Medieval Polyphonic Patterns — Part IIB
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 IIB: The F-G-A question (continued)
---------------------------------------------------------------------------------
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
2004, Copyleft
Index of articles:
Medieval Sonorities and Instruments, some of the content preceding the main essays (not done)
|
