Medieval Polyphonic Patterns — Part IIA
Author: Margo Schulter
Fretboard illuminations: Roger E. Blumberg
Directory of images (fretboard illustrations of the medieval
chords and progressions covered in these articles)
Medieval Polyphonic Patterns:
Part IIA: The F-G-A question
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.
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1. F-G-A and alternation: Fifthing and mediating sonorities
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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.
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2. Stepping up and down: Opposing and connecting sonorities
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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 fro 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
2004, Copyleft
Index of articles:
Medieval Sonorities and Instruments, some of the content preceding the main essays (not done)
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