Thirteenth-Century Polyphony

5. Multi-voice Obliquely Resolving Sonorities

Having looked at directed cadential progressions for three or four voices, we now turn to resolutions by oblique motion. Some popular combinations lend themselves readily to both treatments: for example, 5/3, 5/4, 5/2, 6/5, and 7/5.

As we saw in Section 2.3, two-voice music frequently features resolutions from an unstable to a stable interval where one voice remains stationary while the other moves by a step, or by a third (sometimes with the middle step filled in), e.g. 7-8, 7-(6)-5.

Extending this technique to music for three or voices, composers often apply these basic resolutions to the unstable intervals of various combinations, with one or more voices moving by oblique motion while the others remain stationary. Let us consider some of the most common resolutions of this kind, with a definite caution that the following presentation is only a very partial sampling.

5.1. The "split fifth" unsplit (5/3, 8/5/3)

While the "split fifth" or 5/3 often resolves by directed cadential action (Section 4.1), it can also resolve by oblique motion of the middle voice which "splits" the fifth into two unstable thirds:

      a     -                               d'     -
      f-(e)-d                               b-(c')-d'
      d     -                               g      -

      5       -                             5      -
      m3-(M2)-1                             M3-(4)-5

[m3-(M2)-1 + M3-(4)+5]                [M3-(4)-5 + m3-(M2)-1]

(Notation graphics: 1, 2)

The middle voice descends or ascends by a third, possibly moving through the intervening step, to arrive at a unison with one of the outer voices and a fifth with the other. Thus we are left with a stable "unsplit" fifth. From a vertical point of view, we might say that the mild tension of the two thirds has "evaporated" without impelling a directed progression. Of course, the motion of the middle voice (often in quick note values) also adorns the music melodically.

In music for four voices, the 8/5/3 sonority likewise invites this kind of oblique resolution as well as the standard directed resolutions. Here the resolution of the two unstable thirds - and also an unstable sixth with respect to the highest voice - leaves us with a complete 8/5 trine:

          f'    -                               d'    -
          c'    -                               a     -
          a-(g)-f                               f-(g)-a
          f     -                               d     -

          8       -                             8       -
          5       -                             5       -
          M3-(M2)-1                             m3-(M2)-1

[M3-(M2)-1 + m3-(4)-5 + m6-(m7)-8]   [m3-(M2)-1 + M3-(4)-5 + M6-(5)-4]

(Notation graphics: 1, 2)

5.2. Mildly unstable quintal/quartal sonorities (9/5, 7/4, 5/4, 5/2)

These relatively blending combinations very frequently resolve by oblique motion, sometimes with impressive effect indeed. The 9/5, 5/4, and 5/2 combinations can neatly resolve to a stable trine or fifth by the stepwise motion of a single voice, while 7/4 invites a beautiful resolution in which the two upper voices ascend stepwise in fourths to the octave and fifth of an 8/5 trine.

The 9/5 combination most typically resolves to an 8/5 trine by the stepwise descent of the upper voice (M9-8), and may alternatively resolve to an 8/4 trine by the stepwise descent of both upper voices in fifths:

g'-f'                 b'-a'
c' -                  e'-d'
f  -                  a  -

M9-8                  M9-8
5  -                  5 -4

[M9-8]                [M9-8]

(Notation graphics: 1, 2)

As just mentioned, 7/4 often resolves by a stepwise ascent of the two upper voices to the octave and fifth of a complete trine:

g  -

4 -5


(Notation graphic)

The energetic but relatively concordant qualities of the 7/4 sonority, the pleasant motion of the upper voices in parallel fourths, and the arrival at an ideal 8/5 combination make this a strikingly beautiful progression. Especially in the music of Perotin's time, it sometimes serves as a very felicitous final or sectional cadence.

While the 5/4 and 5/2 combinations rather frequently resolve by directed cadential motion (Section 4.2), they also invite oblique resolutions rather similar to those of 5/3 (Section 5.1). The middle voice, which here "splits" the outer fifth into a euphonious fourth and a relatively tense major second, typically moves stepwise into a unison with the nearer outer voice (M2-1):

d' -                      c'-
c'-d'                     g-f
g  -                      f -

5 -                       5  -
4-5                       M2-1

[M2-1]                    [M2-1]

(Notation graphics: 1, 2)

Thus we are left with an "unsplit" stable fifth.

5.3. Sixth combinations (6/3, 6/5, 6/5/3, 6/2, 6/4)

Again we move to more tense combinations. In addition to their vital role as directed cadential sonorities, combinations with an outer sixth also permit a variety of resolutions by oblique motion. Here we consider only a few main possibilities.

The 6/5 combination, in addition to inviting one of the most effective directed progressions of the 13th century (Section 4.3), also has an alternative resolution by oblique motion in which the upper voice descends from the sixth to the fifth:

    d'-c'                                   c'-b
    c' -                                    b  -
    f  -                                    e  -

    M6-5                                    m6-5
    5  -                                    5  -

[M6-5 + M2-1]                           [m6-5 + m2-1]

(Notation graphics: 1, 2)

This motion of the upper voice produces two simultaneous resolutions: a 6-5 resolution with the lowest voice, and a 2-1 resolution with the middle voice. Our examples show the milder M6/5 form, where both unstable intervals (M6 and M2) are relatively tense but not sharply discordant, and one of the more intense forms: m6/5 (with m6 and m2).

The 6/2 combination, when it does not resolve in a directed manner, sometimes resolves by the stepwise descent of both upper voices, arriving at a stable fifth:

    a -g
    g  -


[M6-5 + M2-1]

(Notation graphic)

Here both upper voices have standard oblique resolutions with the lower voice: 6-5 for the highest voice, and 2-1 for the middle voice. The parallel fifths between the upper voices add an element of texture and color.

5.4. Seventh Combinations (7/3, 7/5, 7/5/3)

While many oblique resolutions are possible for these combinations as alternatives to their superb directed resolutions (Section 4.4), we here consider an especially important form in which the seventh of 7/5 ascends to the octave of a complete trine:

   c'-d'                            e'-f'
   a  -                             c' -
   d  -                             f  -

   m7-8                             M7-8
   5  -                             5  -

[m7-8 + m3-4]                   [M7-8 + M3-4]

(Notation graphics: 1, 2)

The motion of the upper voice produces a 7-8 resolution with the lowest voice and a 3-4 resolution with the middle voice. Both the milder form with m7/5 and the dramatically intense one with M7/5 are very common.

A complete discussion would look at various other resolutions: for example, the seventh in the above examples might descend to the fifth rather than ascending to the octave, and 7/3 can also resolve by oblique motion in various ways.

To Section 6 - Concluding words.

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Margo Schulter