Tuesday, July 5, 2022

On Perfect Fifths and Complex Chords

 In a previous post (Bauer, Part 1), I created a chordal reduction and wrote the following about the last bars of the B section, leading to the reprise:

"Also, the V7/ii itself [see the final bars in the graphic below] can be explained by separating out the left-hand elements in bar 17 [at the farthest right]. The first thing we hear is in fact ii—not V—as iiadd6; only on the third quarter beat is the bass G2 sounded. Although the overall effect here is certainly that of a break, the harmony does offer some continuity."

The device that the composer uses in this passage is firmly within late-19th and early-20th century practice. Recall that the notion of the identity of viiø7 as V9 without its root goes back to the 18th century. By the time we reach an era where the voicing of sonorities becomes an important factor, it is not surprising to see what we might call a "play of functions," grounded in perfect fifths. In the graphic below, (a) is the major dominant ninth chord with the two P5s bracketed; (a1) and (a2) depict what Bauer does in "Epitaph"--that is, briefly drop the root and thereby "expose" the upper fifth D-A. I have filled out the scheme with V9#11 at (b), and V13 at (c). At (b1) is the common diatonic -2 voicing of V11, which offers a third P5. By the time we reach (c), there are four P5s, and--theoretically at least--any of the upper ones could replace the lowest fifth. As an aside, (a3) and (c5) as quintal chords lose almost all the character of the traditional V9 and V13.


Here are some additional examples of the play of functions and bass/upper-voice layering. The simplest type is the familiar common-tone modulation, a single note held between the two keys. Schubert uses it for a striking textural punctuation that announces the beginning of the second theme in the Unfinished Symphony, first movement:

Because the relationship is diatonic (B minor to G major), this passage often appears in harmony textbooks. Johann Strauss, jr., does something similar in the transition--moving from Eb major to Ab major--out of the second into the third waltz in Frühlingsstimmen ("Voices of Spring"; second box below):


Appropriately for our blog, he gives strong expressive emphasis to V9 in the cadence (first box) and in the transition, too (second box again). The cadential V9 is very prominent in the vocal edition of this waltz set:


Another textbook example--indeed, the one that almost inevitably shows up in a section on V9--is the opening of Franck's Violin Sonata. I wrote a long post about the entire movement in 2019: link. Franck briefly drops the root and third of E9 (box), creating a wonderful expressive effect that contrasts the simple minor triad against the fuller colors of the major dominant ninth on either side of it.


In an earlier post I referred to Brahms as "
a genius at suggesting but avoiding the two characteristic chords of scale degree ^6: the dominant ninth and the add6" (link to post). The moment boxed below--from the Intermezzo in A Major, op. 118 no. 2--is a familiar style device of his that involves layering of bass and upper voices and "suggests but avoids" a directly stated V9/V.


In its "proper" form, the passage should have been built on one or the other of these: at (a), E in the bass is understood as a pedal point; at (b), the bass note changes to match the upper-voice chords and a V9/V is fully expressed. In both cases, I have inserted the tonic chord that Brahms only hints at with the bass A2.



Here is a version with the tonic chord repositioned so that the strongly marked IV6/4 remains on the first beat:



This compacted progression can be related to its opposite, where the bass does move as expected but the upper-voices don't correspond as neatly as one might like. The final cadence of the "Russian Dance" from Stravinsky's Petrushka is a famous example: C5 as the top note doesn't budge, nor does the A5 below it, as the bass pounds out a simple ii-V-I.

Given the presumed Impressionist influence on "The Epitaph of a Butterfly," it should be easy to locate examples of the "play of functions" in Debussy. Layering is of course a basic technique in his music, but as to using layers to suggest a change of function or modulation, my admittedly brief search has offered only this from the reprise in Reflets dans l'Eau ("Reflections in the Water"). A strongly defined Db: V9 (root and fifth circled) loses it root, perhaps by the second but certainly by the third bar, leaving eb7. The reverse process follows, as a b-flat minor triad is undergirded a couple bars later by a tonic fifth Db2-Ab2. 

Unlike Bauer's iiadd6, which gives an entirely plausible V7/ii–iiadd6–V9 progression, here it would be V9–ii7–vi–I, but better as V9–(ii7–vi)–I. The overall effect is not much different from that in the opening of Franck's Violin Sonata.