as far as I know - no doubt
because modern strings permit reasonable weight and tensions.

This is all just my opinion, detective work if you like. It may all be
bullshit. But I think Arabic origins, string technology, use for
monophonic parts, nature of the 3rd interval before modern temperaments
began to be fixed - etc - all would favour straight fourths in mediaeval
instruments of four or five courses; and that the unsatifactory fit of
fourths to six or more courses ensured later instruments (renaissance
baroque and beyond) used closer intervals; while improved strings meant
that 4-5 course instruments like viols changed from close intervals, to
straight fifths.

David

[Roman Turovsky]

Post by David Kilpatrick
I've always understood that the Arabic ud tuning in straight fourths for
four or five courses was the tuning carried back to Europe with the
lute (ud) in its unfretted form.

1.Oud was originally fretted.
2. Lutes were played in Europe BEFORE hijra, but their tuning is NOT
documented.
RT
______________
Roman M. Turovsky
http://turovsky.org
http://polyhymnion.org

[John Briggs]

Post by Roman Turovsky

Post by David Kilpatrick
I've always understood that the Arabic ud tuning in straight fourths for
four or five courses was the tuning carried back to Europe with the
lute (ud) in its unfretted form.

1.Oud was originally fretted.
2. Lutes were played in Europe BEFORE hijra, but their tuning is NOT
documented.

What were they called?

[Roman Turovsky]

Post by John Briggs

Post by Roman Turovsky

Post by David Kilpatrick
I've always understood that the Arabic ud tuning in straight fourths for
four or five courses was the tuning carried back to Europe with the
lute (ud) in its unfretted form.

1.Oud was originally fretted.
2. Lutes were played in Europe BEFORE hijra, but their tuning is NOT
documented.

What were they called?

PANDOURAS, among a few other names. I have a few paragraphs on the subject
at
http://polyhymnion.org/torban
in Chapter II.
RT

[Roman Turovsky]

Post by Roman Turovsky

Post by John Briggs

Post by Roman Turovsky

Post by David Kilpatrick
I've always understood that the Arabic ud tuning in straight fourths for
four or five courses was the tuning carried back to Europe with the
lute (ud) in its unfretted form.

1.Oud was originally fretted.
2. Lutes were played in Europe BEFORE hijra, but their tuning is NOT
documented.

What were they called?

PANDOURAS, among a few other names. I have a few paragraphs on the subject
at
http://polyhymnion.org/torban
in Chapter II.

And of course CITHARAE, of which Moroccan KUITRA is a descendant.
RT

[Roman Turovsky]

Post by David Kilpatrick
The 4434 4344 choice, on a fretted four-course instrument, might be
convenient but might not be sonorous in all the required keys.

Oud, in its 444, is equally unsonorous in all the keys. The 3rd actually
seems to add overtones.
RT

[Roman Turovsky]

Post by David Kilpatrick
Following the
expulsion of the Moors, the lute became unfashionable socially (though I
don't believe the myth that it was banned)

Antonio Corona has put the former myth to rest as well, recently on the lute
list. There is plenty of iconographic evidence that lute was never
persona-non-grata is Spain.
RT

[Roman Turovsky]

Post by David Kilpatrick
have any connection with historic
'pre-Columbus' tunings. Ditto all South and Central American stringed
instruments.

Pre-Colombian amerinds had no stringed instruments, only winds.
RT

[David Kilpatrick]

Post by Roman Turovsky

Post by David Kilpatrick
have any connection with historic
'pre-Columbus' tunings. Ditto all South and Central American stringed
instruments.

Pre-Colombian amerinds had no stringed instruments, only winds.

Post-Columbian ones = colonisers = most certainly did and the reverse
migrations from Venezuela back to Europe in the 20th century brought new
instruments 'back' in their modified form. I was not saying anything
about pre-Columbus tunings except in Europe, or about post-Columbian
ones except in America.

David

[Roman Turovsky]

Post by David Kilpatrick
'old tunings' - i.e. Victorian era tunings - which were different from
the modern ones, in the case of Portugal that seems to be open major
triad chord (totally 18th c influenced)

Eastern European lutes are thought to have open major triad tunings at least
from 1600.
RT

[Roger E. Blumberg]

Post by David Kilpatrick

Post by Roger E. Blumberg
Hi Stephen;
I'm glad to hear someone else out there is interested and playing along as
well ;')
About the tuning; As I understand it, 4 course 434 is early "lute kernel"
tuning to which additional courses, both high and low, were added over time.
If one begins with 344 kernel and just adds lower courses that could make
enough sense too. Ultimately, this family of tunings encompasses early
Vihuela/Guitar as well (so if you start with 344 you'd be both adding lower
courses and eliminating one higher course eventually). It's all the same
animal as far as I'm concerned though, and there probably were any number of
possible variations used, nevertheless I'd be happy to be corrected
regarding the 434 kernel if I'm wrong. The whole topic _is_ rather central
to me (actually). I believe there is documentation of a mid-1500's Vihuelist
saying that Guitarra Latina tuning (for example) was the same as the 4
center courses of 6 course lute/vihuela (i.e. 434)
[Roman, (or anyone else) what's your take on early 4 course lute tuning?]

I've always understood that the Arabic ud tuning in straight fourths for
four or five courses was the tuning carried back to Europe with the
lute (ud) in its unfretted form.

that's what I thought too, mostly 4ths on unfretted Oud and carried into
Europe from either of two (or more) routes. Roman often reminds that Ouds
originally had frets too (and Arabs had harmony), but I don't know what
tunings were used, nor what sonorities they recognized in their harmony.

Post by David Kilpatrick
The problem with introducing a major
third interval is that it fixes a kind of 'temperament' when different
regions of Europe probably used a slightly different third. Both the
3rds and 7ths of monophonic instruments, like pipes/gaita, have retained
their peculiar sharpening or flattening relative to modern 3rds even
today, and tuning in fourths on an unfretted (or movable tied fret)
stringed polyphonic instrument allows the required pitch variations in
these intervals, relative to open strings which were used a great deal
on early short necked instruments (and continued to be, more so than on
modern guitar).

well, if you have frets you're going to have thirds all over the place no
matter what you do, even without having a third in the tuning pattern. And
with tied frets the temperament isn't fixed, you can tweak it, move your
frets up or down a hair. And once you have frets, 4ths tuning isn't very
good for open string drones in any event, even straight fourths. Having one
or more 5ths and Octave (or Unison) intervals in a tuning pattern is better
for drones (even with frets). Actually, I think 443 is better for a little
bit of droned open stings than 444 is (it's still not great but there's at
least some droney potential to it). I think the 3rd in the tuning pattern
has to do with fingerings and stretches on the 5 and higher course
instruments, and (I'm begining to think) perhaps 434 (on 4 courses) was an
_after-the-fact_ reduction of the large lute-tuned instruments, a
de-evolution of a sort (dropping strings to make a simpler "baby lute"),
then as you again start adding lower courses from there you get the 4, 5, 6,
string guitar family tunings, 434, 4434, 44434. I don't know.

Post by David Kilpatrick
The 4434 4344 choice, on a fretted four-course instrument, might be
convenient but might not be sonorous in all the required keys.

again, once you have frets you have thirds all over the place, and you
aren't using open string droning too much in 4ths anyway (I don't believe).
And it's actually not particular convenient nor necessary on 4 courses. The
3rd is a pain in the butt until it's functionality/necessity is reached in
the larger instruments, 6 courses in particular, and thus tips the scale in
it's favor. It _was_ me who originally suggested that 434 was likely on
early four course instruments (because I was under the impression that's how
the evolution happened, and it's still not entirely inconceivable) and as
recently as a couple of days ago I repeated that belief/assertion, but I'm
getting close to retracting and rejecting that notion myself. If nessesity
is the mother of invention, I'm not sure what would have nessecitated a 3rd
_anywhere_ in a 4 course tuning, whether 344, 434, or 443. 444 is the
simplest and very functional (and isomorphic) tuning, it's a very good
universal for both melody and chords. So I'm agreeing with you below
"Fourth-interval tuning is excellent on a four-courser". I've been using it
here for the last couple of months and find it perfect.

Post by David Kilpatrick
Fourth-interval tuning is excellent on a four-courser and I have small
single-string four course instrument which works very well this way.
Fourth interval tuning also works on five courses, as with the later
Turkish ud, but is less convenient for any kind of chordal playing once
you reach six courses.

right, we agree on this

Post by David Kilpatrick
The Spanish laud retains a full six double
courses in fourths all the way, and is supposed be tuned this way
because the six-course ud of Moorish Spain was in fourths.

Is Cuban 6 course metal string Laud all 4ths too? I heard one played in that
PBS Rye Cooter documentary on Cuban Jazzmen. It sounded great.

Post by David Kilpatrick
Following the
expulsion of the Moors, the lute became unfashionable socially (though I
don't believe the myth that it was banned). So did the characteristic
sound produced by the one-semitone difference in pitch (plus two
octaves) created in the 1st and 6th courses by 4th interval tuning, and
the laud went underground as a purely folk instrument, keeping this. The
guitar and northern European lute had an entirely different sonority,
due to the use of a fixed third interval (eventually, in a modern equal
temperament) between one pair of open strings - and the benefit of 1st
and 6th strings exactly two octaves apart, removing the odd
'unsympathetic' ring of the laud.
Once you go beyond six strings, 4th interval tuning simply isn't fun at
all as each successive open string ends up a semitone different in pitch
(plus octaves) from another.If you had a big enough instrument, fourth
intervals would eventually cover the entire chromatic scale.
The same can be said of any fixed interval, but there is another
technical reason why fourth intervals are used - string tension and
instrument design. Early three-string instruments typically used 1-5-8,
root fifth octave. This was essentially a fourth interval between the
mean and treble, and the bourdon might not be a particularly wonderful
sound but only had to act as a drone much of the time. They were already
at the limit of the string technology. Four strings in fourth intervals
could be achieved too, but string making had to be improved before the
modern violin (etc) tuning of four strings in fifths was possible. This
is a wide pitch range and even today cheaper strings rarely manage it
nicely.

right, all 5ths is tough beyond 3 strings

Post by David Kilpatrick
Today we can manage five strings in fifth intervals (and Robert Fripp
tunes his six-string guitar in fifths all the way, aided by a special
string set - steel/PB - made by John Pearse and sold as 'New Standard
Tuning'). I've tried this and found that while it's wonderful for easily
transposed melody playing, it is not so great for chords or polyphonic
'moving parts' - at which the standard 444344 guitar or 443444 lute
tunings really excel.

right. This is what underlies my assertion re the lute/vihuela/viol/guitar
family being "polyphony engines" and their huge (but under-appreciated) role
and influence upon European music making all along. 4ths tuning "works", it
facilitates methodic exploration of polyphony, and long before and much
wider spread/used/accessable-to-all than any keyboard (the other mechanical
polyphony engine of note).

Post by David Kilpatrick
Unfortunately, cross-Atlantic and 19th century influences make it
impossible to guess whether the 43444 tuning of a Venezuelan or Canarian
five-string ukelele/tiple (miniature vihuela), or the odd tunings of
things Portuguese guitarra, have any connection with historic
'pre-Columbus' tunings. Ditto all South and Central American stringed
instruments. My instruction books tell me that both the Portuguese
guitarra and the Spanish laud (six course wire strung instruments) had
'old tunings' - i.e. Victorian era tunings - which were different from
the modern ones, in the case of Portugal that seems to be open major
triad chord (totally 18th c influenced) and in Spain, I am unsure -
maybe they used a 3rd interval at some past date, because it's certainly
easier to play the laud with chords that way.
The modern Turkish lavta (a four-course, double strung courses, long
neck, fretted lute) is in 5th intervals as far as I know - no doubt
because modern strings permit reasonable weight and tensions.
This is all just my opinion, detective work if you like. It may all be
bullshit. But I think Arabic origins, string technology, use for
monophonic parts, nature of the 3rd interval before modern temperaments
began to be fixed - etc - all would favour straight fourths in mediaeval
instruments of four or five courses; and that the unsatifactory fit of
fourths to six or more courses ensured later instruments (renaissance
baroque and beyond) used closer intervals; while improved strings meant
that 4-5 course instruments like viols changed from close intervals, to
straight fifths.

but then viols never did go 5ths (violins and cellos did)


We're in agreement about 4ths in the end, excepting a few of the details.


Thanks
Roger

Post by David Kilpatrick
David

[Roger E. Blumberg]

Post by Roger E. Blumberg
I think the 3rd in the tuning pattern
has to do with fingerings and stretches on the 5 and higher course
instruments, and (I'm begining to think) perhaps 434 (on 4 courses) was an
_after-the-fact_ reduction of the large lute-tuned instruments, a
de-evolution of a sort (dropping strings to make a simpler "baby lute"),
then as you again start adding lower courses from there you get the 4, 5, 6,
string guitar family tunings, 434, 4434, 44434. I don't know.

Post by Roger E. Blumberg
And it's actually not particular convenient nor necessary on 4 courses. The

3rd is a pain in the butt until it's functionality/necessity is reached in
the larger instruments, 6 courses in particular, and thus tips the scale in
it's favor. It _was_ me who originally suggested that 434 was likely on
early four course instruments (because I was under the impression that's how
the evolution happened, and it's still not entirely inconceivable) and as
recently as a couple of days ago I repeated that belief/assertion, but I'm
getting close to retracting and rejecting that notion myself. If nessesity
is the mother of invention, I'm not sure what would have nessecitated a 3rd
_anywhere_ in a 4 course tuning, whether 344, 434, or 443. 444 is the
simplest and very functional (and isomorphic) tuning, it's a very good
universal for both melody and chords. So I'm agreeing with you below
"Fourth-interval tuning is excellent on a four-courser". I've been using it
here for the last couple of months and find it perfect.

But then again, as Stephan verified, the mid-1500's Vihuelist Fray Juan
Bermudo wrote that Guitarra Latina tuning was the same as the 4 center
courses of 6 course lute/vihuela, meaning 434.

So who knows just how old 434 across 4 courses is. Is Bermudo's referenced
"Guitarra Latina" the same Guitarra Latina in the Cantigas (300 years
earlier)? Is early Vihuela (4 and 5 course) just another name for Guitarra
Latina? And also the same as 4 course Renaissance Guitar?

Alphanso X's (same King of Spain who commissioned the Cantigas) "Book of
Games" clearly shows a fretted 6 course lute i.e. in 1260! Was later classic
44344 6 course lute tuning already in use in 1260? i.e. early precedence of
employing a 3rd somewhere in the pattern. Were they (already) playing chords
on their 6 course fretted Lutes in 1260, in medieval Spain, in Alphanso's
court, two notes at a time, three?
Loading Image...


Roger

[Margo Schulter]

Post by Stephen Fryer
To Margo, Roger, et alii, greetings!

Dear Stephen,

Thank you warmly for joining in on this discussion, asking some excellent
questions, and contributing your own interest and enthusiasm in medieval
music.

Here I want in turn to offer my encouragement and welcome to our dialogue,
and to answer some of your questions -- while looking forward to answering
more when I have taken the time to consider them more adequately. Your
closing example of a song with a text seeming to date it to 1193 (I'd be
interested in the historical context here, by the way) has given me some
ideas, and I'd like to consider the whole passage before posting a
possible solution. Anyway, I've heard rhythms at the end of phrases like
this in performances of Perotin's three-voice conductus _Salvatoris
hodie_, and might be influenced by that piece in considering an
accompaniment here. Thank you for an engaging problem!

By the way, please let me add an endorsement for your support of selective
quoting, and resolve to follow your advice, especially in a thread where
my new comments in a post are often long enough.

Post by Stephen Fryer
Being interested in 13th c. music, I was trying to find something about
the implications of counterpoint with 3rds treated as unstable intervals
- and this discussion has given me considerable insight. It also
presents me with a new and most pleasurable way of listening to 13th c.
motets (In mari miserie - Gemma pudicicie - MANERE seems a particularly
apt example).

Yes, the general idea of "alternation" fits many pieces, like the fine
example you posted from La Clayette, although some pieces better than
others. Please let me warmly second your point that the horizontal aspects
are equally important, and add that the balance between these dimensions
is something that I find charming in this music.

Post by Stephen Fryer
I do have a few questions (of course - see tag line below).
Margo: I was a little confused at first by your ocatve designations, being
used to counting from A to a, etc. For instance, in your example
1 2 3 | 1 2 3 | 1
C4 B3 C4 D4
F4 G3 A3
F3 E3 D3
the sequence C4-B3-C4 looked two consecutive skips of a ninth, which would
have been rather odd. I did eventually realize that you were counting C
to c, etc. Perhaps you could tell me why you prefer this?

First, please let me admit that apart from your very reasonable question,
this example might be puzzling because my octave number for the opening F4
in the middle voice is wrong -- it should be F3, so that we have an
ascending major second F3-G3 rather than a descending minor seventh F4-G3.
That's my mistake, which you've given me a welcome opportunity to note and
acknowledge, but let me now respond to your question.

I'd agree that counting octave numbers based on octaves of A-a, etc.,
better fits medieval conventions than counting C-c, a point I confirmed by
looking at one version of the Guidonian hand. Jacobus of Liege sometimes
counts notes from A also -- for example, C as a "third" step. The reason
I use C-c is a convention of MIDI notation, no more logical and a
divergence from this kind of convention. Of course, the MIDI notation
might in turn reflect or be influenced by something like Helmholtz
notation, also based on C-c octaves -- but the A-a has a certain
historical felicity which I must recognize and acknowledge.

In other words, I'd call my usage mostly force of habit in following
recent conventions -- and yours historically apt as well as equally
logical.

Post by Stephen Fryer
On the idea of stable-unstable-stable sequences, it has been said that this is
the driving force of all music, and that the history of polyphonic music has
been the defining of ever more unstable combinations as stable and the search
for more unstable combinations to keep the music driving forward.

This sounds to me like a very fair statement about what has happened in
Western European polyphony; Ludmila Ulehla, in a discussion about "The
Control of Dissonance" in her book _Contemporary Harmony_, has a
fascinating presentation about changing definitions of
stability/instability in 18th-20th century European music, and I wonder
how she might have addressed earlier centuries.

Post by Stephen Fryer
Here is the opening of a motet (O Maria virgo-O Maria maris-IN VERITATE) from
the La Clayette manuscript (I posted a notation [Noteworthy Composer]file at
1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |1 2 3 |
F4-E4-D4-C4-D4-E4-G4-A5-F4-G4----r--E4-C4-D4-E4-D4-E4-F4-E4-D4-C4----r-
C4----D4-F4----E4-D4----C4-C4----B4-A4----G3-A4----B4-C4-------r-------
F3-------F3-------G3-------r--------A4-------A4-------F3-------r-------
You can hear it as played on guitar or lute at
http://home.prcn.org/~sfryer/temp/MOTET%20V2.mid
There are some features here which haven't been discussed, such as the tenor
part being broken into repeated rhythmic figures (in this case separated by
rests). The differing phrase lengths of the triplum and motetus help keep
the music going throuhg cadences (as at measure 4).

Yes, the rhythmic modes and patterns are very important, and in focusing
on vertical combinations I wouldn't want to distract from their
importance. Here the tenor melody is broken into rhythmic patterns or
_ordines_, with an _ordo_ or pattern having three perfect longs plus a
rest of the same length -- in Anderson's transcription, each a dotted
crotchet or quarter in 6/8 (with one measure equal to perfect longs). This
is a very common pattern for a tenor.

More generally, the tenor is rhythmic mode 5 -- with two perfect longs to
a rhythmic unit or foot. The duplum or motetus, the middle voice, is in
mode 1 (imperfect long-breve, or in a 6/8 transcription crotchet-quaver or
quarter-eighth), with some ornamentation. The triplum or highest voice is
in mode 6, with three breves to a foot, or in 6/8 three quavers or
eighths.

I much agree that while the element of alternating stability-instability
that I've been focusing on tends to create an artistic unity, the rhythmic
stratification and also the often overlapping phrases which you point out
provide diversity and also forward motion at cadences where the voices
dovetail, if that's the right word.

Thank you for adding some very important balance.

Post by Stephen Fryer
While the vertical aspect of the music is important, it is dependent on the
horizontal melodies which comprise it, unlike what we are used to hearing in
more recent music. Listening to a double motet is truly wonderful because it
requires attention to both vertical and horizontal aspects of the music to
fully appreciate.

One theme Todd McComb often has raised is the greater freedom of melody in
medieval music than in some later genres -- a kind of development also
noted, in another stylistic setting, in compositions of Ockeghem, for
example (who might be considered to reflect some "medieval" traits as well
as new 15th-century trends of a kind often classified as "Renaissance").

Anyway, I very much agree with you about the appeal of these motets.

Please let me have a good with that song you quote at the end of your
post, and in the meantime thank you for adding balance and insight to the
dialogue.

Most appreciatively,

Margo Schulter
***@calweb.com

[Margo Schulter]

Dear Stephen,

Please let me propose a few possible solutions for three-voice
textures to accompany the example you posted, and also an idea for
distinguising the counting of octaves in the two systems we were
discussing, based on octaves of A-a or C-c.

Post by Stephen Fryer
Here is the final phrase of a tune of which the words would imply
that it was written in 1193. All seems reasonably conventional
until the suspension at the beginning of the last bar forces the
final cadential resolution to be delayed until the weak second beat.
Are there other songs which do this? Up until this point, devising
a suitable accompaniment embodying the ideas you have been
discussing works quite easily. I haven't come up with a solution
for the last two bars that I really like yet - perhaps you would
like to see what you can do with it.
1--+--2--+--3--+--|1--+--2--+--3---+---|1--+--2--+--3--+--||
F4----G4----F4-E4--D4----------E4-D4-C4-C4----D4----------

When I sang this, I realized that it might be the conclusion of the
famous "Prisoner's Song" of King Richard I of England, and your date
of 1193 seemed to fit that attribution -- so I checked it in the
_Historical Anthology of Music_, and indeed this is _Ja nuns hons
pris_, where he complains of the slowness of his ransom.

Anyway, here are some solutions which I'll give in two octave
notations with different numbering schemes. The first is a standard
MIDI notation based on C-c octaves, with C4 as middle C. The second is
a notation based, as you suggest, on A-a octaves, with A1 as the
lowest A of the standard medieval gamut, a tenth below middle C, and
thus the lowest step of the gamut or G gamma ut as G0.

Let's start with a rather simple solution, first in MIDI notation and
then in the A-a notation that you've suggested with octave numbers as
I've proposed above. Here I should note that while I tend to take the
three short notes at the end of the second measure as triplets, a
procedure followed in the transcription I mentioned above, one could
also take this as a binary subdivision (e.g. in 6/4 a quaver or eighth
and two semiquavers or sixteenths). Your notation suggests to me such
a subdivision, and it occurs in modern transcriptions.

MIDI notation

1 2 3 + | 1 2 3 + + | 1 2 3 ||
F4 G4 F4 E4 D4 E4 D4 C4 C4 D4
C4 D4 B3 A3 G3 G3 A3
F3 G3 E3 E3 D3

A-a notation

1 2 3 + | 1 2 3 + + | 1 2 3 ||
F2 G2 F2 E2 D2 E2 D2 C2 C2 D2
C2 D2 B2 A2 G1 G1 A2
F1 G1 E1 E1 D1

Note that with this A-a convention it's easy to tell the two systems
apart, since the lowest note of the gamut in MIDI is G2 (an eleventh
below middle C), and we're unlikely to find notes like MIDI F1 in
medieval music of this era, or even Franco-Flemish music where I've
heard of parts going as low as MIDI C2 (a fifth below gamma ut).

Anyway, this example illustrates a point that you made in another
post: often mostly filling in stable consonances can interact with a
monophonic melody to produce some idiomatic progressions, as here in
moving from the first to the second measure. Now let's consider a bit
more elaborate solution:

MIDI notation

1 2 3 + | 1 2 3 + + | 1 2 3 ||
F4 G4 F4 E4 D4 E4 D4 C4 C4 D4
C4 A3 G3 A3 B3 A3 G3 G3 A3
F3 G3 F3 E3 E3 D3

A-a notation

1 2 3 + | 1 2 3 + + | 1 2 3 ||
F2 G2 F2 E2 D2 E2 D2 C2 C2 D2
C2 A2 G1 A2 B2 A2 G1 G1 A2
F1 G1 F1 E1 E1 D1

Here the rhythmic interactions get more complex. Another yet more
elaborated version:

MIDI notation

1 2 3 + | 1 2 3 + + | 1 2 3 ||
F4 G4 F4 E4 D4 E4 D4 C4 C4 D4
C4 B3 A3 G3 A3 B3 A3 G3 G3 A3
F3 G3 F3 E3 E3 D3

A-a notation

1 2 3 + | 1 2 3 + + | 1 2 3 ||
F2 G2 F2 E2 D2 E2 D2 C2 C2 D2
C2 B2 A2 G1 A2 B2 A2 G1 G1 A2
F1 G1 F1 E1 E1 D1

I like the effect of the parallel fifths between the upper voices in
the first measure, and also the momentary diminished fifth B2-F2 in
A-a notation or B3-F4 in MIDI notation, although this might be a bit
"busy" for a straightforward accompaniment, and more like a motet kind
of texture.

Finally, here's a variation on the final cadence that could be used
with any of these examples. To this point, I've used the standard
progression of a sixth sonority m6|3_4 expanding to a complete trine,
but we could also have the lowest voice move to D before the others
resolve:

MIDI notation

1 2 3 + | 1 2 3 + + | 1 2 3 ||
F4 G4 F4 E4 D4 E4 D4 C4 C4 D4
C4 B3 A3 G3 A3 B3 A3 G3 G3 A3
F3 G3 F3 E3 D3 D3

A-a notation

1 2 3 + | 1 2 3 + + | 1 2 3 ||
F2 G2 F2 E2 D2 E2 D2 C2 C2 D2
C2 B2 A2 G1 A2 B2 A2 G1 G1 A2
F1 G1 F1 E1 D1 D1

The result of this is a "split seventh" consisting of two fourths,
D3-G3-C4 in MIDI or D1-G1-C2 in A-a notation; the middle voice at the
fourth then moves obliquely to the fifth, and the minor seventh to the
octave. This is a beautiful cadence characteristic of Perotin around
1200, so it fits period style. If I were doing this, I might use any
of these choices, very possibly doing things a bit differently each
time.

Post by Stephen Fryer
Again, thank you both for this fascinating discussion!

Thank you for raising the question of this very famous song, and I'd
emphasize that my ideas merely illustrate one possible approach for a
solution.

Most appreciatively,

Margo Schulter
***@calweb.com

[Stephen Fryer]

Post by Margo Schulter
Please let me propose a few possible solutions for three-voice
textures to accompany the example you posted, and also an idea for
distinguising the counting of octaves in the two systems we were
discussing, based on octaves of A-a or C-c.

Post by Stephen Fryer
1--+--2--+--3--+--|1--+--2--+--3---+---|1--+--2--+--3--+--||
F4----G4----F4-E4--D4----------E4-D4-C4-C4----D4----------

When I sang this, I realized that it might be the conclusion of the
famous "Prisoner's Song" of King Richard I of England, and your date
of 1193 seemed to fit that attribution -- so I checked it in the
_Historical Anthology of Music_, and indeed this is _Ja nuns hons
pris_, where he complains of the slowness of his ransom.

That is indeed where this comes from - Richard was captured in Dec. 1192 and
wasn't finally ransomed until Feb. 1194, and since the song complains that it
would be a dishonour to his friends if he were held for two winters, that
makes it seem likely that it was written in late 1193, possibly with the
aproach of winter.

Post by Margo Schulter
Anyway, here are some solutions which I'll give in two octave
notations with different numbering schemes. The first is a standard
MIDI notation based on C-c octaves, with C4 as middle C. The second is
a notation based, as you suggest, on A-a octaves, with A1 as the
lowest A of the standard medieval gamut, a tenth below middle C, and
thus the lowest step of the gamut or G gamma ut as G0.

Actually I can work with either, so don't feel you have to write everything
twice, now that I realized what was happening

Post by Margo Schulter
Here I should note that while I tend to take the
three short notes at the end of the second measure as triplets, a
procedure followed in the transcription I mentioned above, one could
also take this as a binary subdivision (e.g. in 6/4 a quaver or eighth
and two semiquavers or sixteenths). Your notation suggests to me such
a subdivision, and it occurs in modern transcriptions.

The triplet is what I intended. Of course it occurs to me that it would be
possible to see this as 9/8 time rather than 3/4, with relevant consequences
for the parts involving pairs of eighth notes in the 3/4 transcription.

Thank you for the various ideas on this phrase. I did note that in all of
them you have "standard" cadential "chords" in the last measure:
C2 - D2
G1 - A2
E1 = D1
with the stable final "chord" coming on the weak beat. I was treating it as it
looks - a suspension on the first beat:
C2 - D2
A2
D1
And the lead-in measure to that wasn't quite right either; going to an open
fifth on G on the first beat and leaving the E till the last beat works quite
well.

Post by Margo Schulter
Thank you for raising the question of this very famous song, and I'd
emphasize that my ideas merely illustrate one possible approach for a
solution.

What I was trying for was a simple accompaniment such as might have been
played on a small harp, since that seemed like a possible situation for the
time. Most of it worked out quite nicely, and when played with the chords on
the main beats played with slight arpeggiation it sounds quite good. I was
not trying for full three part counterpoint for this particular instance -
though no doubt it could be turned into a double motet, as was done with many
other songs. You can see my original results at
http://home.prcn.org/~sfryer/temp/Ja%20nuns%20hons%20pris.nwc
or hear it at
http://home.prcn.org/~sfryer/temp/Ja%20nuns%20hons%20pris.mid

This discussion is just what I need. Some time ago I set myself the goal of
learning to write in 13th century motet style, and was having trouble finding
any information about how intervals were treated at that time (never having
really studied 16th c. style counterpoint didn't help my cause either). This
discussion has helped a lot. About all I had found previously were your
online essay _Thirteenth-Century Polyphony:A Quick Guide to Combinations and
Cadences_, which was helpful, and the book _Music of the Middle Ages: Style
and Structure_ by David Fenwick Wilson. The goal seems to be getting closer!
And faster than I had originally feared.

Best regards.

[Margo Schulter]

Post by Stephen Fryer
That is indeed where this comes from - Richard was captured in Dec. 1192 and
wasn't finally ransomed until Feb. 1194, and since the song complains that it
would be a dishonour to his friends if he were held for two winters, that
makes it seem likely that it was written in late 1193, possibly with the
aproach of winter.

Thank you for the history here.

[On the C-c or A-a notation question]

Post by Stephen Fryer
Actually I can work with either, so don't feel you have to write everything
twice, now that I realized what was happening

Curious: now that I've tried the A-a notation, I like it, and it fits a
scheme for the Guidonian hand, more or less. A main argument for C-c is
that people might find it more familiar (e.g. Helmholtz or MIDI notation);
but A-a has a certain medievalist flavor that I like.

Post by Stephen Fryer
The triplet is what I intended. Of course it occurs to me that it would be
possible to see this as 9/8 time rather than 3/4, with relevant consequences
for the parts involving pairs of eighth notes in the 3/4 transcription.

This is a usual interpretation of later 13th-century practice in the
Franconian era, which 9/8 transcriptions fit well; Jacobus of Liege,
writing around 1325 in defense of the style of his youth, notes that
characteristically in such an unequal division of the breve into two
semibreves, the shorter note comes first.

Post by Stephen Fryer
Thank you for the various ideas on this phrase. I did note that in all of
C2 - D2
G1 - A2
E1 = D1
with the stable final "chord" coming on the weak beat. I was treating
C2 - D2
A2
D1

Please let me confirm that you could also do this, for example, taking my
simpler version (in the A-a notation we're using, with C2 as middle C):

1 2 3 + | 1 2 3 + + | 1 2 3 ||
F2 G2 F2 E2 D2 E2 D2 C2 C2 D2
C1 D2 B2 A2 G1 A2
F1 G1 E1 D1

The D1-A2-C2 sonority has an outer minor seventh, lower fifth, and upper
minor third; here the resolution is oblique, with the upper voice moving
min7-8 with respect to the lowest voice and min3-4 with respect to the
middle voice. This is quite idiomatic.

Post by Stephen Fryer
And the lead-in measure to that wasn't quite right either; going to an open
fifth on G on the first beat and leaving the E till the last beat works quite
well.

I'm glad that this seems to fit. Striving to keep the accompaniment
relatively simple, for example in the harp style that you describe, can be
an excellent musical discipline, and an opportunity for someone like me to
exercise a bit of self-restraint. Maybe it's a bit like the art of playing
a good continuo part that supports rather than overly distracts from the
melody.

Of course, the double motet kind of style is rewarding, also; but this
whole question of accompaniments can encourage us to explore a range of
styles, and sometimes, as Roger has said, "less is more."

Needless to say, I want to lend every encouragement to you and others
involved in this kind of composition or improvisation, and to say how much
I'm enjoying this dialogue.

Most appreciatively,

Margo Schulter
***@calweb.com

[Stephen Fryer]

Post by Margo Schulter
Note that with this A-a convention it's easy to tell the two systems
apart, since the lowest note of the gamut in MIDI is G2 (an eleventh
below middle C), and we're unlikely to find notes like MIDI F1 in
medieval music of this era, or even Franco-Flemish music where I've
heard of parts going as low as MIDI C2 (a fifth below gamma ut).

Just a comment I left out of my previous reply. The standard tuning for lute
in the 16th century gives it precisely the full range of the medieval gamut,
from Gamma to e' - two octaves and a sixth. I somehow doubt this was a
coincidence.

[Margo Schulter]

Post by Stephen Fryer
Just a comment I left out of my previous reply. The standard tuning for lute
in the 16th century gives it precisely the full range of the medieval gamut,
from Gamma to e' - two octaves and a sixth. I somehow doubt this was a
coincidence.

Thank you for educating me on this: I guess that this would be G0-E3 in an
A-a notation with Gamma as G0, and G2-E5 in MIDI notation. Not only is it
very interesting, but it could help me in getting oriented to the usual
tuning of the strings.

Most appreciatively,

Margo Schulter
***@calweb.com

[Stephen Fryer]

Post by Margo Schulter
Thank you for educating me on this: I guess that this would be G0-E3 in an
A-a notation with Gamma as G0, and G2-E5 in MIDI notation. Not only is it
very interesting, but it could help me in getting oriented to the usual
tuning of the strings.

The standard tuning ('vieil acord') in the 16th century for lute and vihuela
was G0-C1-F1-A2-D2-G2. The five-course guitar was A1-D1-G1-B2-E2 and the
four-course guitar was D1-G1-B2-E2. When two extra strings were added to the
lute around the end of the 16th century, they were usually tuned D0 and F0.
In the 17th century they kept piling on more strings and playing around with
alternate tunings, which greatly decreased its popularity.

Best regards

[Roman Turovsky]

Post by Stephen Fryer
four-course guitar was D1-G1-B2-E2. When two extra strings were added to the
lute around the end of the 16th century, they were usually tuned D0 and F0.
In the 17th century they kept piling on more strings and playing around with
alternate tunings, which greatly decreased its popularity.
Stephen Fryer

To the point of a traveler writing around 1700 that "there is a sufficient
number of lutes in Prague to tile the roofs of the entire city".
RT
______________
Roman M. Turovsky
http://turovsky.org
http://polyhymnion.org

[Margo Schulter]

-----------------------------------------
Medieval Polyphonic Patterns:
An Essay with Thanks to Cait
Part IIB: The F-G-A question (2)
-----------------------------------------

--------------------------------------------------------
3. A-G-F as antepenultimate-penultimate-ultimate (A-P-U)
--------------------------------------------------------

Having surveyed a few usages of mediating, opposing, and connecting
sonorities, we now consider a typical manifestation of the F-G-A
relationship nicely tying in with the theme of A as "home away from
home."

In describing 13th-century passages, we might call the final sonority
or its lowest note the _ultimate_, or U for short; and the immediately
preceding sonority (often unstable) or its lowest note as the
_penultimate_, or P for short.

Most often, the penultimate is located a step above or below the
ultimate. If F is the ultimate or U, for example, then G or E is often
the penultimate or P, as in these directed progressions:

D4 C4 E4 F4 E4 F4
B3 C4 B3 C4 D4 C4
G3 F3 G3 F3 G3 F3

(Maj3-5 + min3-1) (Maj6-8 + Maj3-5) (Maj6-8 + Maj2-4)


B3 C4 D4 C4 D4 C4
G3 F4 B3 C4 G3 F3
E3 F3 E3 F3 E3 F3

(min3-1 + Maj3-5) (min7-5 + min3-1) (min7-5 + min3-1)


Similarly, if U is G, then P is often A or F, as in these similar
three-voice progressions:

E4 D4 F4 G4 F4 G4
C4 D4 C4 D4 E4 D4
A3 G3 A3 G3 A3 G3

(min3-5 + Maj3-1) (min6-8 + min3-5) (min6-8 + min2-4)


C4 D4 E4 D4 E4 D4
A3 G4 C4 D4 A3 G3
F3 G3 F3 G3 F3 G3

(Maj3-1 + min3-5) (Maj7-5 + Maj3-1) (Maj7-5 + Maj3-1)


Adding the term _antepenultimate_ or A to describe the sonority or its
lowest note that precedes P, let us consider this approach to a
cadence on F:

1 2 3 | 1 2 3 | 1 2 3 ||
A4 F4 G4 F4 E4 F4
E4 C4 D4 C4 B3 C4
A3 G3 F3

A P U
(P/P)

We start with a trine on A, the antepenultimate, with an opposing
sixth sonority of A3-C4-F4 leading to a trine on G, the penultimate
step where a connecting sonority m7|4_4 leads to a cadential sixth
sonority G3-B3-E4 and a trine on F, the ultimate step.

An important feature of this idiom is that the A-P progression, here
from A3-C4-F4 to G3-D4-G4 (min6-8 + min3-5) could also serve as a
satisfying final or sectional cadence on G, in other words as a P-U
progression where G is the ultimate.

We might therefore describe the antepenultimate A as "the penultimate
of the penultimate" G, abbreviated P/P in the example. That is, the
antepenultimate-penultimate or A-P progression has a cadence-like
quality, with the step A acting rather like a penultimate to G, in
turn the penultimate to F in the concluding P-U progression.

This affinity between A-P and P-U is strengthened by the use in both
progressions of opposing sonorities of 6|3_4 (6-8 + 3-5) formed by
basic patterns of 8-6-8 and 5-3-5 in the two upper voices, varied by
the addition of connecting intervals (8-7-6-8, 5-4-3-5) in the second
progression. By adding these connecting intervals to the first or A-P
progression also, we could make the two progressions yet more
symmetrical:

1 2 3 | 1 2 3 | 1 2 3 ||
A4 G4 F4 G4 F4 E4 F4
E4 D4 C4 D4 C4 B3 C4
A3 G3 F3

A P U
(P/P)

This kind of A-P-U theme need not be so symmetrical, and in practice
composers find many charming variations, as with these passages from
the motet _Dieus! ou porrai/Chesont amouretes/OMNES_, Montpellier #288,
and the rondeau _Fines amouretes ai_ by Adam de la Halle, with the
order of voices arranged so as to place the lowest line in the lowest
voice:

1 2 3 | 1 2 + 3 | 1 ...
E4 F4 G4 F4 E4 D4 F4
E4 C4 D4 B3 C4
A3 G3 F3


1 + 2 3 | 1 2 3 + | 1 ...
E4 D4 E4 F4 G4 F4 E4 F4
A3 C4 D4 C4 B3 C4
A3 A3 G3 G3 F3

In these two examples we start from a fifth rather than a trine on A,
so that the A-G progressions have a mediating 5-6-8 pattern in the
highest voice, followed by G-F progressions with connecting and
opposing intervals. The middle voice of the first example has
symmetrical opposing patterns of 5-3-5 for both progressions, combined
with the varied interval patterns and rhythms in the highest voice.

This kind of "cadential chain" for the descent of A-G-F is one example
of a more general technique in which almost any motion from one
rhythmic unit to the next might be the occasion for a directed
progression involving the resolution of instability by contrary
motion.


---------------------------------
4. The step A as penultimate of F
---------------------------------

While progressions based on relationships such as F-G-F, F-G-A, or
A-G-F are typical of a style favoring directed resolutions based on
stepwise contrary motion, sometimes the step A can serve as a
penultimate to F, as in this beautiful final or internal cadence:

E4 F4
B3 C4
A3 F3

(Maj2-5)

A mildly unstable 5|M2_4 sonority expands to a complete trine, with
the lowest voice descending by a third and the upper voices ascending
stepwise in fourths. The lower voices have a resolution by what might
be called "near-conjunct" contrary motion from an unstable major
second to a fifth, with one voice moving by step and the other by a
third; the outer voices expand from a fifth to the octave of a trine.

A related formula has another mildly unstable sonority, 5|4_M2 -- the
same intervals as 5|M2_4, but with the fourth below and the major
second above:

E4 F4
D4 C4
A3 F3

(Maj2-4)

Here the major second expands to the upper fourth of the trine by
stepwise contrary motion, while the fifth of the first sonority again
expands to the outer octave of the resolving trine on F.

Jacobus of Liege catalogues and approves of both 5|4_M2 and 5|M2_4 as
partitions of the fifth, with the major second placed either above the
fourth, or conversely. We might refer to such sonorities with the same
intervals differently arranged as "conversities."

A 13th-century variation on the first progression, however, involves
two more acutely tense intervals considered full or thorough discords
by such theorists as Johannes de Garlandia, Franco, and Jacobus: the
minor second and the tritone:

E4 F4
Bb3 C4
A3 F3

(min2-5)

Here we have a sonority of A3-Bb3-E4, or 5|m2_A4, with the fifth
divided into minor second below and tritone above: the minor second
expands to a fifth, while the tritone moves by parallel motion to a
stable fourth and the outer fifth again expands to the octave of the
trine on F.

Although excluded because of its acutely tense intervals from the
catalogue of Jacobus, a sonority like A3-Bb3-E4 and its resolution
shown above seem to fit some remarks by Johannes de Garlandia around
the middle of the 13th century. He advises that any dissonant interval
followed by a stable concord is "equipollent" to that concord, giving
as one example a minor second before a fifth, a progression common in
two-voice as well as multi-voice compositions.

The term "equipollent" has been interpreted by modern scholars to mean
either that a discord when aptly resolved becomes "equivalent" in its
good musical effect to that of a stable concord; or that it should,
especially in freer rhythmic styles, be given a duration "equal" to
that of the resolving concord, thus lending extra emphasis to the
progression.

The above A-F resolutions with a 2-5 or 2-4 progression are open to
a range of treatments, for example with 5|M2_4 or 5|4_M2 occurring as
a mediating sonority:

1 2 3 | 1... 1 2 3 | 1
E4 F4 E4 F4
A3 B3 C4 E4 D4 C4
A3 F3 A3 F3

The first example has a mediating pattern of 1-2-5 between the lower
voices, and the second 1-2-4 between the upper voices.

Variations on these A-F progressions can occur, for example, when the
lowest voice has a figure of G-A-F, as in these two excerpts from the
motet _Salve, virgo virginum/Est il donc einsi/APTATUR_, Montpellier
#268, with triplets in the highest voice (actually the middle voice of
the texture) at the third beat of the second excerpt:

1 2 + 3 | 1... 1 + 2 3 + + | 1...
G4 F4 E4 D4 C4 D4 C4 D4 D4 C4 B3 C4
D4 E4 F4 D4 E4 F4
G3 A3 F3 G3 A3 F3

(Maj2-4) (Maj2-5)


-------------------------------------------------
5. A quick aside on melodic A-F: A gentle cadence
-------------------------------------------------

The above discussion of the step A as a penultimate to F addresses a
situation where the _lowest_ voice moves A-F.

However, a monophonic song with the melodic figure A-F can also be
treated as the middle voice of a mild and gentle cadence featuring
only stable intervals:

E4 F4
A3 C4
Accompaniment: E3 F3

Melody: A3 F3

Here the first sonority E3-A3-E4 or 8|4_5 has the fourth below and the
fifth above, relatively stable but less smooth and conclusive in
13th-century terms than the following F3-C4-F4 or 8|5_4. The effect
draws in part of a melodic attraction to F where that step or trine
is "home," and in part on the distinction between 8|4_5 and 8|5_4 as
conversities, or sonorities with the same intervals differently
arranged.


---------------------------------------------------
6. A theoretical digression on the F-A relationship
---------------------------------------------------

In response to Cait's suggestion that the treatment of the step A in a
piece with F as "home" and G as "away" can sometimes seem problematic,
I might offer a curious theoretical aside relating to polyphony.

Suppose we take a diatonic scale or octave species of F-F, and number
the degrees in ascending order from the final to its octave, using the
sign ^ to mark our degree numbers. Since the fourth degree is often
fluid, with both B and Bb included in the basic _musica recta_ gamut,
let's indicate this step flexibly as B/Bb:

^1 ^2 ^3 ^4 ^5 ^6 ^7 ^8
F3 G3 A3 B3/Bb3 C4 D4 E4 F4

Thus a complete trine on F, or F3-C4-F4, is ^1-^5-^8. Given that
directed medieval progressions often involve resolutions from unstable
to stable intervals by stepwise contrary motion, we might expect to
see and hear degrees _adjacent_ to these featured in penultimate
cadential sonorities. Consider this four-voice progression:

E4 F4 ^7 ^8
D4 C4 ^6 ^5
B3/Bb3 C4 ^4 ^5
G3 F3 or ^2 ^1

The penultimate sixth sonority G3-B3-D4-E4 and the stable F3-C4-F4
together include seven of the eight steps of our F-F octave species
(counting B and Bb as alternative versions of the same ^4, either of
which might occur in this cadential formula). The unstable sonority
features each step within the octave range which is adjacent to a step
of the resolving ^1-^5-^8 trine.

As this example illustrates, more generally in 13th-century cadences
we often have melodic motions of ^2-^1, ^4-^5, ^6-^5, and ^7-^8 in
relation to a given trine or octave species -- whether the final for
the whole piece, or simply the local goal of some directed
progression.

From a vertical point of view, this four-voice cadence also features
four directed resolutions of unstable intervals by stepwise contrary
motion: Maj6-8 between the outer voices, Maj2-4 between the upper pair
of voices, Maj3-5 or min3-5 between the lower pair (respectively with
B3 or Bb3), and min3-1 or Maj3-1 between the middle pair.

E4 F4 ^7-^8 E4 F4 ^7-^8 B3/Bb3 C4 ^4-^5 D4 C4 ^6-^5
G3 F3 or ^2-^1 D4 C4 or ^6-^5 G3 F3 or ^2-^1 B3/Bb3 C4 or ^4-^5

(Maj6-8) (Maj2-4) (Maj3-5 or (min3-1 or
min3-5) Maj3-1)

Curiously, the one step not represented in this cadence is ^3, or A3,
the only step which is neither part of the ^1-^5-^8 trine nor adjacent
to any of its steps.

When it occurs in a penultimate cadential role, ^3 might progress
either to the final or lowest note of the trine, or to the fifth,
moving a third to arrive at either step: that is ^3-^1 or ^3-^5, for
example:

E4 F4 ^7-^8 E4 F4 ^7-^8
B3/Bb3 C4 ^4-^5 A3 C4 ^3-^5
A3 F3 or ^3-^1 G3 F3 or ^2-^1

In the first progression, discussed in Section 4 on A-F resolutions,
the lowest voice moves ^3-^1, with a 2-5 progression between the lower
pair of voices.

In the second progression, a sonority of M6|M2_5, catalogued and
approved by Jacobus, resolves with another 2-5 progression between the
lower voices in which the middle voice moves ^3-^5, with a resolution
from major sixth to octave between the outer voices.

While the ^3-^1 and ^3-^5 motions thus can play a useful and colorful
role in 13th-century polyphonic cadences, they seem less prevalent
than the stepwise motions of ^2-^1, ^4-^5, ^6-^5, and ^7-^8.

Of course, this digression into the modern theory of trinic polyphony
in a medieval or neo-medieval style might be taken as a bit tangential
to questions regarding the treatment of the step A in monophonic songs
with a final of F. The traditional role of this step as a confinal or
reciting tone in Gregorian chant for example, might provide one
pattern to which vernacular songs with F as "home" could be compared.

Most appreciatively,

Margo Schulter
***@calweb.com

[Margo Schulter]

Hello, everyone, and please let me correct two mistaken octave numbers
in Part I of my recent post for Cait and others on the F-A
relationship in 13th-century polyphony and possible implications for
accompaniments to monophonic melodies. My warmest thanks to Roger

Post by Margo Schulter
Another three-voice solution for the F-G-A theme involves descending
motion of the outer voices, which again engage in fifthing, while the
middle voice ascends in contrary motion, treating A as the upper note
C4 B3 A4
F4 G3 A3
F3 E3 D3
(min3-5 + Maj3-1)

Please note that this should be:

C4 B3 A3
F3 G3 A3
F3 E3 D3

As a general guideline, I'd suggest that if my octave numbers indicate
the melodic skip of an interval like a seventh or ninth that I haven't
commented on in my post, then it's likely a mistake in the octave
numbers. I regret that despite my tendency to such mistakes, I can
find it easier to predict that they might happen again than to develop
an effective proofreading strategy, which is where helpful people like
Roger can at least help me alleviate some of the problem by posting
corrections.

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Hello again Margo (and all);

here's the figures to accompany Part IIB.

Again, these are for 4 course 4ths-tuned chromatic fretted string
instruments: lute, citole, guitarra latina, etc. [note; common lute tuning
would be 4-3-4 across four courses rather than the 4-4-4 used here.] Tuning
used is EADG (4ths tuning) like the lowest pitched 4 strings of guitar. A
Fretboard note speller (EADG) is at the top of the following URL list:

again, Figures having "v2" in their file-names are slightly modified
simplified voicings and fingerings, typically changing a sonority that
contains a Unison into a Trine, e.g. an F3-F3-C4 vertical stack might become
F3-C4-F4. Figures with no v2 are verbatim, exactly as given in the essay,
including Unisons (octave range is changed in some figures however).



whew! ;')

Alrighty. In a few days I'll be able to come back and start fresh (with more
tools at hand now), as if you had just posted your two-part essay, and make
some comments and ask questions.

Thanks
Roger


http://www.thecipher.com/mschulter_figs/fretspeller_4ths_EADG.gif


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Post by Margo Schulter
-----------------------------------------
An Essay with Thanks to Cait
Part IIB: The F-G-A question (2)
-----------------------------------------

.

Post by Margo Schulter
Most appreciatively,
Margo Schulter

[Margo Schulter]

( Dear Roger,

Please note that here I'm replying to a post before your latest one, and
I'll try to reply to the new one promptly.)

Post by Roger E. Blumberg
Hi Margo;
no problem, I hope it went well, and I'm happy to participate
(learn).

Hi, Roger. My project went well, and I'm pleased to be able to reply
to this post a bit more rapidly than the last time (thank you again
for your patience!).

[On the variety of unstable 13th-century sonorities, for example those
using thirds]

Post by Roger E. Blumberg
alrighty, I'm glad to be more clear on that now. It'll still take a
little more "re-programing" I suspect, made firm by putting it into
practice, to counter-act the long ingrained misconceptions
surrounding those sonorities in relation to medieval music, but I
think I'm getting it burned in now.

Yes, and please let me try to state this positively: my purpose is to
emphasize the wealth of unstable intervals and sonorities used in the
13th century, and the progressions and patterns that grow out of this
musical vocabulary.

Post by Roger E. Blumberg
[And my saying "analogous to Major and minor triads" was more for
the benefit of a reader who might be jumping in cold, that they'd at
least know which sonorities were being referred to ]

Please let me apologize if I was or seemed too judgmental in my
response; one's choice of language in making such comparisons might
often be a delicate dilemma.

Obviously, for example, a fretboard player accustomed to major and
minor triads might find it helpful to learn that 13th-century split
fifth sonorities (5|M3_m3 or 5|m3_M3) have the same basic interval
structures on the fretboard and can be found at the same locations.

If I were writing this for a textbook or other guide, I might say
something like the following:

"Readers may note that the mildly unstable split fifth sonority
of 5|M3_m3 or 5|m3_M3 has an interval structure analogous to
that of a stable major or minor triad in later European styles.
However, the musical contexts and usages are different: the
thirds of the medieval split fifth sonority are unstable
intervals, and often resolve by contracting to a unison or
expanding to a fifth, for example. This important stylistic
distinction is underscored by medieval Pythagorean tuning,
which makes major thirds, especially, more tense and active
intervals than in the later historical European tuning systems
favored for 16th-19th century music based on stable thirds."

Please let me also explain, for now, that as a medievalist I likely
have a certain sensitivity about fine points of language such as this
as a kind of reaction to things that get written in the literature;
that's a topic we can take up at more length, if you like.

Post by Roger E. Blumberg
ornaments and decorations, inter-mediating unstable sonorities --
the growing pallet.

Thank you for sharing my excitement about these themes, and for
expressing them in your own words. Obviously we both want to "get the
word out" to a wider community of musicians.

Post by Roger E. Blumberg
oh, good. That helps alot. Much accompaniment really is about taking
a skeletal motif and filling time in and around it in interesting
and tasteful ways, with variety, ornament and decoration, etc. So
anything that adds to that basic vocabulary of techniques, the ways
and means of doing it, adds up. And again, this is one of those
"universal logics" or approaches, it seems to me, as is the
split-time concept generally, i.e. the little tricks one uses over
and over to create the musical interest woven in and around a basic
framework.

Yes, I've sometimes compared these facets of 13th-century technique to
the figures of 17th-century continuo or thoroughbass. More generally,
it might be a question of the best approach to understand a given
style.

With 13th-century polyphony, as with some styles of 20th-century
counterpoint, there are few absolute "rules" -- rather, there are some
frequent and characteristic procedures that occur over and over again,
and lots of less common procedures that also occur.

That's why I'm hesitant to make categorical statements about what's
"legal" or "illegal" in 13th-century style -- especially when someone
might post a passage from a motet or conductus, etc., to contradict
one of my not-so-accurate generalizations!

What I try to do is to say, "This seems more characteristic to me," or
"Here's what I might do based on my own musical intuition, however
representative or otherwise of 13th-century practice."

Post by Roger E. Blumberg

Post by Margo Schulter
Yes, I love this kind of progression also! Again, we have the
"split time" theme as you have called it, or alternation between
stability and instability. What I'd want to emphasize is that
recognizing patterns like this can, in my view, much enhance the
enjoyment of 13th-century polyphony.

yep, they really are beautiful. And it seems to be coming true and
apparent that these alternations between stable and unstable, or
maybe repose-energetic-repose (because they certainly energize me
when I hear them ;') really is key. i.e. they are a "definer" of
this music and actually provide and embody the enjoyment, that's
where the pleasure lies. Remove that, and you no longer have the
music. So it's beyond enhancement, it's really the _is_ of it.

Please let me agree here: the alternation we're discussing is a very
basic feature of lots of 13th-century writing. One thing I should do
soon is to analyze a 13th-century passage to illustrate this point:
for example, there's such a passage which I recall is cited in an
article by Christopher Page.

[On distinction between what I call "mediating" and "opposing"
intervals or sonorities, the first approached and left in the same
direction, the second approached and left in opposite directions,
e.g. these M7|M3_5 sonorities both resolving Maj7-5 + Maj3-1:

F4 E4 D4 C4 E4 D4
C4 A3 G3 F3 A3 G3
F3 G3 F3 G3

(mediating) (opposing) ]

Post by Roger E. Blumberg
ok. So one can "inter-mediate" between intervals,
stable-unstable-stable, by using either mediating or opposing
_directional_ motion. (how's that?)

That's a nice statement of what I'm getting at.

Post by Roger E. Blumberg

Post by Margo Schulter
With this kind of cycle you can repeat it with various touches of
ornamentation or the like.

more ornamentation, ornamentation is good ;')

I'll give you another example below, warning you here and there that
my suggested figure is anything but original!

Post by Roger E. Blumberg

Post by Margo Schulter

Post by Roger E. Blumberg

Post by Margo Schulter
1 2 3 | 1 ...
D4 E4 F4
D4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)

http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.07.gif

I might note a complication of my nomenclature: here the highest
voice has a mediating tone (D4-E4-F4) giving the mediating interval
of major sixth between fifth and octave (5-M6-8), while the middle
voice has an opposing tone (D4-B3-C4) giving the opposing interval
of a major third between two fifths (5-M3-5). There are many
combinations or permutations for these patterns, and your general
usage of "mediating sonority" certainly applies.

"inter-mediating" sonorties (got it)

Yes, that might be about as descriptive a term as any. Maybe we could
speak generally of "bridging" sonorities -- mediating, opposing, or
connecting.

Post by Roger E. Blumberg

Post by Margo Schulter
E4 F4 G4
D4 E4 D4
A3 G3

that variation is beautiful too, and complex, and even discordant,
but hardly "inexplicable" i.e. if one "gets it".
This kind of sound is what I'm coming to expect and the thing that I
_like_ about it, this rich and sophisticated pallet, and
accomplished in a "less is more" fashion, a purity, where you can
really _feel_ and hear and appreciate and distinguish what's in the
mix. I might use an analogy of a deceptively "simple" inked or
etched line drawing that captures an "essence", expresses it more
purely, than a full-out oil painting might. The analogy might extend
to a Renaissance master's figure drawing or a 19th century Japanese
print, purity of line, and the fewer lines the better. It's really
the definition of sophisticated classic design, in all things and
ages. Again, we know what humans were producing in all other art
forms, their level of sophistication and capacity, so we can
extrapolate what they might have been striving for in their
music. i.e. if one is known to have appreciated "fine" art and
craftsmanship you know it applied to _all_ things. If you assume and
expect sophistication and you look for it, it's there. If you go in
expecting and presuming infantile or somehow adolescent and
under-developed capacity, taste, and practice, then that's probably
what you'll see -- and we would dis-honor them and ourselves if we
did that.

Thank you for these eloquent words. Too often, the literature does do
the kind of stereotyping which you're resisting: for example,
describing the style of a great 14th-century composer like Guillaume
de Machaut as "precocious polyphony." Here "precocious" seems to mean
mainly "in a style other than those taught in familiar counterpoint
and composition classes, starting around the 16th century."

Post by Roger E. Blumberg

Post by Margo Schulter
F4 E4 F4 E4
B3 A3 Bb3 A3
G3 A3 G3 A3
(min7-5 + Maj3-1) (min7-5 + min3-1)
Note that in both progressions the lower two voices have a 3-1, the
outer voices a 7-5, and the upper voices move together in fifths --
diminished and perfect in the first version, and both perfect in the
second version.

alrighty, and I can hear a lot of potential in that second
progression -- a "droney minor" (as it were).

To use another term which might capture the same quality you're
hearing as "minor," I'd call the second progression consistently
"remissive," that is, involving two-voice resolutions featuring
descending semitone motion. Let's quickly look at four permutations of
this general type of progression with an outer seventh resolving to a
fifth, and a lower third resolving to a unison (7-5 + 3-1):

Omnitonal Intensive Remissive Mixed

E4 D4 D4 C4 F4 E4 F4 E4
A3 G3 G3 F3 Bb3 A3 B3 A3
F3 G3 E3 F3 G3 A3 G3 A3

(Maj7-5 + Maj3-1) (min7-5 + min3-1) (min7-5 + min3-1) (min7-5 + Maj3-1)

In an omnitonal progression, unstable intervals resolve with each
voice moving by a whole-tone, here major seventh to fifth and major
third to unison.

In an intensive progression, we have resolutions where one voice
descends by a whole-tone while the other ascends by a semitone, as
with the min7-5 and min3-1 resolutions in our second example.

In a remissive progression, we have resolutions where one voice
ascends by a whole tone while the other descends by semitone, as with
the min7-5 and min3-1 resolutions in our third examples -- the same
unstable vertical intervals of the minor seventh and third as in the
second example, but motions involving descending rather than ascending
semitones.

In a "mixed" progression like our last example, we have two-voice
resolutions following different or "mixed" patterns: here the outer
min7-5 resolution is remissive (as in the previous example), but the
Maj3-1 resolution between the two lower voices is omnitonal.

What I want to point out is the diversity of melodic and vertical
colors that you get with these different "manners" of progressing, as
I call them, something I really relish in this music.

Post by Roger E. Blumberg
before I go, I wonder if I could explore that "chaining" idea a little
further. Using that same F-G-A progression kernel (and I'll use trines and
uncross some voices),
here's the one I inquired about, which got an "ok"
1 2 3 | 1
F4 C4 G4 D4 A4
C4 A3 D4 B3 E4
F3 G3 A3

Just a quick comment: if you wanted complete trines on the main beats
with more conjunct voice-leading, you could do this in four parts, for
example as I'd write it for voices (on a fretboard, you might
disregard the unisons):

1 2 3 | 1 2 3 | 1
F4 G4 A4
C4 D4 E4
C4 A3 G3 B3 A3
F3 G3 A3

Post by Roger E. Blumberg
so how about these next two?
F4 G4 A4
C4 D4 E4
F3 A3 G3 B3 A3

This is fine, I'd say -- you're doing sixth sonorities, or more
specifically 6|3_4, with opposing tones in the _lowest_ voice forming
patterns of 8-6-8 with the highest voice and 5-3-5 with the middle
voice.

Post by Roger E. Blumberg
and below, using 9th sonorities . .
G4 F4 A4 G4 A4
C4 D4 E4
F3 A3 G3 B3 A3

A 13th-century writer, Mechthild of Magdeburg if I recall correctly,
warns that "Power is dangerous" -- and this warning might apply not
least to people setting out to teach polyphony or counterpoint!

It's all too easy to formulate "rules" which happen not to fit the
actual style, or to do so less precisely and consistently than the
teacher might suppose.

We may really be discussing at least three different questions: what a
13th-century composer might do; what I would do; and what you should
do.

To attempt an answer to the first question, I'd want to survey
carefully what happens in 13th-century compositions when a split ninth
sonority occurs on a main beat, both generally and more specifically
in the rhythmic situation where the middle voice moves more slowly
than the two outer voices, as in your example. What I can tell you is
that passages with a lot more tension and prolonged instability than
in yours do occur, and this is a style with few categorical "rules."

Here's a first-blush musical reaction as to how I might go about this,
and in fact did find myself going about it on keyboard:

1 2 3 | 1 2 3 + | 1...
G4 E4 F4 A4 G4 F4 G4 A4
C4 A3 C4 D4 D4 E4
F3 A3 G3 B3 A3

In the first measure, the split ninth F3-C4-G4 resolves to the fifth
A3-E4, moving from there to your mediating sonority A3-C4-F4, which
invites a resolution to a trine on G.

Following your example, however, I've opened the next measure with a
split ninth on G, with the ninth then resolving obliquely to the
octave of the expected trine (M9-8); then we have a momentary sonority
with a diminished fifth, B3-D4-F4, leading to your sixth sonority
B3-D4-G4 and resolution to the trine A3-E4-A4.

Here's a variation featuring another quick sonority with a diminished
fifth at the end of the first measure, the sixth sonority A3-B3-F4 or
m6|M2_d5:

1 2 3 | 1 2 3 + | 1...
G4 E4 F4 A4 G4 F4 G4 A4
C4 A3 B3 D4 D4 E4
F3 A3 G3 B3 A3

By the way, as a nuance of color, we might also have an optional F#4
leading up to the conclusion of this example or my previous version:

1 2 3 | 1 2 3 + | 1...
G4 E4 F4 A4 G4 F#4 G4 A4
C4 A3 B3 D4 D4 E4
F3 A3 G3 B3 A3

Please be warned that in these examples I'm leaning toward things that
seem "characteristic" to me of more or less stock figures that might
often be repeated -- a choice reflecting certain patterns familiar to
me, or fitting a certain scheme of analysis. For example, I'm leaning
here toward the theme of "frequently alternating stability and
instability," biasing me toward more or less "standard" resolutions;
actual 13th-century practice is not always so conventional, and yours
needn't be either.

Post by Roger E. Blumberg
here's two more that are just excursions I'm curious about and I don't know
where else to insert them.
The first progression might be in the midst of something else or even a
concluding three chord phrase (slow and deliberate).

[Your first progression]

Post by Roger E. Blumberg
D4 F4 A4
C4 D4 E4
F3 A3

Here, again, I might do things a bit differently, although I wouldn't
be too surprised to find this or something like it in a 13th-century
source.

Let's consider that F3-C4-D4 sonority, or M6|5_M2. One "standard"
resolution is by directed contrary motion to a trine on E:

D4 E4
C4 B3
F3 E3

Here we have Maj6-8 plus Maj2-4 between the upper voices; this is what
I call a cadence in the remissive manner, by the way, with both
two-voice resolutions involving ascending whole-tone motion in the
highest voice and descending semitonal motion in a lower voice.

Another standard resolution is to have the sixth of the sonority
resolve to the fifth by oblique motion, leaving us with the stable
fifth F3-C4, to which the sixth could be considered a decoration:

D4 C4
C4
F3

Note that the highest voice has a Maj6-5 resolution with the lowest
voice, and a Maj2-1 resolution with the middle voice. This is what I
call an "obliquely resolving sonority," or ORS for short.

Here, however, there's a third kind of resolution which I'd be
inclined to use in order to follow the idea of moving from F to A in
the lowest voice:

1 2 3 | 1
D4 E4 F4 E4
C4 A3 D4 E4
F3 A3 A3

In this version, F3-C4-D4 resolves to the stable fifth A3-E4, with the
two upper voices making a Maj2-5 resolution by directed contrary
motion. Then A3-D4-F4 appears as a kind of decoration to this fifth
A3-E4, to which we then return, reaffirming it as a center either
momentarily or in a final cadence, for example.

Post by Roger E. Blumberg
The second progression is just combining some ideas suggested by
earlier progressions. The center voice is carrying the melody for
the most part, effecting a kind of voice-led melody-chording similar
to what we heard earlier and even intentionally moving to Unison
(which I've previously avoided due to fingering issues), and also
including some "rich" sonorities (e.g. FCD to FCE) of the kind I'm
beginning to sense might be "period appreciated". The first chord,
call it a "suspended quinta fissa" which I already know was
"appreciated" (not to mention all of the other rich progressions
you've shown us), pretty much sets the tone and stage for those
later rich sonorities, they seem to fit the definition of
appropriate (or at least plausible) taste by now (to me)
E4 D4 E4 G4 F4 ...
D4 C4 A3 C4 D4 B3 C4
A3 F3 G3 F3 A3

Here's what I might do -- and did find myself doing on keyboard

1 2 3 | 1 2 3 | 1 2 3 | 1 ...
E4 D4 C4 E4 G4 F4
D4 C4 B3 C4 D4 B3 C4
A3 F3 G3 F3

Post by Roger E. Blumberg
and I know that in the seventh (from the beginning) sonority above
(GBG) you might like to see an additional voice move, but I like it
this way, call it a "signature sonority" as long as it passes muster
generally I'd prefer to use it, it has a bell-like clearity that I
like and keep returning to, I resonate to it I guess.

Please note that I've left that progression as is, and would emphasize
that it's a perfectly valid resolution.

Why don't I explain how I went about my example. In the first measure,
we might describe A3-D4-E4 at the beginning and A3-B3-E4 at the end as
"co-directed" sonorities, both of which can invite a directed
resolution to the trine F3-C4-F4. Thus these unstable sonorities can
seem related, since both can point toward a common goal. We get more
into the topic of co-directed sonorities, but this is a first quick
mention of that topic.

Then A3-B3-E4 actually moves to F3-C4-D4, and I have the upper voice
resolve obliquely to the fifth F3-C4, so that the effect is that of a
decorated variation of the simple resolution to the trine on F. Then
the upper voice moves to the seventh of your sonority of F3-C4-E4,
which resolves to a G trine -- a variation on the resolution by
stepwise contrary motion to the fifth G3-D4. From there, I follow your
version.

Again, I'm not trying to define what's "right" or "wrong," only to
give my own musical responses; it's much easier with the kind of
conventional later 16th-century counterpoint often taught in music
education programs, for example, to make such judgments as to what's
"part of the style" or "out of the style."

More specifically, in my examples I'm leaning toward progressions
which have directed resolutions of unstable intervals by contrary
motion. This isn't so much a "rule" as one useful pattern, a bit like
a counterpoint example where the idea is to write suspensions at as
many appropriate points as possible. It's an interesting exercise, as
opposed to a definition of "correct" technique.

It's really important I emphasize this point with much due musicianly
humility, especially when sharing such a dialogue in public. You and
others deserve protection against the possible abuse of power which
someone discussing a less-often-taught style -- namely me -- might
inflict even unintentionally.

With that caution, I'd like to say again how much I'm enjoying the
dialogue, and how indebted I am to your participation and eloquent
statements about your own response to 13th-century music.


Most appreciatively,

Margo Schulter
***@calweb.com

P.S. Now for the ornamentation that I promised earlier in my reply,
and give with the caution that it's a commonplace which could easily
become a cliche if used too consistently. With the last example, if I
repeated the passage twice, I might the second time embellish the
concluding cadence:

1 2 3 | 1 2 3 | 1 2 3 | 1 ...
E4 D4 C4 E4 G4 F4
D4 C4 B3 C4 D4 B3 C4
A3 F3 G3 F3

1 2 3 | 1 2 3 | 1 + 2 + 3 | 1 ...
E4 D4 C4 E4 G4 F4 E4 D4 E4 F4
D4 C4 B3 C4 D4 B3 C4
A3 F3 G3 F3

This is a figure I heard around 1967 in one of the first medieval
albums I got: it's from a 13th-century motet in the Bamberg Codex
(#28), _Dieus! je fui ja pres de joir/Dieus! je n'i puisla nuit
dormir/ET VIDE ET INCLINA AUREM TUAM. This is an Archive recording by
Safford Cape and the Pro Musica Antiqua. By the way, the conclusion of
this motet shows how cadential figures lend themselves to lots of
variations, with the notation here representing 6/4 or 6/8, and with
"r" showing a rest:

1 2 3 4 + 5 + 6 | 1
F4 E4 G4 F4 E4 D4 E4 F4
C4 B3 G3 A3 B3 C4
F3 r G3 G3 F3

Notice, for example, that while lots of my examples tend to have
complete trines or fifths as stable sonorities on main beats, there's
no rule against having a simple octave, as here on the fourth beat;
there's lots of room for variety.

[Roger E. Blumberg]

Post by Margo Schulter
( Dear Roger,
Please note that here I'm replying to a post before your latest one, and
I'll try to reply to the new one promptly.)

Post by Roger E. Blumberg
Hi Margo;
no problem, I hope it went well, and I'm happy to participate
(learn).

Hi, Roger. My project went well, and I'm pleased to be able to reply
to this post a bit more rapidly than the last time (thank you again
for your patience!).
[On the variety of unstable 13th-century sonorities, for example those
using thirds]

Post by Roger E. Blumberg
alrighty, I'm glad to be more clear on that now. It'll still take a
little more "re-programing" I suspect, made firm by putting it into
practice, to counter-act the long ingrained misconceptions
surrounding those sonorities in relation to medieval music, but I
think I'm getting it burned in now.

Yes, and please let me try to state this positively: my purpose is to
emphasize the wealth of unstable intervals and sonorities used in the
13th century, and the progressions and patterns that grow out of this
musical vocabulary.

Post by Roger E. Blumberg
[And my saying "analogous to Major and minor triads" was more for
the benefit of a reader who might be jumping in cold, that they'd at
least know which sonorities were being referred to ]

Please let me apologize if I was or seemed too judgmental in my
response; one's choice of language in making such comparisons might
often be a delicate dilemma.
Obviously, for example, a fretboard player accustomed to major and
minor triads might find it helpful to learn that 13th-century split
fifth sonorities (5|M3_m3 or 5|m3_M3) have the same basic interval
structures on the fretboard and can be found at the same locations.
If I were writing this for a textbook or other guide, I might say
"Readers may note that the mildly unstable split fifth sonority
of 5|M3_m3 or 5|m3_M3 has an interval structure analogous to
that of a stable major or minor triad in later European styles.
However, the musical contexts and usages are different: the
thirds of the medieval split fifth sonority are unstable
intervals, and often resolve by contracting to a unison or
expanding to a fifth, for example. This important stylistic
distinction is underscored by medieval Pythagorean tuning,
which makes major thirds, especially, more tense and active
intervals than in the later historical European tuning systems
favored for 16th-19th century music based on stable thirds."

Thanks, I'll make note of this -- I feel a quote or least a paraphrase
coming on ;')

Post by Margo Schulter
Please let me also explain, for now, that as a medievalist I likely
have a certain sensitivity about fine points of language such as this
as a kind of reaction to things that get written in the literature;
that's a topic we can take up at more length, if you like.

Post by Roger E. Blumberg
ornaments and decorations, inter-mediating unstable sonorities --
the growing pallet.

Thank you for sharing my excitement about these themes, and for
expressing them in your own words. Obviously we both want to "get the
word out" to a wider community of musicians.

Post by Roger E. Blumberg
oh, good. That helps alot. Much accompaniment really is about taking
a skeletal motif and filling time in and around it in interesting
and tasteful ways, with variety, ornament and decoration, etc. So
anything that adds to that basic vocabulary of techniques, the ways
and means of doing it, adds up. And again, this is one of those
"universal logics" or approaches, it seems to me, as is the
split-time concept generally, i.e. the little tricks one uses over
and over to create the musical interest woven in and around a basic
framework.

Yes, I've sometimes compared these facets of 13th-century technique to
the figures of 17th-century continuo or thoroughbass. More generally,
it might be a question of the best approach to understand a given
style.
With 13th-century polyphony, as with some styles of 20th-century
counterpoint, there are few absolute "rules" -- rather, there are some
frequent and characteristic procedures that occur over and over again,
and lots of less common procedures that also occur.
That's why I'm hesitant to make categorical statements about what's
"legal" or "illegal" in 13th-century style -- especially when someone
might post a passage from a motet or conductus, etc., to contradict
one of my not-so-accurate generalizations!
What I try to do is to say, "This seems more characteristic to me," or
"Here's what I might do based on my own musical intuition, however
representative or otherwise of 13th-century practice."

alrighty, I understand the caution

Post by Margo Schulter

Post by Roger E. Blumberg

Post by Margo Schulter
Yes, I love this kind of progression also! Again, we have the
"split time" theme as you have called it, or alternation between
stability and instability. What I'd want to emphasize is that
recognizing patterns like this can, in my view, much enhance the
enjoyment of 13th-century polyphony.

yep, they really are beautiful. And it seems to be coming true and
apparent that these alternations between stable and unstable, or
maybe repose-energetic-repose (because they certainly energize me
when I hear them ;') really is key. i.e. they are a "definer" of
this music and actually provide and embody the enjoyment, that's
where the pleasure lies. Remove that, and you no longer have the
music. So it's beyond enhancement, it's really the _is_ of it.

Please let me agree here: the alternation we're discussing is a very
basic feature of lots of 13th-century writing. One thing I should do
for example, there's such a passage which I recall is cited in an
article by Christopher Page.
[On distinction between what I call "mediating" and "opposing"
intervals or sonorities, the first approached and left in the same
direction, the second approached and left in opposite directions,
F4 E4 D4 C4 E4 D4
C4 A3 G3 F3 A3 G3
F3 G3 F3 G3
(mediating) (opposing) ]

Post by Roger E. Blumberg
ok. So one can "inter-mediate" between intervals,
stable-unstable-stable, by using either mediating or opposing
_directional_ motion. (how's that?)

That's a nice statement of what I'm getting at.

Post by Roger E. Blumberg

Post by Margo Schulter
With this kind of cycle you can repeat it with various touches of
ornamentation or the like.

more ornamentation, ornamentation is good ;')

I'll give you another example below, warning you here and there that
my suggested figure is anything but original!

Post by Roger E. Blumberg

Post by Margo Schulter

Post by Roger E. Blumberg

Post by Margo Schulter
1 2 3 | 1 ...
D4 E4 F4
D4 B3 C4
G3 F3
(Maj6-8 + Maj3-5)

http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_fig2.07.gif

I might note a complication of my nomenclature: here the highest
voice has a mediating tone (D4-E4-F4) giving the mediating interval
of major sixth between fifth and octave (5-M6-8), while the middle
voice has an opposing tone (D4-B3-C4) giving the opposing interval
of a major third between two fifths (5-M3-5). There are many
combinations or permutations for these patterns, and your general
usage of "mediating sonority" certainly applies.

"inter-mediating" sonorties (got it)

Yes, that might be about as descriptive a term as any. Maybe we could
speak generally of "bridging" sonorities -- mediating, opposing, or
connecting.

"bridging sonorities" it is then

Post by Margo Schulter

Post by Roger E. Blumberg

Post by Margo Schulter
E4 F4 G4
D4 E4 D4
A3 G3

that variation is beautiful too, and complex, and even discordant,
but hardly "inexplicable" i.e. if one "gets it".
This kind of sound is what I'm coming to expect and the thing that I
_like_ about it, this rich and sophisticated pallet, and
accomplished in a "less is more" fashion, a purity, where you can
really _feel_ and hear and appreciate and distinguish what's in the
mix. I might use an analogy of a deceptively "simple" inked or
etched line drawing that captures an "essence", expresses it more
purely, than a full-out oil painting might. The analogy might extend
to a Renaissance master's figure drawing or a 19th century Japanese
print, purity of line, and the fewer lines the better. It's really
the definition of sophisticated classic design, in all things and
ages. Again, we know what humans were producing in all other art
forms, their level of sophistication and capacity, so we can
extrapolate what they might have been striving for in their
music. i.e. if one is known to have appreciated "fine" art and
craftsmanship you know it applied to _all_ things. If you assume and
expect sophistication and you look for it, it's there. If you go in
expecting and presuming infantile or somehow adolescent and
under-developed capacity, taste, and practice, then that's probably
what you'll see -- and we would dis-honor them and ourselves if we
did that.

Thank you for these eloquent words. Too often, the literature does do
the kind of stereotyping which you're resisting: for example,
describing the style of a great 14th-century composer like Guillaume
de Machaut as "precocious polyphony." Here "precocious" seems to mean
mainly "in a style other than those taught in familiar counterpoint
and composition classes, starting around the 16th century."

Post by Roger E. Blumberg

Post by Margo Schulter
F4 E4 F4 E4
B3 A3 Bb3 A3
G3 A3 G3 A3
(min7-5 + Maj3-1) (min7-5 + min3-1)
Note that in both progressions the lower two voices have a 3-1, the
outer voices a 7-5, and the upper voices move together in fifths --
diminished and perfect in the first version, and both perfect in the
second version.

alrighty, and I can hear a lot of potential in that second
progression -- a "droney minor" (as it were).

To use another term which might capture the same quality you're
hearing as "minor," I'd call the second progression consistently
"remissive," that is, involving two-voice resolutions featuring
descending semitone motion. Let's quickly look at four permutations of
this general type of progression with an outer seventh resolving to a
Omnitonal Intensive Remissive Mixed
E4 D4 D4 C4 F4 E4 F4 E4
A3 G3 G3 F3 Bb3 A3 B3 A3
F3 G3 E3 F3 G3 A3 G3 A3
(Maj7-5 + Maj3-1) (min7-5 + min3-1) (min7-5 + min3-1) (min7-5 + Maj3-1)
In an omnitonal progression, unstable intervals resolve with each
voice moving by a whole-tone, here major seventh to fifth and major
third to unison.
In an intensive progression, we have resolutions where one voice
descends by a whole-tone while the other ascends by a semitone, as
with the min7-5 and min3-1 resolutions in our second example.
In a remissive progression, we have resolutions where one voice
ascends by a whole tone while the other descends by semitone, as with
the min7-5 and min3-1 resolutions in our third examples -- the same
unstable vertical intervals of the minor seventh and third as in the
second example, but motions involving descending rather than ascending
semitones.
In a "mixed" progression like our last example, we have two-voice
resolutions following different or "mixed" patterns: here the outer
min7-5 resolution is remissive (as in the previous example), but the
Maj3-1 resolution between the two lower voices is omnitonal.
What I want to point out is the diversity of melodic and vertical
colors that you get with these different "manners" of progressing, as
I call them, something I really relish in this music.

ok, making note of four new terms:
Omnitonal, Intensive, Remissive, Mixed

these seem to be describing progression types by _resolution_ (but not
necessarily describing the texture or "sound" of a sonority, as one
containing both minor 3rd and minor 7th intervals, for example, sounds
"minor" to me ;') I don't know that there is a better term? I don't think
"Remissive" communicates the same thing.

Post by Margo Schulter

Post by Roger E. Blumberg
before I go, I wonder if I could explore that "chaining" idea a little
further. Using that same F-G-A progression kernel (and I'll use trines and
uncross some voices),
here's the one I inquired about, which got an "ok"
1 2 3 | 1
F4 C4 G4 D4 A4
C4 A3 D4 B3 E4
F3 G3 A3

Just a quick comment: if you wanted complete trines on the main beats
with more conjunct voice-leading, you could do this in four parts, for
example as I'd write it for voices (on a fretboard, you might
1 2 3 | 1 2 3 | 1
F4 G4 A4
C4 D4 E4
C4 A3 G3 B3 A3
F3 G3 A3

Post by Roger E. Blumberg
so how about these next two?
F4 G4 A4
C4 D4 E4
F3 A3 G3 B3 A3

This is fine, I'd say -- you're doing sixth sonorities, or more
specifically 6|3_4, with opposing tones in the _lowest_ voice forming
patterns of 8-6-8 with the highest voice and 5-3-5 with the middle
voice.

alrighty. This was the more important of the two for me, I seem to resort to
it alot.

Post by Margo Schulter

Post by Roger E. Blumberg
and below, using 9th sonorities . .
G4 F4 A4 G4 A4
C4 D4 E4
F3 A3 G3 B3 A3

A 13th-century writer, Mechthild of Magdeburg if I recall correctly,
warns that "Power is dangerous" -- and this warning might apply not
least to people setting out to teach polyphony or counterpoint!

we have pushed the boundaries at last I believe ;') (that's ok though, I
had to see what reaction it got. I'd probably never string that many
together like that anyway. On to your examples below now . . . )

Post by Margo Schulter
It's all too easy to formulate "rules" which happen not to fit the
actual style, or to do so less precisely and consistently than the
teacher might suppose.
We may really be discussing at least three different questions: what a
13th-century composer might do; what I would do; and what you should
do.
To attempt an answer to the first question, I'd want to survey
carefully what happens in 13th-century compositions when a split ninth
sonority occurs on a main beat, both generally and more specifically
in the rhythmic situation where the middle voice moves more slowly
than the two outer voices, as in your example. What I can tell you is
that passages with a lot more tension and prolonged instability than
in yours do occur, and this is a style with few categorical "rules."
Here's a first-blush musical reaction as to how I might go about this,
1 2 3 | 1 2 3 + | 1...
G4 E4 F4 A4 G4 F4 G4 A4
C4 A3 C4 D4 D4 E4
F3 A3 G3 B3 A3

well that wasn't so bad! I though I had crossed way over the line or
something. I like what you did, and in fact and you also just gave us a
sonority that had slipped through the crackes until just now, that B3-D4-F4
to B3-D4-G4 combo is cool. Wait a minute, the first of those is the missing
dim triad analogue! So what do we call this that sonority Margo, Diabolus
fissa?

Post by Margo Schulter
In the first measure, the split ninth F3-C4-G4 resolves to the fifth
A3-E4, moving from there to your mediating sonority A3-C4-F4, which
invites a resolution to a trine on G.
Following your example, however, I've opened the next measure with a
split ninth on G, with the ninth then resolving obliquely to the
octave of the expected trine (M9-8); then we have a momentary sonority
with a diminished fifth, B3-D4-F4, leading to your sixth sonority
B3-D4-G4 and resolution to the trine A3-E4-A4.
Here's a variation featuring another quick sonority with a diminished
fifth at the end of the first measure, the sixth sonority A3-B3-F4 or
1 2 3 | 1 2 3 + | 1...
G4 E4 F4 A4 G4 F4 G4 A4
C4 A3 B3 D4 D4 E4
F3 A3 G3 B3 A3

Wow! that's _really_ cool.

Post by Margo Schulter
By the way, as a nuance of color, we might also have an optional F#4
1 2 3 | 1 2 3 + | 1...
G4 E4 F4 A4 G4 F#4 G4 A4
C4 A3 B3 D4 D4 E4
F3 A3 G3 B3 A3

that's very nice too -- those last 5 chords as a free standing unit even,
excellent bit of vocabulary. It doesn't get much better than that under any
circumstances or periods, me thinks.

Post by Margo Schulter
Please be warned that in these examples I'm leaning toward things that
seem "characteristic" to me of more or less stock figures that might
often be repeated -- a choice reflecting certain patterns familiar to
me, or fitting a certain scheme of analysis. For example, I'm leaning
here toward the theme of "frequently alternating stability and
instability," biasing me toward more or less "standard" resolutions;
actual 13th-century practice is not always so conventional, and yours
needn't be either.

again, if this is "conventional", standard resolutions, I'm perfectly
content.

Post by Margo Schulter

Post by Roger E. Blumberg
here's two more that are just excursions I'm curious about and I don't know
where else to insert them.
The first progression might be in the midst of something else or even a
concluding three chord phrase (slow and deliberate).

[Your first progression]

Post by Roger E. Blumberg
D4 F4 A4
C4 D4 E4
F3 A3

Here, again, I might do things a bit differently, although I wouldn't
be too surprised to find this or something like it in a 13th-century
source.
Let's consider that F3-C4-D4 sonority, or M6|5_M2. One "standard"
D4 E4
C4 B3
F3 E3

that's a nice one

Post by Margo Schulter
Here we have Maj6-8 plus Maj2-4 between the upper voices; this is what
I call a cadence in the remissive manner, by the way, with both
two-voice resolutions involving ascending whole-tone motion in the
highest voice and descending semitonal motion in a lower voice.
Another standard resolution is to have the sixth of the sonority
resolve to the fifth by oblique motion, leaving us with the stable
D4 C4
C4
F3
Note that the highest voice has a Maj6-5 resolution with the lowest
voice, and a Maj2-1 resolution with the middle voice. This is what I
call an "obliquely resolving sonority," or ORS for short.
Here, however, there's a third kind of resolution which I'd be
inclined to use in order to follow the idea of moving from F to A in
1 2 3 | 1
D4 E4 F4 E4
C4 A3 D4 E4
F3 A3 A3

I can live with that. It's really just a little more fill, something that
even the singers could be adding, the extra bits, more implied melody
smoothing (or something).

Post by Margo Schulter
In this version, F3-C4-D4 resolves to the stable fifth A3-E4, with the
two upper voices making a Maj2-5 resolution by directed contrary
motion. Then A3-D4-F4 appears as a kind of decoration to this fifth
A3-E4, to which we then return, reaffirming it as a center either
momentarily or in a final cadence, for example.

Post by Roger E. Blumberg
The second progression is just combining some ideas suggested by
earlier progressions. The center voice is carrying the melody for
the most part, effecting a kind of voice-led melody-chording similar
to what we heard earlier and even intentionally moving to Unison
(which I've previously avoided due to fingering issues), and also
including some "rich" sonorities (e.g. FCD to FCE) of the kind I'm
beginning to sense might be "period appreciated". The first chord,
call it a "suspended quinta fissa" which I already know was
"appreciated" (not to mention all of the other rich progressions
you've shown us), pretty much sets the tone and stage for those
later rich sonorities, they seem to fit the definition of
appropriate (or at least plausible) taste by now (to me)
E4 D4 E4 G4 F4 ...
D4 C4 A3 C4 D4 B3 C4
A3 F3 G3 F3 A3

Here's what I might do -- and did find myself doing on keyboard
1 2 3 | 1 2 3 | 1 2 3 | 1 ...
E4 D4 C4 E4 G4 F4
D4 C4 B3 C4 D4 B3 C4
A3 F3 G3 F3

actually, I had a B in the first measure originally, but still concluding
the measure with a Unison (AAE), so the run went DCBA at one point.
resolving on the droney Unison. And I like the C4 in the second measure too
(if I finger pick this a little I can strike that C4 an extra time before I
switch to the E4, meaning I can get a similar effect, similar emphasized
melody line, without having to form the literal FCC voicing. I just hold the
FCD shape and give the C note an extra pluck at the end before moving to the
FCE fingering). Again, I'm thinking in terms of accompaniment underneath any
number of possible melody ornaments and variations. So your suggestions help
verify for me additional options. I thought I was doing a "good thing"
resolving to a Unison in the first measure (AAE), having been avoiding
Unisons as much as possible previously. But I like leaving it at B even
more. So good. Danka

Post by Margo Schulter

Post by Roger E. Blumberg
and I know that in the seventh (from the beginning) sonority above
(GBG) you might like to see an additional voice move, but I like it
this way, call it a "signature sonority" as long as it passes muster
generally I'd prefer to use it, it has a bell-like clearity that I
like and keep returning to, I resonate to it I guess.

Please note that I've left that progression as is, and would emphasize
that it's a perfectly valid resolution.

ok, thanks, cool. We are valid! And I think it's pretty too ;')

Post by Margo Schulter
Why don't I explain how I went about my example. In the first measure,
we might describe A3-D4-E4 at the beginning and A3-B3-E4 at the end as
"co-directed" sonorities, both of which can invite a directed
resolution to the trine F3-C4-F4. Thus these unstable sonorities can
seem related, since both can point toward a common goal. We get more
into the topic of co-directed sonorities, but this is a first quick
mention of that topic.
Then A3-B3-E4 actually moves to F3-C4-D4, and I have the upper voice
resolve obliquely to the fifth F3-C4, so that the effect is that of a
decorated variation of the simple resolution to the trine on F. Then
the upper voice moves to the seventh of your sonority of F3-C4-E4,
which resolves to a G trine -- a variation on the resolution by
stepwise contrary motion to the fifth G3-D4. From there, I follow your
version.
Again, I'm not trying to define what's "right" or "wrong," only to
give my own musical responses; it's much easier with the kind of
conventional later 16th-century counterpoint often taught in music
education programs, for example, to make such judgments as to what's
"part of the style" or "out of the style."
More specifically, in my examples I'm leaning toward progressions
which have directed resolutions of unstable intervals by contrary
motion. This isn't so much a "rule" as one useful pattern, a bit like
a counterpoint example where the idea is to write suspensions at as
many appropriate points as possible. It's an interesting exercise, as
opposed to a definition of "correct" technique.
It's really important I emphasize this point with much due musicianly
humility, especially when sharing such a dialogue in public. You and
others deserve protection against the possible abuse of power which
someone discussing a less-often-taught style -- namely me -- might
inflict even unintentionally.

I remain pain free, no wounds, not a one, Margo ;') (and I appreciate your
sensitivity).

Post by Margo Schulter
With that caution, I'd like to say again how much I'm enjoying the
dialogue, and how indebted I am to your participation and eloquent
statements about your own response to 13th-century music.

thanks, me too.

Roger

Post by Margo Schulter
Most appreciatively,
Margo Schulter
P.S. Now for the ornamentation that I promised earlier in my reply,
and give with the caution that it's a commonplace which could easily
become a cliche if used too consistently. With the last example, if I
repeated the passage twice, I might the second time embellish the
1 2 3 | 1 2 3 | 1 2 3 | 1 ...
E4 D4 C4 E4 G4 F4
D4 C4 B3 C4 D4 B3 C4
A3 F3 G3 F3
1 2 3 | 1 2 3 | 1 + 2 + 3 | 1 ...
E4 D4 C4 E4 G4 F4 E4 D4 E4 F4
D4 C4 B3 C4 D4 B3 C4
A3 F3 G3 F3
This is a figure I heard around 1967 in one of the first medieval
albums I got: it's from a 13th-century motet in the Bamberg Codex
(#28), _Dieus! je fui ja pres de joir/Dieus! je n'i puisla nuit
dormir/ET VIDE ET INCLINA AUREM TUAM. This is an Archive recording by
Safford Cape and the Pro Musica Antiqua. By the way, the conclusion of
this motet shows how cadential figures lend themselves to lots of
variations, with the notation here representing 6/4 or 6/8, and with
1 2 3 4 + 5 + 6 | 1
F4 E4 G4 F4 E4 D4 E4 F4
C4 B3 G3 A3 B3 C4
F3 r G3 G3 F3
Notice, for example, that while lots of my examples tend to have
complete trines or fifths as stable sonorities on main beats, there's
no rule against having a simple octave, as here on the fourth beat;
there's lots of room for variety.

(and that has two more momentary sonorites we haven't heard before here, GAE
and GAD) . . .

[Roger E. Blumberg]

Hi Margo (and fellow players);

Here's the fretboard illustrations of the three chaining solutions I asked
about in the above message . . .
Loading Image...

and then the three solution variations Margo gave for the last chaining
idea, the one incorporating 9th sonorities . . .

Loading Image...

the solutions you gave, Margo, are too cool to let them get away without
illustrations.

Thanks
Roger

Post by Roger E. Blumberg

Post by Margo Schulter
( Dear Roger,
Please note that here I'm replying to a post before your latest one, and
I'll try to reply to the new one promptly.)

Post by Roger E. Blumberg
before I go, I wonder if I could explore that "chaining" idea a little
further. Using that same F-G-A progression kernel (and I'll use trines

and

Post by Margo Schulter

Post by Roger E. Blumberg
uncross some voices),
here's the one I inquired about, which got an "ok"
1 2 3 | 1
F4 C4 G4 D4 A4
C4 A3 D4 B3 E4
F3 G3 A3
so how about these next two?
F4 G4 A4
C4 D4 E4
F3 A3 G3 B3 A3

This is fine, I'd say -- you're doing sixth sonorities, or more
specifically 6|3_4, with opposing tones in the _lowest_ voice forming
patterns of 8-6-8 with the highest voice and 5-3-5 with the middle
voice.

alrighty. This was the more important of the two for me, I seem to resort to
it alot.

Post by Margo Schulter

Post by Roger E. Blumberg
and below, using 9th sonorities . .
G4 F4 A4 G4 A4
C4 D4 E4
F3 A3 G3 B3 A3

A 13th-century writer, Mechthild of Magdeburg if I recall correctly,
warns that "Power is dangerous" -- and this warning might apply not
least to people setting out to teach polyphony or counterpoint!
It's all too easy to formulate "rules" which happen not to fit the
actual style, or to do so less precisely and consistently than the
teacher might suppose.
We may really be discussing at least three different questions: what a
13th-century composer might do; what I would do; and what you should
do.
To attempt an answer to the first question, I'd want to survey
carefully what happens in 13th-century compositions when a split ninth
sonority occurs on a main beat, both generally and more specifically
in the rhythmic situation where the middle voice moves more slowly
than the two outer voices, as in your example. What I can tell you is
that passages with a lot more tension and prolonged instability than
in yours do occur, and this is a style with few categorical "rules."
Here's a first-blush musical reaction as to how I might go about this,
1 2 3 | 1 2 3 + | 1...
G4 E4 F4 A4 G4 F4 G4 A4
C4 A3 C4 D4 D4 E4
F3 A3 G3 B3 A3

well that wasn't so bad! I though I had crossed way over the line or
something. I like what you did, and in fact and you also just gave us a
sonority that had slipped through the crackes until just now, that B3-D4-F4
to B3-D4-G4 combo is cool. Wait a minute, the first of those is the missing
dim triad analogue! So what do we call this that sonority Margo, Diabolus
fissa?

Post by Margo Schulter
In the first measure, the split ninth F3-C4-G4 resolves to the fifth
A3-E4, moving from there to your mediating sonority A3-C4-F4, which
invites a resolution to a trine on G.
Following your example, however, I've opened the next measure with a
split ninth on G, with the ninth then resolving obliquely to the
octave of the expected trine (M9-8); then we have a momentary sonority
with a diminished fifth, B3-D4-F4, leading to your sixth sonority
B3-D4-G4 and resolution to the trine A3-E4-A4.
Here's a variation featuring another quick sonority with a diminished
fifth at the end of the first measure, the sixth sonority A3-B3-F4 or
1 2 3 | 1 2 3 + | 1...
G4 E4 F4 A4 G4 F4 G4 A4
C4 A3 B3 D4 D4 E4
F3 A3 G3 B3 A3

Wow! that's _really_ cool.

Post by Margo Schulter
By the way, as a nuance of color, we might also have an optional F#4
1 2 3 | 1 2 3 + | 1...
G4 E4 F4 A4 G4 F#4 G4 A4
C4 A3 B3 D4 D4 E4
F3 A3 G3 B3 A3

that's very nice too -- those last 5 chords as a free standing unit even,
excellent bit of vocabulary. It doesn't get much better than that under any
circumstances or periods, me thinks.

Post by Margo Schulter
Please be warned that in these examples I'm leaning toward things that
seem "characteristic" to me of more or less stock figures that might
often be repeated -- a choice reflecting certain patterns familiar to
me, or fitting a certain scheme of analysis. For example, I'm leaning
here toward the theme of "frequently alternating stability and
instability," biasing me toward more or less "standard" resolutions;
actual 13th-century practice is not always so conventional, and yours
needn't be either.

again, if this is "conventional", standard resolutions, I'm perfectly
content.

[Margo Schulter]

Post by Roger E. Blumberg
Hi Margo (and fellow players);
Here's the fretboard illustrations of the three chaining solutions I asked
about in the above message . . .
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_chains.gif
and then the three solution variations Margo gave for the last chaining
idea, the one incorporating 9th sonorities . . .
http://www.thecipher.com/mschulter_figs/ms01-19-04_PrtI_chain3-alts.gif

Hi, there, Roger, and please let me just thank you for these fretboard
illustrations; I'm about to post another set of possible solutions, and
want to express my appreciation for your efforts to make this music
more accessible.

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Hi Margo;

ok, a few comments and questions on Part IIB. . .

You open with a list of a dozen directed two-chord progressions. Amoung them
are three that are new to us, these . . .

Post by Margo Schulter
D4 C4 D4 C4
B3 C4 G3 F3
E3 F3 E3 F3
(min7-5 + min3-1) (min7-5 + min3-1)
E4 D4
C4 D4
F3 G3
(Maj7-5 + Maj3-1)

that last one in particular is "today's favorite" ;') I've been playing
that all along within my own little excursions, so I'm very happy to
see/hear it included for our "everyday-fare" concideration.

two figures later is this (below), in which I just want to make note of the
first four chord phrase. It seems to have potential as free standing cycle
(something to add to our vacabulary)
http://www.thecipher.com/mschulter_figs/ms01-19-04_Prt2_fig3.04.gif
I just don't want it to get away without making note of it.

Post by Margo Schulter
1 2 3 | 1 2 3 | 1 2 3 ||
A4 G4 F4 G4 F4 E4 F4
E4 D4 C4 D4 C4 B3 C4
A3 G3 F3
A P U
(P/P)

Next, are two variations of the above. In the first, (passage from the motet
_Dieus! ou porrai/Chesont amouretes/OMNES_, Montpellier #288) in the forth
chord we see a G B F sonirity (no flat on the B), this I inquired about in a
P.S. at end of my Part IIA coments. In this particulat passage we skip right
through it but I wonder if we can take a little time to explore it a little
further.

Post by Margo Schulter
1 2 3 | 1 2 + 3 | 1 ...
E4 F4 G4 F4 E4 D4 F4
E4 C4 D4 B3 C4
A3 G3 F3

In General, this progresson is moving A to G to F, and everything in between
is the fill, the interest and color (the stuff that makes it music). Can we
reduce this a little and see how this stands up, or see if we can milk or
emphasis that chord a little? as here . . .

E4 F4 G4 F4 F4
E4 C4 D4 B3 C4
A3 G3 F3


. . or, how about making a short repeating cyle of this three chord phrase,
some kind of bouncy dance rhythm, and end on the F trine, or insert that
little turnaround (ACF) and repeat the whole thing again?

F4 E4 D4 F4 [F4]
B3 C4 [C4]
G3 F3 [A3]
[repeat 2x] [turn-around and repeat]


This sonority has the makings of a Dominant 7th chord (no 5th -- R, 3, b7)
and even when it's not used in a V-I configuration or resolution it's a very
distinct "sound" to have in one's pallet. In our original example it's used
only "in passing", but somewhere along the line someone stopped and said
"hey this is an intersting sound (this along with the minor 7th varient, no
5th -- R, b3, b7), maybe we can milk this a little".

here's the "minor" variation, using Bb -- which I like even more. Though it
has a more "minor" sound to it, I'm playing it in a kind of care-free
"skipping along" rhythum. And this is employing that kind of melody-chord
voice-leading we saw in PartIIA, here it's a descending line . . .

F4 E4 D4 E4 F4 [F4]
Bb3 C4 [C4]
G3 F3 [A3]
[turn-around and repeat]


This is straying a bit from the A-G-F theme, but that's how music works I
guess, one thing leads to another, and I for one have to follow to see where
it leads me ;') Actually, you can see where this came from if you tack it on
to the original begining of the example:

1 2 3 | 1 2 [new stuff .....
E4 F4 G4 F4 F4 E4 D4 E4 F4
E4 C4 D4 B3 Bb3 C4
A3 G3 G3 F3


now, let me tack that on to another phrase I came up with a few days ago
playing with the general F to A theme:

[a few days ago . . [today's stuff .....
D4 F4 A4 F4 E4 D4 E4 F4
C4 D4 E4 Bb3 C4
F3 A3 A3 G3 F3

and now we'll sex it up just a little more ;'). .(with that third chord)
*
D4 F4 G4 F4 E4 D4 E4 F4
C4 D4 E4 Bb3 C4
F3 A3 A3 G3 F3


Margo, you open up a Pandora's box when you show me all those pretty chords
and passages ;') I think any musician would have run with them. And I
think I'm beginning to sense what they might have liked. They were not
strangers to "richness", they liked it. And they liked "sexy" chords -- I've
heard too many already, in the examples you give, to believe otherwise. And
I'm sure they liked "sexy" rhythms too. Secret's out ;').

And of course, now that I think of it, many of these are sonorities the
_3rds_ in them. Virtually all (?) of the "interest" in the many examples
we've seen so far was a function of the inter-mediating and connecting
sonorities, containing either 3rds or their inversions (6ths), or 7ths and
their inversions, 9ths. i.e. today, that's how we might conceptualize them.
There was also the third specie of split fifth analogous to a suspension
(4th or 11th), e.g. G3 C4 D4. In other words we have a full pallet here, and
some very rich sophisticated music, simple as it might seem. We have the
functional equivalent or triads, 6ths, 7ths, 9ths, 11ths/sus, nothing is
missing (i.e. by "modern" standards). For much of this, I don't even _want_
to add a fourth voice (so I could do a full strum, lets say) because in many
of these cases "less is more". It's also a little more artful to have to
"design" everthing to occure within just three voices. "Dropping tones", as
it were, was common. Even back then, they were "dropping the fifth" from
their 7th sonorities. They might drop 3rds from their 6th sonorities, and of
course in their suspensions too. So both the pallet and the technique is
not so different from today.
[And if we ever allow, matter-of-factly, that they might have been doing
this on their fretted 4ths or lute tuned string instruments as well, then
the parallels are _really_ striking. I feel right at home playing this on my
instrument, it feels right, and I think it would have felt right to them
too. It's certianly a great way to compose songs, then as now. How else were
they doing it, I might ask, particularly the secular and dance music?]

At any rate, I guess that's enough for that aside, back to business . .


We left off at the second variation, this one by Adam Hale, similar to the
full Rondeau we heard at the end of Part I of this essay.
http://www.thecipher.com/mschulter_figs/ms01-19-04_Prt2_fig3.05b.gif
http://www.thecipher.com/mschulter_figs/ms01-19-04_Prt2_fig3.05bV2.gif

this time I'll just make note of the mediating melody-leading
connecting-chords between the primary degrees, A - G - F, particularly the
final 5 sonorities of which the middle three are the fill between degrees G
and F.
Here are those final 5 chords. When I say "make note" I just mean as a
reminder to myself of what's taking place. It's very pretty of course, as
it is in the full Randeau.

1 2 3 + | 1 ...
G4 F4 E4 F4
D4 C4 B3 C4
G3 G3 F3


Now we move to point 4, The step A as penultimate of F.

Post by Margo Schulter
E4 F4
B3 C4
A3 F3
(Maj2-5)

Margo, how about this variation (A3 in bass of Ultimate)? Played in a
slightly higher register/octave perhaps:


E4 F4
B3 C4
A3 A3





second example is . .

Post by Margo Schulter
E4 F4
D4 C4
A3 F3
(Maj2-4)

that employs the suspended-type split-fifth


how about inserting this for extra smoothing/mediation and melody. . ?

E4 F4
D4 C4 C4
A3 F3



at any rate, here we've been cataloguing species of split-fifth, so far
including these four (in modern notion anologues):

R 2 5
R 3 5
R b3 5
R 4 5

We just did R,4,5 and R,2,5 and now a surprise . . .

the third example (below next) is, ouch! where'd that come from Margo! ;')

Post by Margo Schulter
A 13th-century variation on the first progression, however, involves
two more acutely tense intervals considered full or thorough discords
by such theorists as Johannes de Garlandia, Franco, and Jacobus: the
E4 F4
Bb3 C4
A3 F3
(min2-5)

this extremly dissonant member of the split-fifth family I never in my life
would have expected to see/hear, let alone learn it was judged and prescibed
by famous theorists as being ok?, useful? fair game? flirting with the devil
were they?! I was going to ask at some point about some kind of diminished
triad analogue. But if this sonority is ok there definately could be no
objection to diminished chords, I'm guessing. Boy, this is really pushing
the envelope, by anyone's or any ages' standards. I'd like to hear this
executed in context someday. In the mean time, it goes in my "truth is
stranger than fiction" files. If nothing else (because I can't imagine I'd
personally ever use it myself) it'll remain as my strongest reminder of how
tolerant the environment probably was. Seems to me there's some mighty big
misconceptions floating around and persisting, being perpetuated, regarding
the medieval musician's mind-set -- e.g. their supposed
love/appreciation/acceptance of consonance only (which seems utterly silly
after hearing all of the sonorities and progressions we're gone though in
the course of this essay). This particular sonority is some kind of monkey
wrench in that wide-spread misperception. You say; "a progression common in
two-voice as well as multi-voice compositions". I'll take your word for it
and will try to understand it (till the day I die ;'). On the other hand,
perhaps it was meant to be played as a passing ornament? Virtually anything
goes in ornamentation if you pass through it quick enough, so that I could
understand.

Post by Margo Schulter
Variations on these A-F progressions can occur, for example, when the
lowest voice has a figure of G-A-F, as in these two excerpts from the
motet _Salve, virgo virginum/Est il donc einsi/APTATUR_, Montpellier
#268, with triplets in the highest voice (actually the middle voice of
1 2 + 3 | 1... 1 + 2 3 + + | 1...
G4 F4 E4 D4 C4 D4 C4 D4 D4 C4 B3 C4
D4 E4 F4 D4 E4 F4
G3 A3 F3 G3 A3 F3
(Maj2-4) (Maj2-5)

the last part of that second example above. . .

D4 C4 B3 C4
E4 F4
A3 F3

. . . is very much like the "excursion" example I included at the end of my
PartIIA comments, so this answers half of my questions regarding it.




Moving to point #5

here's an intersting dirge

Post by Margo Schulter
E4 F4
A3 C4
Accompaniment: E3 F3
Melody: A3 F3

http://www.thecipher.com/mschulter_figs/ms01-19-04_Prt2_fig5.01.gif

this could be quintessential Hollywood cliché of medieval "impending doom",
death and darkness, plague and inquisition, theme.


Alrighy, I'm going to end here, but I want to recall one progression from
weeks or months ago, an early one that bowled me over, stunned me with it's
beauty, and still does. It must have left a big impression on me because
I've played it at least once every day since I first heard it, and every
time I do I'm reminded of how much medieval Europeans loved polyphony, and
how well they could do it. This little progression says it all to me. It's
really all I needed to hear.

D4 E4 F4
C4 B3 C4
G3 F3


Thanks Margo
Roger

[Roman Turovsky]

Post by Roger E. Blumberg
_3rds_ in them. Virtually all (?) of the "interest" in the many examples
we've seen so far was a function of the inter-mediating and connecting
sonorities, containing either 3rds or their inversions (6ths), or 7ths and
their inversions, 9ths. i.e. today, that's how we might conceptualize them.
There was also the third specie of split fifth analogous to a suspension
(4th or 11th), e.g. G3 C4 D4. In other words we have a full pallet here, and
some very rich sophisticated music, simple as it might seem.

In fact, at the Mala Punica concert in NYC a couple years ago there was a
13th cent. motet with suspended 9ths that made one think of
Puccini.................
RT

[Margo Schulter]

Post by Margo Schulter
E4 D4
C4 D4
F3 G3
(Maj7-5 + Maj3-1)
that last one in particular is "today's favorite" ;') I've been
playing that all along within my own little excursions, so I'm very
happy to see/hear it included for our "everyday-fare" concideration.

Hello, there, Roger, and this occurs with various degrees of rhythmic
emphasis in 13th-century pieces; for example, Petrus de Cruce uses it
very beautifully in a motet.

[On idiom of "antepenultimate-penultimate-ultimate" or A-P-U variety,
with a vertical sequence of 8-7-6-8 and 5-4-3-5 figures]

Post by Margo Schulter
A4 G4 F4 G4 F4 E4 F4
E4 D4 C4 D4 C4 B3 C4
A3 G3 F3
A P U
(P/P)
Next, are two variations of the above. In the first, (passage from
the motet _Dieus! ou porrai/Chesont amouretes/OMNES_, Montpellier
#288) in the forth chord we see a G B F sonirity (no flat on the B),
this I inquired about in a P.S. at end of my Part IIA coments. In
this particulat passage we skip right through it but I wonder if we
can take a little time to explore it a little further.

Certainly, and your examples are helpful in pointing out certain
distinctions.

Post by Margo Schulter
1 2 3 | 1 2 + 3 | 1 ...
E4 F4 G4 F4 E4 D4 F4
E4 C4 D4 B3 C4
A3 G3 F3
In General, this progresson is moving A to G to F, and everything in between
is the fill, the interest and color (the stuff that makes it music). Can we
reduce this a little and see how this stands up, or see if we can milk or
emphasis that chord a little? as here . . .
E4 F4 G4 F4 F4
E4 C4 D4 B3 C4
A3 G3 F3

Here I would say that if we keep the goal of this passage as F, then
the sonority G3-B3-F4 is rather incidental, although colorful, and the
sonority G3-B3-E4 or G3-B3-D4 the point of directed instability. Thus
if our purpose is to do a "reduction" with a simplified second measure,
following this rhythm, I would prefer either of these:

1 2 3 | 1 2 3 | 1 ...
E4 F4 G4 E4 F4
E4 C4 D4 B3 C4
A3 G3 F3

or

1 2 3 | 1 2 3 | 1 ...
E4 F4 G4 D4 F4
E4 C4 D4 B3 C4
A3 G3 F3

If we want the G3-B3-F4 sonority, and a goal of F, then I might do
something like this, more ornamented than these examples but still a
bit simpler than the original passage from the motet:

1 2 3 | 1 2 3 | 1 ...
E4 F4 G4 F4 E4 F4
E4 C4 D4 B3 C4
A3 G3 F3

Here's another option:

1 2 3 | 1 2 3 | 1 ...
E4 F4 G4 F4 E4
E4 C4 D4 B3 A4
A3 G3 A3

Note that I've followed your reduction in having a more prolonged
G3-B3-F4, and then followed it with a standard directed resolution to
the fifth A3-E4: the lower major third contracts to a unison, and the
outer minor seventh to a fifth.

. . or, how about making a short repeating cyle of this three chord phrase,
some kind of bouncy dance rhythm, and end on the F trine, or insert that
little turnaround (ACF) and repeat the whole thing again?

Post by Margo Schulter
F4 E4 D4 F4 [F4]
B3 C4 [C4]
G3 F3 [A3]
[repeat 2x] [turn-around and repeat]

Here some ideas occur to me. First, that A3-C4-F4 sonority seems to me
to invite a resolution to G3-D4-G4; note that a minor sixth in the
13th century is generally a rather tense interval, more so than a
major sixth, both of which are generally considered somewhat more
tense or dissonant than the mildly unstable thirds (this changes in
the 14th century). We could try a revision as follows:

1 2 3 + | 1 2 3 :|
G4 F4 E4 D4 F4 F4
D4 B3 C4 C4
G3 F3 A3

[turnaround]

Note that when we turnaround, we get a nice standard progression with
the minor sixth sonority A3-C4-F4 expanding to G3-D4-G4.

Since you like G3-B3-F4, how about a rondeaux a bit like the kind
written by Adam de la Halle with an internal cadence showcasing that
seventh sonority? Here the form is AB AAAB AB, and credits go both to
the composer of the motet we're discussing and to you:

A

1 2 3 | 1 2 3 + | 1 2 3 | 1 2 3 | 1 2 ...
E4 F4 G4 F4 E4 D4 F4 G4 F4 E4
E4 C4 D4 B3 C4 D4 B3 A3
A3 G3 F3 A3 G3 A3

B

3 | 1 2 3 | 1 2 3 + | 1 2 3 ||
E4 F4 G4 F4 E4 D4 F4
B3 C4 D4 B3 C4
G3 F3 A3 G3 F3

Post by Margo Schulter
This sonority has the makings of a Dominant 7th chord (no 5th -- R,
3, b7) and even when it's not used in a V-I configuration or
resolution it's a very distinct "sound" to have in one's pallet. In
our original example it's used only "in passing", but somewhere
along the line someone stopped and said "hey this is an intersting
sound (this along with the minor 7th varient, no 5th -- R, b3, b7),
maybe we can milk this a little".

Maybe the best general term is "tritonic minor seventh sonority" --
or, more strictly speaking, typically a semitritonic minor seventh
sonority, since the diminished fifth is actually called a semitritone
(smaller than a full tritone, or three whole tones) by Jacobus, and in
fact it is smaller in Pythagorean tuning, 1024:729 (~588.27 cents) as
compared with three 9:8 tones or an augmented fourth at 729:512
(~611.73 cents). However, since "tritonic" is often used freely to
refer to the diminished fifth as well as the augmented fourth,
regardless of their precise tunings, I'll just say "tritonic minor
seventh sonority."

Here my caution, or explanation, would relate to the different use of
this kind of tritonic minor seventh sonority in different eras and
styles. In the 13th century, it can be used as a rather dramatically
tense cadential sonority, or more incidentally; in the 18th century,
it plays a vital role in the major/minor key system as V7; in some
21st-century musics, especially with an intonation like 4:5:6:7, it
can serve as a stable tetrad (e.g. Paul Erlich's music in 22-tone
equal temperament, which offers an approximation of this ideal
tuning).

Someone might look at both the 13th-century and 18th-century usages as
moving toward the 21st-century idiom of a stable 4:5:6:7 tetrad; but
each usage also has its own musical logic and context.

For now, I'll suggest two main points, both intended to put
13th-century usage in better perspective. First, it's noteworthy that
tritonic seventh sonorities, and seventh sonorities in general, are
more freely treated in either the 13th century or the 18th century
than in the 15th-16th century era, when sevenths are approached rather
cautiously, with the suspension normally being the most prominent use
(this changes by around 1600).

My second point that is that the 13th-century and 18th-century usages
are distinct, and both can be "milked" based on an understanding of
the style of each period. Let's compare these resolutions of the
sonority we're discussing, G3-B3-F4:

13th-century 18th-century

F4 E4 F4 E4
B3 A3 B3 C4
G3 A3 G3 C3

(min7-5 + Maj3-1) (dim5-Maj3 + Maj3-8)

In our 13th-century resolution, the guiding intervals in the unstable
G3-B3-F4 sonority are the lower major third and outer minor seventh,
which contract to unison and fifth, moving to the stable fifth A3-E4.
The diminished fifth, B3-F4, while it adds color and tension, resolves
by parallel motion to the perfect fifth A3-E4: the directed progression
is guided mostly by the other two unstable intervals which resolve by
stepwise contrary motion. Either of these resolutions could define a
standard two-voice cadence, and they harmonize nicely in a three-voice
texture:

B3 A3 F4 E4
G3 A3 G3 A3

(Maj3-1) (min7-5)

Now let's consider the 18th-century resolution. A big difference is
that here, major and minor thirds are stable intervals, and the
diminished fifth could be viewed as the most important guiding
interval! From this point of view, we have here, too, a simultaneous
pair of two-voice resolutions. The upper diminished fifth B3-F4
resolves by stepwise contrary motion to the stable major third C4-E4,
while the lower pair of voices characteristically moves from major
third to octave -- in 18th-19th century terms, with one voice
ascending a semitone from the leading tone to the tonic, and the other
moving from dominant to tonic (down a fifth, as here, or up a
fourth). Again, either progression might define a two-voice cadence:

F4 E4 B3 C4
B3 C4 G3 C3

(dim5-Maj3) (Maj3-8)

Just as the diminished fifth adds color and tension to the
13th-century resolution, so here the minor seventh between the outer
voices does the same.

What I want to emphasize is that these are two different musical
languages, each with its own style of "milking" a range of
combinations. While there's much more that could be discussed about
the history, maybe a good topic for another thread, I do want to
distinguish the 13th-century and 18th-century contexts.

Post by Margo Schulter
here's the "minor" variation, using Bb -- which I like even
more. Though it has a more "minor" sound to it, I'm playing it in a
kind of care-free "skipping along" rhythum. And this is employing
that kind of melody-chord voice-leading we saw in PartIIA, here it's
a descending line . . .
F4 E4 D4 E4 F4 [F4]
Bb3 C4 [C4]
G3 F3 [A3]
[turn-around and repeat]

Here's how I would write this, again adding a G3-D4-G4 sonority to
resolve your "turn-around" sonority of A3-C4-F4:

1 2 + 3 + | 1 2 3 :|
G4 F4 E4 D4 E4 F4 F4
D4 Bb3 C4 C4
G3 F3 A3

[turnaround]

Using Bb3 instead of B3 has the effect of reducing the tension level
for the minor seventh sonority (G3-Bb3-F4 rather than G3-B3-F4 with a
diminished fifth) while increasing it for the cadential major sixth
sonority (G3-Bb3-E4 with a tritone rather than G3-B3-E4). In fact, the
cadence of G3-Bb3-E4 to F3-C4-F4 is very common in 13th-century
pieces, maybe a bit more so in the earlier part of the century. This
is what I'd call a mixed cadence, in contrast to the intensive
G3-B3-E4 to F3-C4-F4:

Mixed Intensive

M6|m3_A4 M6|M3_4

E4 F4 E4 F4
Bb3 C4 B3 C4
G3 F3 G3 F3

(Maj6-8 + min3-5) (Maj6-8 + Maj3-5)

Note that in the mixed cadence with the tritone, the lower voices have
an omnitonal resolution of min3-5 (both voices moving by whole-tone),
while the outer voices have an intensive Maj6-8 (one voice descending
by whole-tone, another ascending by a semitone). In the intensive
cadence, both the Maj6-8 and Maj3-5 resolutions are intensive.

Post by Margo Schulter
This is straying a bit from the A-G-F theme, but that's how music
works I guess, one thing leads to another, and I for one have to
follow to see where it leads me ;') Actually, you can see where this
1 2 3 | 1 2 [new stuff .....
E4 F4 G4 F4 F4 E4 D4 E4 F4
E4 C4 D4 B3 Bb3 C4
A3 G3 G3 F3

If I were going after a "standard" kind of 13th-century progression,
more or less -- and lots of "nonstandard" things can happen in these
pieces, let alone creative spinoffs on them -- using both Bb and B, I
might alternate B and Bb something like this:

1 2 3 | 1 2 3 + | 1 2 3 | 1 2 3 | 1 2 3 | 1
E4 F4 G4 F4 E4 D4 F4 F4 G4 F4 E4 D4 E4 F4
E4 C4 D4 B3 C4 C4 D4 Bb3 A3 B3 C4
A3 G3 F3 A3 G3 A3 G3 F3

Here's another version to bring the B/Bb contrasts closer together:

1 2 3 | 1 2 3 + | 1 2 3 | 1 2 3 | 1
E4 F4 G4 F4 E4 D4 F4 F4 E4 D4 E4 F4
E4 C4 D4 B3 C4 Bb3 A3 B3 C4
A3 G3 F3 G3 A3 G3 F3

Post by Margo Schulter
*
D4 F4 G4 F4 E4 D4 E4 F4
C4 D4 E4 Bb3 C4
F3 A3 A3 G3 F3

Here I might do something like this, consistently using Bb (which
often appears as a signature in 13th-century music, sometimes in all
of the voices, and sometimes in the lowest part or lower two parts of
a three-voice texture, for example):

1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1
D4 E4 F4 G4 G4 F4 F4 E4 D4 E4 F4
C4 A3 C4 D4 E4 F4 D4 C4 Bb3 A3 Bb3 C4
F3 A3 G3 A3 Bb3 G3 A3 G3 F3

Post by Margo Schulter
And of course, now that I think of it, many of these are sonorities
the _3rds_ in them. Virtually all (?) of the "interest" in the many
examples we've seen so far was a function of the inter-mediating and
connecting sonorities, containing either 3rds or their inversions
(6ths), or 7ths and their inversions, 9ths. i.e. today, that's how
we might conceptualize them.

How I would conceptualize this is that we have, within an octave, the
simple intervals of the stable unison, fourth, fifth, and octave; and
unstable seconds, thirds, sixths, and sevenths, all of which
participate in these progressions. The major ninth, or major second
plus an octave, might be regarded simply as an octave extension of
this simple interval, but Jacobus and some 20th-century theorists make
a point that it is somewhat more blending than a simple major second.

The theory of inversion (let's say a relation between sonorities with
the same "pitch classes") or conversity (a relation between sonorities
with the same intervals) can apply in some contexts rather than
others. This could be quite a discussion, and I'll just caution, for
example, that octave complements are not always musically
"equivalent." For example, in the 13th century, a major third is
relatively blending or concordant but a minor sixth quite tense, often
ranked together with the minor second and major seventh and tritone;
in 16th-century counterpoint, a simple fourth is treated much more
cautiously than a simple fifth.

Post by Margo Schulter
There was also the third specie of split fifth analogous to a suspension
(4th or 11th), e.g. G3 C4 D4.

This is mentioned by Jacobus: we can have either 5|4_M2, with the
fourth below and the major second above (e.g. your G3-C4-D4), or
5|M2_4 with the converse arrangement (e.g. G3-A3-D4), and indeed these
are very important and useful sonorities. (This is an example of
conversity: two sonorities with the same intervals differently
ordered.) They can resolve by directed contrary motion or oblique
motion, or lead for example to a cadential sixth sonority:

5|4_M2

directed oblique to cadential to cadential
resolution resolution 6th sonority 6th sonority

D4 E4 || D4 || D4 E4 | F4 || D4 E4 | F4 ||
C4 A3 C4 D4 C4 B3 C4 C4 D4 C4
G3 A3 G3 G3 F4 G3 F3

5|M2_4

directed oblique to cadential to cadential
resolution resolution 6th sonority 6th sonority

D4 E4 || D4 || D4 E4 | F4 || D4 | E4
A3 B3 A3 G3 A3 B3 C4 A3 B3
G3 E3 G3 G3 F3 G3 F3 E3

They can be considered as having interval structures like either
15th-19th century suspensions or stable 20th-21st century fourth
chords or fifth chords. However, their musical role is somewhat
distinct from either later usage.

Post by Margo Schulter
In other words we have a full pallet here, and some very rich
sophisticated music, simple as it might seem. We have the functional
equivalent or triads, 6ths, 7ths, 9ths, 11ths/sus, nothing is
missing (i.e. by "modern" standards).

Here I'll very enthusiastically agree that just about any combination
for three or four voices you can find in 18th-19th century tonality,
say, you can also find in 13th-century polyphony -- and each system
has some very creative uses for its rich pallet!

I would also say that while the interval structures are often the
same, the "functions" or directed tendencies of these structures are
generally different. Of course, there are some common features, like
the resolution of directed tension by stepwise contrary motion
(various interval resolutions in a 13th-century style, e.g. 3-1, 3-5,
6-8, 7-5, 2-4, 2-5; and in an 18th-century style, especially dim5-Maj3
or Aug4-min6, the resolution of tritone tension to define a tonal
center or key).

Post by Margo Schulter
For much of this, I don't even _want_ to add a fourth voice (so I
could do a full strum, lets say) because in many of these cases
"less is more". It's also a little more artful to have to "design"
everthing to occure within just three voices. "Dropping tones", as
it were, was common. Even back then, they were "dropping the fifth"
from their 7th sonorities. They might drop 3rds from their 6th
sonorities, and of course in their suspensions too.

Please forgive me if I communicate imperfectly here: possibly I am in
a situation similar to that of someone who speaks a language and is
trying to explain it to the speaker of another language. Many of the
consonants and vowels are the same, but the grammar can be quite
different.

From what you say about "dropping tones," and especially dropping
thirds, I might take this to be an 18th-19th century kind of
description based on the model of building sonorities or chords by
stacking thirds. Here, I'd say that we're building sonorities by
combining a variety of intervals and two-voice progressions -- an
approach also favored in some styles of 20th-century European practice
and theory.

In any of these styles, of course, there's a process of choosing and
selecting intervals and sonorities and progressions. We can discuss
this more, but maybe I should save some of theory that occurs to me
for another post.

What I would caution, given your mention of "suspensions," is that a
13th-century sonority like G3-C4-D4 or G3-A3-D4 might have the same
interval structure as a 16th-18th century suspension -- some modern
chord notations use "sus4" and "sus2," if I have it correctly -- but
the musical usage is different, as it often is also for these
sonorities in a 20th-century setting favoring quartal or quintal
harmony. That's one reason why I prefer other terms.

[...]

Post by Margo Schulter
How else were they doing it, I might ask, particularly
the secular and dance music?]

Well, the rondeaux of Adam de la Halle for three voices show one kind
of secular song technique, not too different than what we see in the
conductus (which can be liturgical, secular, or somewhere in between)
or motet (which often includes French songs, for example).

There's also some dance music for two untexted voices which follows
more or less the same patterns as for vocal polyphony, and some
untexted motets from three voices, including _In seculum viellatoris_
or "the vielle player's _In seculum_" recently mentioned on this
newsgroup, which follow a kind of technique also found in texted
motets -- sometimes involving hoqueting (literally "hiccuping"), the
quick alternation of notes where one voice sounds while another
pauses, so that they "truncate each other," as Johannes de Grocheio
puts it.

In England, both sacred and secular styles sometimes show a
predilection for lots of freely treated thirds, which can in certain
pieces be stable and conclusive. A famous round, _Sumer is icumen in_,
illustrates this kind of style.

Post by Margo Schulter
Now we move to point 4, The step A as penultimate of F. the first
E4 F4
B3 C4
A3 F3
(Maj2-5)
Margo, how about this variation (A3 in bass of Ultimate)? Played in a
E4 F4
B3 C4
A3 A3

This A3-C4-F4 sonority is something rather different than what I'd
call an Ultimate, which implies stability: this is a sonority with a
minor sixth which I'd consider more tense than the mildly unstable
A3-B3-E4, and suggests a neat cadential progression:

E4 F4 G4
B3 C4 D4
A3 G3

This is an example of the pattern where a 5|M2_4 (or 5|4_M2) sonority
leads to a sixth sonority of some kind, in turn resolving to a stable
trine (here min6-8 + min3-5).

second example is . .

Post by Margo Schulter
E4 F4
D4 C4
A3 F3
(Maj2-4)
that employs the suspended-type split-fifth

Here I'd say "suspended-type" relates more to 16th-19th century theory
than the 13th-century practice or theory of this sonority. Maybe we
could call this the "fourth-second" type of split fifth, understood to
mean that in ascending order we're splitting the fifth into a fourth
and a major second.

Post by Margo Schulter
how about inserting this for extra smoothing/mediation and melody. . ?
E4 F4
D4 C4 C4
A3 F3

Why don't I explain why I might prefer something else, although the
progression A3-C3-E4 to F3-C4-F4 can occur. You mention the idea of
"smoothing/mediation," and a mediating sonority generally brings about
the resolution of unstable intervals by contrary motion, making a
progression more efficiently directed. Here, however, I wouldn't call
A3-C4-E4 to F3-C4-F4 a very efficient progression, because both
unstable thirds resolve by oblique rather than contrary motion.

If we simply want some melodic embellishment, I'd go with this, for
example, which we've both discussed:

E4 F4
D4 C4 B3 C4
A3 F3

(Maj2-5)

However, if your idea is using A3-D4-E4 to lead up to a cadence on F
with the 5|3_3 type of split fifth, I like the following choice,
cautioning that I haven't researched its musical pedigree, although I
wouldn't be surprised to find it in a 13th-century piece:

1 2 3 | 1
E4 D4 F4
D4 C4 B3 C4
A3 G3 F3

(Maj3-5)

Here's a variation with a mediating sixth sonority formed by a
mediating tone in the lowest voice (5-6-8), again of unresearched
pedigree -- "Well, I'd use it, anyway":

1 2 3 | 1
E4 F4
D4 C4
A3 G3 F3

(Maj6-8 + Maj2-4)

Another variation with a sixth sonority, here with A3-C4-E4 in the
middle of the first measure, again unresearched:

1 2 3 | 1
E4 E4 F4
D4 C4 B3 C4
A3 G3 F3

(Maj6-8 + Maj3-5)

Also, here are two versions where the A3-D4-E4 sonority moves to
another energetic quintal/quartal sonority, as I call it, this one
with two fourths forming an outer minor seventh or m7|4_4, leading to
a sixth sonority cadence, quite "jazzy" to me:

1 2 3 | 1 1 2 3 | 4
E4 F4 E4 F4 E4 F4 E4 F4
D4 C4 B3 C4 D4 C4 D4 C4
A3 G4 F4 A3 G4 F3

The last one isn't especially inventive in the melodies for the upper
parts <grin>, but I like the total effect.

Now let's consider a progression I really like with your idea of
A3-D4-E4 leading to A3-C4-E4 as the cadential sonority:

1 2 3 | 1
E4 D4
D4 C4 D4
A3 G3

(Maj3-1 + min3-5)

Here the difference is that we resolve to G rather than F, and so get
a resolution where both unstable thirds resolve by stepwise contrary
motion. Again, I'm not sure whether or where this might occur in the
13th-century literature, but would certainly use it myself.

By the way, here are two other progressions starting at A3-D4-E4 and
cadencing on G, both with a mediating tone in the highest voice
(5-6-8):

1 2 3 | 1 1 2 3 | 1
E4 F4 G4 E4 F4 G4
D4 C4 D4 D4 E4 D4
A3 G3 A3 G3

The second example we've discussed, and the first is basically the
same pattern as a cadence to F for which you've expressed a distinct
liking <grin>.

Post by Margo Schulter
E4 F4
Bb3 C4
A3 F3
(min2-5)
this extremly dissonant member of the split-fifth family I never in
my life would have expected to see/hear, let alone learn it was
judged and prescibed by famous theorists as being ok?, useful? fair
game?

Probably the best theoretical authority is the general statement of
Johannes de Garlandia (c. 1240?) that "every discord" when resolved to
a stable concord is "equipollent" to such a concord; he specifically
mentions minor second to fifth, which occurs between the lower two
voices of this progression, and his "every discord" doesn't exclude
the tritone. The "equipollent" statement could be read to mean that "a
discord in effect concords well when aptly resolved," or also that the
discord should have a rhythmic value equal to that of the resolving
stable interval, often giving the progression extra prominence.

Jacobus doesn't recognize partitions with acutely tense intervals like
the minor second or tritone, but they are often used boldly in
practice.

For example, here's the final cadence from the motet _Celi domina/Ave
virgo, virginum/ET SUPER, Bamberg Codex #4, as transcribed by Gordon
Anderson, with Bb signatures in the lower two parts and no signature
in the highest part, following Anderson's 9/8 meter for the
penultimate measure and 6/8 for the final measure, and using "r" to
show a rest:

1 2 3 + 4 + 5 6 7 8 9 | 1 2 3 4 5 6 ||
E4 F4 G4 F4 E4 D4 E4 F4 r
E4 C4 D4 C4 Bb3 A3 Bb3 C4 r
A3 F3 r

Post by Margo Schulter
flirting with the devil were they?!

Actually Jacobus notes that the tritone or semitritone (diminished
fifth) occurs, although rarely, in liturgical chants. For more on the
history of the tritone in practice and theory, see

<http://www.medieval.org/emfaq/harmony/tritone.html>

Post by Margo Schulter
I was going to ask at some point about some kind of diminished triad
analogue. But if this sonority is ok there definately could be no
objection to diminished chords, I'm guessing. Boy, this is really
pushing the envelope, by anyone's or any ages' standards. I'd like
to hear this executed in context someday.

Indeed you'll find lots of adventurous sonorities, and my main caution
is that terms like "diminished triad" or "diminished chords" might
suggest an 18th-century or similar setting where the tritone or
diminished fifth tends to resolve to a stable third or sixth, for
example.

Post by Margo Schulter
In the mean time, it goes in my "truth is stranger than fiction"
files. If nothing else (because I can't imagine I'd personally ever
use it myself) it'll remain as my strongest reminder of how tolerant
the environment probably was.

Just wait until my next post: I'm considering a list of examples.
While, as you rightly ask, sonorities with acutely tense intervals
often occur momentarily in passing, they can also occur quite boldly.

Also, with tritones or diminished fifths, there's the issue of whether
performers on a given occasion might make inflections to obtain a
perfect fourth or fifth; sometimes manuscripts vary in their
accidentals. However, as Gordon Anderson notes, trying to avoid them
all would lead to lots of difficulties.

Why don't I conclude here for now -- a long post as is -- and thank
you for all this dialogue.

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Post by Margo Schulter
[On idiom of "antepenultimate-penultimate-ultimate" or A-P-U variety,
with a vertical sequence of 8-7-6-8 and 5-4-3-5 figures]

Post by Margo Schulter
A4 G4 F4 G4 F4 E4 F4
E4 D4 C4 D4 C4 B3 C4
A3 G3 F3
A P U
(P/P)
Next, are two variations of the above. In the first, (passage from
the motet _Dieus! ou porrai/Chesont amouretes/OMNES_, Montpellier
#288) in the forth chord we see a G B F sonirity (no flat on the B),
this I inquired about in a P.S. at end of my Part IIA coments. In
this particulat passage we skip right through it but I wonder if we
can take a little time to explore it a little further.

Certainly, and your examples are helpful in pointing out certain
distinctions.

Post by Margo Schulter
1 2 3 | 1 2 + 3 | 1 ...
E4 F4 G4 F4 E4 D4 F4
E4 C4 D4 B3 C4
A3 G3 F3
In General, this progresson is moving A to G to F, and everything in between
is the fill, the interest and color (the stuff that makes it music). Can we
reduce this a little and see how this stands up, or see if we can milk or
emphasis that chord a little? as here . . .
E4 F4 G4 F4 F4
E4 C4 D4 B3 C4
A3 G3 F3

Here I would say that if we keep the goal of this passage as F, then
the sonority G3-B3-F4 is rather incidental, although colorful, and the
sonority G3-B3-E4 or G3-B3-D4 the point of directed instability. Thus
if our purpose is to do a "reduction" with a simplified second measure,
1 2 3 | 1 2 3 | 1 ...
E4 F4 G4 E4 F4
E4 C4 D4 B3 C4
A3 G3 F3
or
1 2 3 | 1 2 3 | 1 ...
E4 F4 G4 D4 F4
E4 C4 D4 B3 C4
A3 G3 F3

ok, I'll chose the second of those two as a reduction (the color if the
first one is a little too distinct).

Post by Margo Schulter
If we want the G3-B3-F4 sonority, and a goal of F, then I might do
something like this, more ornamented than these examples but still a
1 2 3 | 1 2 3 | 1 ...
E4 F4 G4 F4 E4 F4
E4 C4 D4 B3 C4
A3 G3 F3
1 2 3 | 1 2 3 | 1 ...
E4 F4 G4 F4 E4
E4 C4 D4 B3 A4
A3 G3 A3
Note that I've followed your reduction in having a more prolonged
G3-B3-F4, and then followed it with a standard directed resolution to
the fifth A3-E4: the lower major third contracts to a unison, and the
outer minor seventh to a fifth.

resolving to "A" is interesting

Post by Margo Schulter
. . or, how about making a short repeating cyle of this three chord phrase,
some kind of bouncy dance rhythm, and end on the F trine, or insert that
little turnaround (ACF) and repeat the whole thing again?

Post by Margo Schulter
F4 E4 D4 F4 [F4]
B3 C4 [C4]
G3 F3 [A3]
[repeat 2x] [turn-around and repeat]

Here some ideas occur to me. First, that A3-C4-F4 sonority seems to me
to invite a resolution to G3-D4-G4; note that a minor sixth in the
13th century is generally a rather tense interval, more so than a
major sixth, both of which are generally considered somewhat more
tense or dissonant than the mildly unstable thirds (this changes in
the 14th century).

um, how narrow of a time-frame are we allowing here? Is 1300's too "late"
already?

Post by Margo Schulter
1 2 3 + | 1 2 3 :|
G4 F4 E4 D4 F4 F4
D4 B3 C4 C4
G3 F3 A3
[turnaround]
Note that when we turnaround, we get a nice standard progression with
the minor sixth sonority A3-C4-F4 expanding to G3-D4-G4.

this seems to change the home to G, so it's basically a G to F (to A and
back to G). This still seems to work. All of the ornamentation in the first
bar then, is variations on G, could be G trine or G split-fifth (yes/no?).
Knowing that the turnaround is (at least) acceptable to G is good to know,
it's a good bit of polyphonic pattern (whether as progression or
turnaround)to add to our collection.

so. .

|
G4 F4 F4 G4
D4 C4 C4 D4
G3 F3 A3 G3

is this not right (as anything)?

Post by Margo Schulter
Since you like G3-B3-F4, how about a rondeaux a bit like the kind
written by Adam de la Halle with an internal cadence showcasing that
seventh sonority? Here the form is AB AAAB AB, and credits go both to
A
1 2 3 | 1 2 3 + | 1 2 3 | 1 2 3 | 1 2 ...
E4 F4 G4 F4 E4 D4 F4 G4 F4 E4
E4 C4 D4 B3 C4 D4 B3 A3
A3 G3 F3 A3 G3 A3
B
3 | 1 2 3 | 1 2 3 + | 1 2 3 ||
E4 F4 G4 F4 E4 D4 F4
B3 C4 D4 B3 C4
G3 F3 A3 G3 F3

well, I think I'm starting to loose it here. I don't know if we're on A or G
or F (amoung other things). This particular use of the GBF sonority is
almost burying it again, I was hopeing to isolate it, hightlight it. It
might be the wrong sonority to highlight in that particular period (at least
if one's abiding formal part-writing practice, it's use of sonorities and
progression getting).


if we go all the way back to the original progression you gave before I
tried to reduce it. . here . .

Post by Margo Schulter

Post by Margo Schulter
1 2 3 | 1 2 + 3 | 1 ...
E4 F4 G4 F4 E4 D4 F4
E4 C4 D4 B3 C4
A3 G3 F3

. . . this (above) is simpler and seems to contain the main elements in the
larger Randeaux. It's really just that G through F run, perhaps repeated a
few times, that I was getting at, and emphasising that GDG to GBF
progression was my main point. But I'm not going to push it. It was just a
"what if".

Post by Margo Schulter

Post by Margo Schulter
This sonority has the makings of a Dominant 7th chord (no 5th -- R,
3, b7) and even when it's not used in a V-I configuration or
resolution it's a very distinct "sound" to have in one's pallet. In
our original example it's used only "in passing", but somewhere
along the line someone stopped and said "hey this is an intersting
sound (this along with the minor 7th varient, no 5th -- R, b3, b7),
maybe we can milk this a little".

Maybe the best general term is "tritonic minor seventh sonority" --
or, more strictly speaking, typically a semitritonic minor seventh
sonority, since the diminished fifth is actually called a semitritone
(smaller than a full tritone, or three whole tones) by Jacobus, and in
fact it is smaller in Pythagorean tuning, 1024:729 (~588.27 cents) as
compared with three 9:8 tones or an augmented fourth at 729:512
(~611.73 cents). However, since "tritonic" is often used freely to
refer to the diminished fifth as well as the augmented fourth,
regardless of their precise tunings, I'll just say "tritonic minor
seventh sonority."

oy. This vacabulary is cumbersome.

Post by Margo Schulter
Here my caution, or explanation, would relate to the different use of
this kind of tritonic minor seventh sonority in different eras and
styles. In the 13th century, it can be used as a rather dramatically
tense cadential sonority, or more incidentally; in the 18th century,
it plays a vital role in the major/minor key system as V7; in some
21st-century musics, especially with an intonation like 4:5:6:7, it
can serve as a stable tetrad (e.g. Paul Erlich's music in 22-tone
equal temperament, which offers an approximation of this ideal
tuning).
Someone might look at both the 13th-century and 18th-century usages as
moving toward the 21st-century idiom of a stable 4:5:6:7 tetrad; but
each usage also has its own musical logic and context.
For now, I'll suggest two main points, both intended to put
13th-century usage in better perspective. First, it's noteworthy that
tritonic seventh sonorities, and seventh sonorities in general, are
more freely treated in either the 13th century or the 18th century
than in the 15th-16th century era, when sevenths are approached rather
cautiously, with the suspension normally being the most prominent use
(this changes by around 1600).

that's interesting

Post by Margo Schulter
My second point that is that the 13th-century and 18th-century usages
are distinct, and both can be "milked" based on an understanding of
the style of each period. Let's compare these resolutions of the
13th-century 18th-century
F4 E4 F4 E4
B3 A3 B3 C4
G3 A3 G3 C3
(min7-5 + Maj3-1) (dim5-Maj3 + Maj3-8)

it certainly is a dramatic difference. The 13th-century example, by the way,
we haven't covered yet, this is the first time I've seen that progression.

Post by Margo Schulter
In our 13th-century resolution, the guiding intervals in the unstable
G3-B3-F4 sonority are the lower major third and outer minor seventh,
which contract to unison and fifth, moving to the stable fifth A3-E4.
The diminished fifth, B3-F4, while it adds color and tension, resolves
by parallel motion to the perfect fifth A3-E4: the directed progression
is guided mostly by the other two unstable intervals which resolve by
stepwise contrary motion. Either of these resolutions could define a
standard two-voice cadence, and they harmonize nicely in a three-voice
B3 A3 F4 E4
G3 A3 G3 A3
(Maj3-1) (min7-5)
Now let's consider the 18th-century resolution. A big difference is
that here, major and minor thirds are stable intervals, and the
diminished fifth could be viewed as the most important guiding
interval! From this point of view, we have here, too, a simultaneous
pair of two-voice resolutions. The upper diminished fifth B3-F4
resolves by stepwise contrary motion to the stable major third C4-E4,
while the lower pair of voices characteristically moves from major
third to octave -- in 18th-19th century terms, with one voice
ascending a semitone from the leading tone to the tonic, and the other
moving from dominant to tonic (down a fifth, as here, or up a
F4 E4 B3 C4
B3 C4 G3 C3
(dim5-Maj3) (Maj3-8)
Just as the diminished fifth adds color and tension to the
13th-century resolution, so here the minor seventh between the outer
voices does the same.
What I want to emphasize is that these are two different musical
languages, each with its own style of "milking" a range of
combinations. While there's much more that could be discussed about
the history, maybe a good topic for another thread, I do want to
distinguish the 13th-century and 18th-century contexts.

alrighty, maybe we can find a way to milk the 13-century usage a little.
It's just a sexy sonority Margo, so I'm wondering if in "formal" practice
how much use it might have gotten and how/where. In secular music (much of
it never recorded on paper, it may have been milked more or differntly, who
knows). There's also some potential (perhaps) of using 4 voice sonorities
(but God help us the vacabulary needed to name a 4 voice sonority ;') and
also the use of 10ths and 14ths (perhaps). We don't need to get bogged down
in it though.

Post by Margo Schulter

Post by Margo Schulter
here's the "minor" variation, using Bb -- which I like even
more. Though it has a more "minor" sound to it, I'm playing it in a
kind of care-free "skipping along" rhythum. And this is employing
that kind of melody-chord voice-leading we saw in PartIIA, here it's
a descending line . . .
F4 E4 D4 E4 F4 [F4]
Bb3 C4 [C4]
G3 F3 [A3]
[turn-around and repeat]

Here's how I would write this, again adding a G3-D4-G4 sonority to
1 2 + 3 + | 1 2 3 :|
G4 F4 E4 D4 E4 F4 F4
D4 Bb3 C4 C4
G3 F3 A3
[turnaround]

so again, maybe it was fundamentally ok as long as we take "G" as home and
final instead of "F"?

Post by Margo Schulter
Using Bb3 instead of B3 has the effect of reducing the tension level
for the minor seventh sonority (G3-Bb3-F4 rather than G3-B3-F4 with a
diminished fifth) while increasing it for the cadential major sixth
sonority (G3-Bb3-E4 with a tritone rather than G3-B3-E4). In fact, the
cadence of G3-Bb3-E4 to F3-C4-F4 is very common in 13th-century
pieces, maybe a bit more so in the earlier part of the century. This
is what I'd call a mixed cadence, in contrast to the intensive
Mixed Intensive
M6|m3_A4 M6|M3_4
E4 F4 E4 F4
Bb3 C4 B3 C4
G3 F3 G3 F3
(Maj6-8 + min3-5) (Maj6-8 + Maj3-5)

but now we're back to "F" as home?
Well, at least the "Mixed" varrient (with Bb) G to F was common (you say
above).

Post by Margo Schulter
Note that in the mixed cadence with the tritone, the lower voices have
an omnitonal resolution of min3-5 (both voices moving by whole-tone),
while the outer voices have an intensive Maj6-8 (one voice descending
by whole-tone, another ascending by a semitone). In the intensive
cadence, both the Maj6-8 and Maj3-5 resolutions are intensive.

I'm tempted to say (respectfully) that this is the kind of minutia that so
very few people would ever have known about (even back then), let alone
adhered to in some simple instrumental accompaniment of secular song writing
or performance.

Post by Margo Schulter

Post by Margo Schulter
This is straying a bit from the A-G-F theme, but that's how music
works I guess, one thing leads to another, and I for one have to
follow to see where it leads me ;') Actually, you can see where this
1 2 3 | 1 2 [new stuff .....
E4 F4 G4 F4 F4 E4 D4 E4 F4
E4 C4 D4 B3 Bb3 C4
A3 G3 G3 F3

If I were going after a "standard" kind of 13th-century progression,
more or less -- and lots of "nonstandard" things can happen in these
pieces, let alone creative spinoffs on them -- using both Bb and B, I
1 2 3 | 1 2 3 + | 1 2 3 | 1 2 3 | 1 2 3 | 1
E4 F4 G4 F4 E4 D4 F4 F4 G4 F4 E4 D4 E4 F4
E4 C4 D4 B3 C4 C4 D4 Bb3 A3 B3 C4
A3 G3 F3 A3 G3 A3 G3 F3
1 2 3 | 1 2 3 + | 1 2 3 | 1 2 3 | 1
E4 F4 G4 F4 E4 D4 F4 F4 E4 D4 E4 F4
E4 C4 D4 B3 C4 Bb3 A3 B3 C4
A3 G3 F3 G3 A3 G3 F3

Post by Margo Schulter
*
D4 F4 G4 F4 E4 D4 E4 F4
C4 D4 E4 Bb3 C4
F3 A3 A3 G3 F3

Here I might do something like this, consistently using Bb (which
often appears as a signature in 13th-century music, sometimes in all
of the voices, and sometimes in the lowest part or lower two parts of
1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1
D4 E4 F4 G4 G4 F4 F4 E4 D4 E4 F4
C4 A3 C4 D4 E4 F4 D4 C4 Bb3 A3 Bb3 C4
F3 A3 G3 A3 Bb3 G3 A3 G3 F3

that's very nice, up until the last measure (or the last 4 sonorites shown
there), it looses me there, but the earlier stuff has some very cool and new
things happening in it (maybe we can issolate that part? and consider a
different ending?). This is again one of those examples where I can't hear
the turnaround, it might be the rhythm specifics again. How about this
ending? The only thing different is in the last measure . .


1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1 2 3 | 1
D4 E4 F4 G4 G4 F4 F4 D4 E4 F4
C4 A3 C4 D4 E4 F4 D4 C4 Bb3 C4
F3 A3 G3 A3 Bb3 G3 F3


this ending sounds fab to me. It seems to go (or resolve) where the previous
passage and implied melody line wants to go. I guess it's the G-Bb-D
sonority in there (that helps me). It might just be my modern ears and
preferences, I don't know. Is there anything fundamentally wrong with this
ending?

Post by Margo Schulter

Post by Margo Schulter
And of course, now that I think of it, many of these are sonorities
the _3rds_ in them. Virtually all (?) of the "interest" in the many
examples we've seen so far was a function of the inter-mediating and
connecting sonorities, containing either 3rds or their inversions
(6ths), or 7ths and their inversions, 9ths. i.e. today, that's how
we might conceptualize them.

How I would conceptualize this is that we have, within an octave, the
simple intervals of the stable unison, fourth, fifth, and octave; and
unstable seconds, thirds, sixths, and sevenths, all of which
participate in these progressions. The major ninth, or major second
plus an octave, might be regarded simply as an octave extension of
this simple interval, but Jacobus and some 20th-century theorists make
a point that it is somewhat more blending than a simple major second.
The theory of inversion (let's say a relation between sonorities with
the same "pitch classes") or conversity (a relation between sonorities
with the same intervals) can apply in some contexts rather than
others. This could be quite a discussion

at some point they will be nessessary to talk about I'm guessing,
inversions/conversity.



and I'll just caution, for

Post by Margo Schulter
example, that octave complements are not always musically
"equivalent." For example, in the 13th century, a major third is
relatively blending or concordant but a minor sixth quite tense, often
ranked together with the minor second and major seventh and tritone;
in 16th-century counterpoint, a simple fourth is treated much more
cautiously than a simple fifth.

Post by Margo Schulter
There was also the third specie of split fifth analogous to a suspension
(4th or 11th), e.g. G3 C4 D4.

This is mentioned by Jacobus: we can have either 5|4_M2, with the
fourth below and the major second above (e.g. your G3-C4-D4), or
5|M2_4 with the converse arrangement (e.g. G3-A3-D4), and indeed these
are very important and useful sonorities. (This is an example of
conversity: two sonorities with the same intervals differently
ordered.) They can resolve by directed contrary motion or oblique
5|4_M2
directed oblique to cadential to cadential
resolution resolution 6th sonority 6th sonority
D4 E4 || D4 || D4 E4 | F4 || D4 E4 | F4 ||
C4 A3 C4 D4 C4 B3 C4 C4 D4 C4
G3 A3 G3 G3 F4 G3 F3
5|M2_4
directed oblique to cadential to cadential
resolution resolution 6th sonority 6th sonority
D4 E4 || D4 || D4 E4 | F4 || D4 | E4
A3 B3 A3 G3 A3 B3 C4 A3 B3
G3 E3 G3 G3 F3 G3 F3 E3

that last one is very cool (and new to us)

D4 E4
A3 B3
G3 F3 E3

Post by Margo Schulter
They can be considered as having interval structures like either
15th-19th century suspensions or stable 20th-21st century fourth
chords or fifth chords. However, their musical role is somewhat
distinct from either later usage.

Post by Margo Schulter
In other words we have a full pallet here, and some very rich
sophisticated music, simple as it might seem. We have the functional
equivalent or triads, 6ths, 7ths, 9ths, 11ths/sus, nothing is
missing (i.e. by "modern" standards).

Here I'll very enthusiastically agree that just about any combination
for three or four voices you can find in 18th-19th century tonality,
say, you can also find in 13th-century polyphony -- and each system
has some very creative uses for its rich pallet!

well, that's about as "positive" a statement I've ever heard and could ever
hope for! ;')

Post by Margo Schulter
I would also say that while the interval structures are often the
same, the "functions" or directed tendencies of these structures are
generally different. Of course, there are some common features, like
the resolution of directed tension by stepwise contrary motion
(various interval resolutions in a 13th-century style, e.g. 3-1, 3-5,
6-8, 7-5, 2-4, 2-5; and in an 18th-century style, especially dim5-Maj3
or Aug4-min6, the resolution of tritone tension to define a tonal
center or key).

Post by Margo Schulter
For much of this, I don't even _want_ to add a fourth voice (so I
could do a full strum, lets say) because in many of these cases
"less is more". It's also a little more artful to have to "design"
everthing to occure within just three voices. "Dropping tones", as
it were, was common. Even back then, they were "dropping the fifth"
from their 7th sonorities. They might drop 3rds from their 6th
sonorities, and of course in their suspensions too.

Please forgive me if I communicate imperfectly here: possibly I am in
a situation similar to that of someone who speaks a language and is
trying to explain it to the speaker of another language. Many of the
consonants and vowels are the same, but the grammar can be quite
different.

yes, I'm sorry, "dropped tones" is too modern a phrase. The point was
designing sonorities so that a lot of texture and color can occure within
just a few select tones.

Post by Margo Schulter
From what you say about "dropping tones," and especially dropping
thirds, I might take this to be an 18th-19th century kind of
description based on the model of building sonorities or chords by
stacking thirds. Here, I'd say that we're building sonorities by
combining a variety of intervals and two-voice progressions -- an
approach also favored in some styles of 20th-century European practice
and theory.
In any of these styles, of course, there's a process of choosing and
selecting intervals and sonorities and progressions. We can discuss
this more, but maybe I should save some of theory that occurs to me
for another post.
What I would caution, given your mention of "suspensions," is that a
13th-century sonority like G3-C4-D4 or G3-A3-D4 might have the same
interval structure as a 16th-18th century suspension -- some modern
chord notations use "sus4" and "sus2," if I have it correctly -- but
the musical usage is different, as it often is also for these
sonorities in a 20th-century setting favoring quartal or quintal
harmony. That's one reason why I prefer other terms.
[...]

Post by Margo Schulter
Now we move to point 4, The step A as penultimate of F. the first
E4 F4
B3 C4
A3 F3
(Maj2-5)
Margo, how about this variation (A3 in bass of Ultimate)? Played in a
E4 F4
B3 C4
A3 A3

This A3-C4-F4 sonority is something rather different than what I'd
call an Ultimate,

sorry, you're right. I just meant the two chord progression (changeing the
second of the two sonorities), which as used below is ok.



which implies stability: this is a sonority with a

Post by Margo Schulter
minor sixth which I'd consider more tense than the mildly unstable
E4 F4 G4
B3 C4 D4
A3 G3
This is an example of the pattern where a 5|M2_4 (or 5|4_M2) sonority
leads to a sixth sonority of some kind, in turn resolving to a stable
trine (here min6-8 + min3-5).
second example is . .

Post by Margo Schulter
E4 F4
D4 C4
A3 F3
(Maj2-4)
that employs the suspended-type split-fifth

Here I'd say "suspended-type" relates more to 16th-19th century theory
than the 13th-century practice or theory of this sonority. Maybe we
could call this the "fourth-second" type of split fifth, understood to
mean that in ascending order we're splitting the fifth into a fourth
and a major second.

"fourth-second" split fifth

Post by Margo Schulter

Post by Margo Schulter
how about inserting this for extra smoothing/mediation and melody. . ?
E4 F4
D4 C4 C4
A3 F3

Why don't I explain why I might prefer something else, although the
progression A3-C3-E4 to F3-C4-F4 can occur.

as long as it _can_ occure, that's what matters

Post by Margo Schulter
You mention the idea of
"smoothing/mediation," and a mediating sonority generally brings about
the resolution of unstable intervals by contrary motion,

this is an older post where I was still using to term "mediating" to mean
"bridging"

Post by Margo Schulter
making a
progression more efficiently directed. Here, however, I wouldn't call
A3-C4-E4 to F3-C4-F4 a very efficient progression, because both
unstable thirds resolve by oblique rather than contrary motion.
If we simply want some melodic embellishment, I'd go with this, for
E4 F4
D4 C4 B3 C4
A3 F3
(Maj2-5)
However, if your idea is using A3-D4-E4 to lead up to a cadence on F
with the 5|3_3 type of split fifth, I like the following choice,
cautioning that I haven't researched its musical pedigree, although I
1 2 3 | 1
E4 D4 F4
D4 C4 B3 C4
A3 G3 F3
(Maj3-5)

alrighty, If you insist, we'll do it this way. So lets start from here.
Could we not then do a variation later that drops the GBD sonority? which
leaves us right back her we started (in other words it _would_ be ok).
Again, we're talking about acompaniment, not nessessarily an all-inclusive
fixed and finished piece, we're talking about _improvisation_ which means
variation and variety.

Post by Margo Schulter
Here's a variation with a mediating sixth sonority formed by a
mediating tone in the lowest voice (5-6-8), again of unresearched
1 2 3 | 1
E4 F4
D4 C4
A3 G3 F3
(Maj6-8 + Maj2-4)

that one's nice

Post by Margo Schulter
Another variation with a sixth sonority, here with A3-C4-E4 in the
1 2 3 | 1
E4 E4 F4
D4 C4 B3 C4
A3 G3 F3
(Maj6-8 + Maj3-5)
Also, here are two versions where the A3-D4-E4 sonority moves to
another energetic quintal/quartal sonority, as I call it, this one
with two fourths forming an outer minor seventh or m7|4_4, leading to
1 2 3 | 1 1 2 3 | 4
E4 F4 E4 F4 E4 F4 E4 F4
D4 C4 B3 C4 D4 C4 D4 C4
A3 G4 F4 A3 G4 F3
The last one isn't especially inventive in the melodies for the upper
parts <grin>, but I like the total effect.
Now let's consider a progression I really like with your idea of
1 2 3 | 1
E4 D4
D4 C4 D4
A3 G3
(Maj3-1 + min3-5)

I like that too

Post by Margo Schulter
Here the difference is that we resolve to G rather than F, and so get
a resolution where both unstable thirds resolve by stepwise contrary
motion. Again, I'm not sure whether or where this might occur in the
13th-century literature, but would certainly use it myself.
By the way, here are two other progressions starting at A3-D4-E4 and
cadencing on G, both with a mediating tone in the highest voice
1 2 3 | 1 1 2 3 | 1
E4 F4 G4 E4 F4 G4
D4 C4 D4 D4 E4 D4
A3 G3 A3 G3
The second example we've discussed, and the first is basically the
same pattern as a cadence to F for which you've expressed a distinct
liking <grin>.

Post by Margo Schulter
E4 F4
Bb3 C4
A3 F3
(min2-5)
this extremly dissonant member of the split-fifth family I never in
my life would have expected to see/hear, let alone learn it was
judged and prescibed by famous theorists as being ok?, useful? fair
game?

Probably the best theoretical authority is the general statement of
Johannes de Garlandia (c. 1240?) that "every discord" when resolved to
a stable concord is "equipollent" to such a concord; he specifically
mentions minor second to fifth, which occurs between the lower two
voices of this progression, and his "every discord" doesn't exclude
the tritone. The "equipollent" statement could be read to mean that "a
discord in effect concords well when aptly resolved," or also that the
discord should have a rhythmic value equal to that of the resolving
stable interval, often giving the progression extra prominence.
Jacobus doesn't recognize partitions with acutely tense intervals like
the minor second or tritone, but they are often used boldly in
practice.
For example, here's the final cadence from the motet _Celi domina/Ave
virgo, virginum/ET SUPER, Bamberg Codex #4, as transcribed by Gordon
Anderson, with Bb signatures in the lower two parts and no signature
in the highest part, following Anderson's 9/8 meter for the
penultimate measure and 6/8 for the final measure, and using "r" to
1 2 3 + 4 + 5 6 7 8 9 | 1 2 3 4 5 6 ||
E4 F4 G4 F4 E4 D4 E4 F4 r
E4 C4 D4 C4 Bb3 A3 Bb3 C4 r
A3 F3 r

this one I'm still having problems with (how that sonority gets worked in).
After the A-Bb-E sonority I hear A-Bb-D as a nice interm resolution
(where-ever it might go from there).

Post by Margo Schulter

Post by Margo Schulter
flirting with the devil were they?!

Actually Jacobus notes that the tritone or semitritone (diminished
fifth) occurs, although rarely, in liturgical chants. For more on the
history of the tritone in practice and theory, see
<http://www.medieval.org/emfaq/harmony/tritone.html>

Post by Margo Schulter
I was going to ask at some point about some kind of diminished triad
analogue. But if this sonority is ok there definately could be no
objection to diminished chords, I'm guessing. Boy, this is really
pushing the envelope, by anyone's or any ages' standards. I'd like
to hear this executed in context someday.

Indeed you'll find lots of adventurous sonorities, and my main caution
is that terms like "diminished triad" or "diminished chords" might
suggest an 18th-century or similar setting where the tritone or
diminished fifth tends to resolve to a stable third or sixth, for
example.

right, well I think we have a big problem with vacalurary here in general,
either non-existing vocabulary, or cumbersome vocabulary, or making it up as
we go (perhaps), etc. And a related problem of linking one body of knowlege
to another. i.e we learn by "association". Given that we moderns already
have a vocabulary (associations already in place for the given sonorities)
we can't help but to tack new things, new concepts, onto things we already
know, it can't be helped. I don't know what the answer is, but I see it as a
problem, particulary if one is hoping to get other people to adopt new terms
and use them regularly. e.g. . .

suspended 4 becomes "fourth-second split fifth"
so by extention we get "major-third minor-third split fifth"? but then I
don't think the terms Major/minor even existed in the 1200's (what terms did
they use by the way for lowered 3rds, 5ths, 6ths, and 7ths).
and "tritonic and semitritonic seventh sonorities"

even feeling obligated to use the word "sonority" all the time, rather than
"chord", is combersome (sometimes annoying) to me, and I suspect will be to
others too.

maybe it's just me. But if people are not allowed to call a rose a rose
anymore, and the proposed alternate terms are too combersome to use, that's
a problem I think. Vocabulary is the currency of a thing, essential,
central, and key, very important to get right and make it usable in
practice.

Post by Margo Schulter

Post by Margo Schulter
In the mean time, it goes in my "truth is stranger than fiction"
files. If nothing else (because I can't imagine I'd personally ever
use it myself) it'll remain as my strongest reminder of how tolerant
the environment probably was.

Just wait until my next post: I'm considering a list of examples.

alrighty, we'll wait and see


Thanks Margo
Roger

Post by Margo Schulter
While, as you rightly ask, sonorities with acutely tense intervals
often occur momentarily in passing, they can also occur quite boldly.
Also, with tritones or diminished fifths, there's the issue of whether
performers on a given occasion might make inflections to obtain a
perfect fourth or fifth; sometimes manuscripts vary in their
accidentals. However, as Gordon Anderson notes, trying to avoid them
all would lead to lots of difficulties.
Why don't I conclude here for now -- a long post as is -- and thank
you for all this dialogue.
Most appreciatively,
Margo Schulter

[Roger E. Blumberg]

Post by Roger E. Blumberg

Post by Margo Schulter
1 2 3 + 4 + 5 6 7 8 9 | 1 2 3 4 5 6 ||
E4 F4 G4 F4 E4 D4 E4 F4 r
E4 C4 D4 C4 Bb3 A3 Bb3 C4 r
A3 F3 r

this one I'm still having problems with (how that sonority gets worked in).
After the A-Bb-E sonority I hear A-Bb-D as a nice interm resolution
(where-ever it might go from there).

sorry,I meant to say . .

"After the A-Bb-E sonority I hear G-Bb-D as a nice interm resolution"
(where-ever it might go from there).

Roger

[Howard Posner]

In a manuscript in Modena (I. Moe Mus. G 239, if I have it right) there's a
song by Bellerofonte Castaldi called "La Lettera d'Heleazaria Hebraica a
Tito Vespasiano" the text of which purports to be a version of a letter from
a Jewish woman in Jerusalem during the Roman siege of that city, in which
she describes how she is killing and eating her own son.

If you're still with me after that last sentence, my question is whether
anyone knows of any other source for such a text, or of anything like it,
anywhere else. It seems pretty bizarre, even for Castaldi, and pretty
gruesome, even by Ukrainian standards.

Howard Posner

[Roman Turovsky]

A item with this content was recorded on Vol.3 of "Lamenti Barocchi",
Capella Musicale di San Petronio, on Naxos (Fede Marincola might have been
in the band). I don't recall if it was Castaldi or some other composer
RT
______________
Roman M. Turovsky
http://turovsky.org
http://polyhymnion.org

Post by Howard Posner
In a manuscript in Modena (I. Moe Mus. G 239, if I have it right) there's a
song by Bellerofonte Castaldi called "La Lettera d'Heleazaria Hebraica a
Tito Vespasiano" the text of which purports to be a version of a letter from
a Jewish woman in Jerusalem during the Roman siege of that city, in which
she describes how she is killing and eating her own son.
If you're still with me after that last sentence, my question is whether
anyone knows of any other source for such a text, or of anything like it,
anywhere else. It seems pretty bizarre, even for Castaldi, and pretty
gruesome, even by Ukrainian standards.
Howard Posner

[Howard Posner]

Post by Roman Turovsky
A item with this content was recorded on Vol.3 of "Lamenti Barocchi",
Capella Musicale di San Petronio, on Naxos (Fede Marincola might have been
in the band). I don't recall if it was Castaldi or some other composer

Thanks.

The Naxos website reveals that it's Antonio Cesti's "Lamento della Madre
Ebreo". Same basic theme, but different text from Castaldi's setting.
Curiouser and curiouser.

[Roman Turovsky]

Do you think the story might come from Josephus?
RT
______________
Roman M. Turovsky
http://turovsky.org
http://polyhymnion.org

Post by Roger E. Blumberg

Post by Roman Turovsky
A item with this content was recorded on Vol.3 of "Lamenti Barocchi",
Capella Musicale di San Petronio, on Naxos (Fede Marincola might have been
in the band). I don't recall if it was Castaldi or some other composer

Thanks.
The Naxos website reveals that it's Antonio Cesti's "Lamento della Madre
Ebrea". Same basic theme, but different text from Castaldi's setting.
Curiouser and curiouser.

[Mole]

Post by Roman Turovsky
Do you think the story might come from Josephus?

Sounds like a classic instance of the Blood Libel to me.

(That is, the old belief of Christian bigots that Jews performed human
sacrifice in mockery of Christ's Passion).

[Howard Posner]

Post by Mole

Post by Roman Turovsky
Do you think the story might come from Josephus?

I just read through Chapter 10 of "Wars of the Jews," which deals with the
starvation caused by the siege of Jerusalem. He says that everyone stole
food from everyone else in, including parents taking food from children and
vice versa. Nothing about parents actually eating their children.
Certainly nothing about mothers eating their children and advertising the
fact in letters to the Roman emperor. But it's not unlikely that the
"letter" is a fiction inspired by Josephus.

Post by Mole
Sounds like a classic instance of the Blood Libel to me.
(That is, the old belief of Christian bigots that Jews performed human
sacrifice in mockery of Christ's Passion).

The blood libel is an accusation that Jews kill Christian children (or,
these days, Muslim children, since the blood libel has been revived in
Muslim countries in recent years) to use their blood in baking matzahs.
Traditionally, Jews don't get accused of cannibalizing each other. Indeed,
it may be the only thing Jews don't get accused of.

HP

[Roger E. Blumberg]

Post by Roger E. Blumberg

Post by Margo Schulter
1 2 3 + 4 + 5 6 7 8 9 | 1 2 3 4 5 6 ||
E4 F4 G4 F4 E4 D4 E4 F4 r
E4 C4 D4 C4 Bb3 A3 Bb3 C4 r
A3 F3 r

this one I'm still having problems with (how that sonority gets worked

in).

Post by Roger E. Blumberg
After the A-Bb-E sonority I hear A-Bb-D as a nice interm resolution
(where-ever it might go from there).

sorry,I meant to say . .

"After the A-Bb-E sonority I hear G-Bb-D as a nice interm resolution"
(where-ever it might go from there).

Roger

[Margo Schulter]

Hello, there, Roger and everyone.

Recently we've been discussing 13th-century cadences which boldly use
tritones or diminished fifths, and I promised a few examples. This
isn't a comprehensive list, but a sample of three or four cadences to
give an idea of what I would consider a "bold" use of sonorities
including such intervals.

First of all, we were considering specifically a kind of cadence
with a dramatically tense sonority where an outer fifth is "split"
into minor second and tritone (e.g. A3-Bb3-E4). Here's a four-voice
cadence with the impressive penultimate sonority A3-Bb3-D4-E4, from
the motet _Mors a primi patris/Mors, que stimulo/Mors morsu nata/MORS_
as transcribed by Gordon A. Anderson from the La Clayette Manuscript
(#11), following his 6/8 meter and with "r" showing a rest:

1 2 3 4 5 6 | 1 2 3 4 5 6 ||
F3 A3 F3 r
D4 E4 F4 r
Bb3 C4 r
D4 C4 r

Here the outer fifth of A3-Bb3-D4-E4 expands to the octave of the
trine F3-C4-F4, while the lower minor second A3-Bb3 expands to a fifth
(a resolution mentioned by Johannes de Garlandia in asserting that
"every discord" resolved to a stable concord is "equipollent" to a
stable concord). The major third Bb3-D4 contracts to a unison on C4,
while the major second D4-E4 expands to a fourth; the tritone Bb3-E4
resolves by parallel motion to a stable fourth C4-F4, the upper fourth
of the trine.

A four-voice sonority has six intervals in all, and here's one
possible notation to show what's happening in this progression:

[5-8 | m2-5 + M3-1 + M2-4 | 4-4 + A4-4]

This notation shows the two-voice progressions for first the outer
interval, then the three adjacent intervals in ascending order, and
then the other two nonadjacent intervals. It's a modern attempt to
craft a rather "algebraic" notation based on the partitions of Jacobus
of Liege in his _Speculum musicae_ (c. 1325). I should add that
Jacobus does not recognize partitions involving acutely tense
intervals such as the minor second or tritone -- but 13th-century
practice is freer, as Garlandia's treatise suggests.

Please note, by the way, you don't have to like my notation in order
to enjoy the progression!

A version of this four-voice motet in the Montpellier Codex (#35) gets
a similar transcription from Tischler, but a transcription by Yvonne
Rokseth where the E4 in the triplum is part of an ornamental figure,
although the minor second A3-Bb4 has the same duration:

1 2 3 4 + 5 6 | 1 2 3 4 5 6 ||
G3 A3 F3 r
G4 F4 E4 D4 E4 F4 r
C4 Bb3 C4 r
D4 C4 r

Rokseth indicates a slowing of tempo at the cadence, a technique also
discussed by authors such as Willi Apel and Christopher Page which
makes the penultimate A3-Bb3-D4-E4 sonority more prominent.

An example of a boldly directed sonority with a diminished fifth
occurs in the three-voice conductus _Pater noster qui es in caelo_:

1 2 3 4 5 6
C4 D4
Bb3 A3
E3 D3
A- men.

Here we have a minor sixth to octave resolution between the outer
voices, and a major second to fourth resolution between the upper
voices.

I'll also give two examples of a four-voice cadence with a major sixth
sonority including a tritone. Here's the final cadence from _De la
virge Katerine/Quant froidure/Agmina milicie/AGMINA, La Clayette #22:

1 2 3 4 5 6 | 1 + 2 + 3 4 5 6 | 1 2 3 4 5 6 ||
D4 C4 Bb3 C4 r
G4 F4 E4 D4 E4 D4 C4 Bb3 A4 D4 C4 r
D4 E4 F4 G4 G4 F4 E4 D4 E4 F4 r
G3 F3 r

Here the penultimate G3-Bb3-D4-E4 sonority progresses to the final
trine on F with no fewer than four two-voice resolutions by stepwise
contrary motion (Maj6-8 + min3-5 + Maj3-1 + Maj2-4). In my algebraic
notation for four-voice resolutions, this would be:

[M6-8 | m3-5 + M3-1 + M2-4 | 5-5 + A4-4]

This cadence also occurs internally in Perotin's organum quadruplum
(organum for four voices) _Sederunt principes_ as transcribed by Ethel
Thurston, in the setting of the last phrase on the syllable [Deus
me-]_us_ that precedes the words _Salvum me fac propter misericordiam
tuam_:

1 2 3 4 5 6 | 1 2 3 4 5 6 | 1 2 3 4 5 6 |
F4 E4 D4 C4 D4 E4 E4 F4 r
C4 Bb3 C4 A3 Bb3 Bb3 C4 r
F3 G3 A3 Bb3 G3 G3 F3 r
C4 C4 D4 D4 C4 r

Anyway, these examples should give some idea of the bold use made of
tritones or diminished fifths in the 13th century -- or also a bit
earlier, since Perotin's four-voice organa _Viderunt omnes_ (where
the G3-Bb3-D4-E4 to F3-C4-F4 cadence also occurs) and _Sederent
principes_ are often dated to around the year 1198, or more generally
the last decade or so of the 12th century.

Most appreciatively,

Margo Schulter
***@calweb.com

[Roger E. Blumberg]

Post by Margo Schulter
Hello, there, Roger and everyone.
Recently we've been discussing 13th-century cadences which boldly use
tritones or diminished fifths, and I promised a few examples. This
isn't a comprehensive list, but a sample of three or four cadences to
give an idea of what I would consider a "bold" use of sonorities
including such intervals.
First of all, we were considering specifically a kind of cadence
with a dramatically tense sonority where an outer fifth is "split"
into minor second and tritone (e.g. A3-Bb3-E4). Here's a four-voice
cadence with the impressive penultimate sonority A3-Bb3-D4-E4, from
the motet _Mors a primi patris/Mors, que stimulo/Mors morsu nata/MORS_
as transcribed by Gordon A. Anderson from the La Clayette Manuscript
1 2 3 4 5 6 | 1 2 3 4 5 6 ||
F3 A3 F3 r
D4 E4 F4 r
Bb3 C4 r
D4 C4 r
Here the outer fifth of A3-Bb3-D4-E4 expands to the octave of the
trine F3-C4-F4, while the lower minor second A3-Bb3 expands to a fifth
(a resolution mentioned by Johannes de Garlandia in asserting that
"every discord" resolved to a stable concord is "equipollent" to a
stable concord). The major third Bb3-D4 contracts to a unison on C4,
while the major second D4-E4 expands to a fourth; the tritone Bb3-E4
resolves by parallel motion to a stable fourth C4-F4, the upper fourth
of the trine.
A four-voice sonority has six intervals in all, and here's one
[5-8 | m2-5 + M3-1 + M2-4 | 4-4 + A4-4]
This notation shows the two-voice progressions for first the outer
interval, then the three adjacent intervals in ascending order, and
then the other two nonadjacent intervals. It's a modern attempt to
craft a rather "algebraic" notation based on the partitions of Jacobus
of Liege in his _Speculum musicae_ (c. 1325). I should add that
Jacobus does not recognize partitions involving acutely tense
intervals such as the minor second or tritone -- but 13th-century
practice is freer, as Garlandia's treatise suggests.
Please note, by the way, you don't have to like my notation in order
to enjoy the progression!
A version of this four-voice motet in the Montpellier Codex (#35) gets
a similar transcription from Tischler, but a transcription by Yvonne
Rokseth where the E4 in the triplum is part of an ornamental figure,
1 2 3 4 + 5 6 | 1 2 3 4 5 6 ||
G3 A3 F3 r
G4 F4 E4 D4 E4 F4 r
C4 Bb3 C4 r
D4 C4 r
Rokseth indicates a slowing of tempo at the cadence, a technique also
discussed by authors such as Willi Apel and Christopher Page which
makes the penultimate A3-Bb3-D4-E4 sonority more prominent.
An example of a boldly directed sonority with a diminished fifth
1 2 3 4 5 6
C4 D4
Bb3 A3
E3 D3
A- men.
Here we have a minor sixth to octave resolution between the outer
voices, and a major second to fourth resolution between the upper
voices.
I'll also give two examples of a four-voice cadence with a major sixth
sonority including a tritone. Here's the final cadence from _De la
1 2 3 4 5 6 | 1 + 2 + 3 4 5 6 | 1 2 3 4 5 6 ||
D4 C4 Bb3 C4 r
G4 F4 E4 D4 E4 D4 C4 Bb3 A4 D4 C4 r
D4 E4 F4 G4 G4 F4 E4 D4 E4 F4 r
G3 F3 r
Here the penultimate G3-Bb3-D4-E4 sonority progresses to the final
trine on F with no fewer than four two-voice resolutions by stepwise
contrary motion (Maj6-8 + min3-5 + Maj3-1 + Maj2-4). In my algebraic
[M6-8 | m3-5 + M3-1 + M2-4 | 5-5 + A4-4]
This cadence also occurs internally in Perotin's organum quadruplum
(organum for four voices) _Sederunt principes_ as transcribed by Ethel
Thurston, in the setting of the last phrase on the syllable [Deus
me-]_us_ that precedes the words _Salvum me fac propter misericordiam
1 2 3 4 5 6 | 1 2 3 4 5 6 | 1 2 3 4 5 6 |
F4 E4 D4 C4 D4 E4 E4 F4 r
C4 Bb3 C4 A3 Bb3 Bb3 C4 r
F3 G3 A3 Bb3 G3 G3 F3 r
C4 C4 D4 D4 C4 r
Anyway, these examples should give some idea of the bold use made of
tritones or diminished fifths in the 13th century -- or also a bit
earlier, since Perotin's four-voice organa _Viderunt omnes_ (where
the G3-Bb3-D4-E4 to F3-C4-F4 cadence also occurs) and _Sederent
principes_ are often dated to around the year 1198, or more generally
the last decade or so of the 12th century.
Most appreciatively,
Margo Schulter

Hi Margo;

Thanks. As it turns out, these particular 4 voice constructions are
impossible to play (find humanly possible fingerings for) on my instrument,
so I'll have to wait for some other means of hearing them someday.

Thanks for the effort
Roger