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.

Brahms, Four Serious Songs, op. 121

The composer Gerd Zacher has written about a phenomenon in the last of the Four Serious Songs, op. 121: "appearances of the major ninth chord always feature the vowel 'i'." From this Zacher makes some observations about a subtle highlighting achieved through "a scalar microtone series." See the reference and abstract at the end of this post.

The ninth chord is especially prominent in setting the word "Liebe." See the first page of the score below. Note that the ninth, F4, is resolved internally but is repeated. To the circled notes: shifting the affect, Brahms uses the minor V9.

Here are the recurrences of the passage. The first repeats the figure from the opening page, the second attaches even more prominence to the ninth by giving it to the voice (C4) and stretching it out to nearly four beats.

Here are two more instances, from the subsequent section. The first is striking because it's unexpected in context, and because the ninth Ab3 isn't resolved, nor is the chord, which changes to an inverted Ab dominant 7 over the pedal Gb. The second is a common type of internal resolution but stands out because the ninth is not only in the voice but is also placed in a cadence.

The last statements are in the final section. The first gives, in its higher alternate note, the only ninth in the song with a direct resolution: G5 to F5 as V9/V goes to V7. The second is in the final cadence, again in the voice, a common figure I call ^6-down-to-^7; note that the ninth is given unusual prominence by this means and is not resolved (for that, one would have to take the Bb3 in the left hand on beat 2 of the next bar). The two boxes with dotted lines are the only two cases in which "Liebe" is not adorned with a dominant ninth.

Reference:

Gerd Zacher, "Komponierte Formanten," Musik-Konzepte 65 (1989): 69-75.

Abstract (from RILM): In the last of Brahms's Vier ernste Gesänge, appearances of the major ninth chord always feature the vowel "i". He lends strong support to the ninths of these chords in the region of the "i" formant. In the registers that Brahms uses here, the partials are separated by semitones. The difference between the equal temperament of the piano and the natural tuning of the partials produces nuanced vibrations that can be arranged as a scalar microtone series. The aural result is a highlighting of the particular tone (such as in setting the word Liebe). (NB: I had access only to the abstract, not to the article.)

Brahms, Waltzes, op. 39, part 2

 In the previous post I showed the direct resolutions of the major dominant ninth (in nos. 2, 7, and 16), plus two others in no. 2. Here are the treatments elsewhere in the set.

The figure 9-8-7, very common in the waltz (especially Ländler) repertoire, occurs three times.

In no. 5 (see second system, second box; figure repeated in the final cadence):

I will discuss the other figures later in this post.

In no. 6 (three times via series of unfolded thirds):

In no. 10: in bar 4 after a scalar ascent from an initial V9; and in the final cadence, where thirds become sixths as 9-8-7 goes into the "right-hand thumb" voice.

A similar figure in no. 7 covers 10-9-8:

Now, to those other figures in no. 7. At (a), the cadence has no dominant ninth. The shape is repeated at (b)--and (b) is repeated, transposed and slightly altered, at (c)--and in these cases there is a ninth forming a major dominant ninth chord. The resolution, however, is ascending: C#5 goes to D#5 in the first instance and F#5 goes to G#5 in the second instance. I don't want to get into the problematic matter of influence, but in this one case I will venture to assert that Brahms borrowed this ascending gesture directly from Schubert. Note, too, that the ascending stepwise line from ^5 to ^8 is repeated in the final cadence against the 9-8-7 figure (see beamed notes in the left hand at (d)).

No. 7 also has an ascending resolution, and it is dramatic, with good metric emphasis to the ninth (see the arrow):

Where my first examples (in Part 1) came from the last waltz, my last examples come from the first, where we find (1) a variant of the (10)-9-8-7 figure in the closing cadence (box at the end), and (2) what I hear as a "just barely" sounding of the ninth in grace notes (boxes in the first and second systems), a characterization that is also justified in that the piece is played without pedal (left-hand staccati preclude it).

Brahms, Waltzes, op. 39, part 1

 The sixteen waltzes of Brahms's op. 39 (1865) manage only six direct resolutions of the dominant ninth chord, four of them in nearly the final bars of the last number. The two earlier examples are both obscured by registral shifts. (Direct resolutions, recall, are external, that is, the ninth over V is resolved in the following I, not before.)

Here is waltz no. 16; the score here lacks only the last phrase and cadence to C# minor.

The voice-leading is impeccable, though I should note that most composers before the 1890s do try to avoid the parallel fifths that can easily arise in resolving the major dominant ninth chord. The invertible counterpoint (cf. bars 1-8 with 9-16) is Brahmsian, not Schubertian!

The resolution in no. 7--see the boxes in the third system--has to be called direct but F#4 goes to E5, not E4, and the contrast is strong: the phrase before is a long descent (starting in the middle of the second system) and the phrase beginning with E5 is an equally strong ascent. I've checked the other versions (piano four-hands and two pianos) and neither has a simple resolution, though it would have been very easy indeed to add the extra notes.

The F#4 is repeated in the left hand (second box) and does move to E4 but the effect is a muddle of A major and D major, made worse if the pedal is held down. The pedal marking, incidentally, is in the manuscript. Note that the composer deleted several before that (arrow).

The other direct resolution is in no. 2, bars 16-17, or from the end of the B section to the beginning of the reprise of A. Here C#3 does go on to B2 but the placement of the ninth very nearly in the bass is unique (at least, I can say that I have never seen it elsewhere, not even in the more adventurous musics of the 1890s and early 1900s) and of course it is completely contrary to all advice about how to treat the major dominant ninth chord (recall that even inversions are suspect).

Two other points of interest in this score: (1) In bars 4-5, what I call an "almost direct resolution", where unfolded thirds clearly show the voice-leading as C#6-B5 and A5-G#5; (2) an expressive highpoint in the final cadence--a cliché of the waltz going all the way back to Schubert's generation--and an internal resolution, if one regards the entire bar as V and, even better, holds the pedal down (which I have never done; the "clean" sound of the higher register ii6 is more appealing).

In a subsequent post I will provide examples of the other internal resolutions and evasions.

Brahms, Symphony no. 2, III

The Allegretto quasi Andantino sits in the position of a 19th century sonata's dance movement. Its ABABA design is in the tradition of the Beethoven symphonic scherzi, including the sharp contrast between sections: A is a pastorale/menuet(?), and B is an agitato/galop(?). Brahms also hints at a Schubertian Ländler with the leap to and from ^6 in bar 2:

Note, however, that the harmony is viiø7, not V9. In fact, the piano reduction has left out a note: a continuing G3 in the bassoons, of course confirming the pastorale topic.

There is a proper V9 in bar 22 (boxed in the first graphic above), but no simple resolution of the 9. 

The pattern continues in the variation of the theme at the beginning of the B-section and in the first reprise of A.

The same is true of the F#-major reprise (circled), but leading into it is a very expressive V9 (boxed), where the 9 is resolved internally in a gesture one finds in Schubert waltzes and also in Brahms's hommage to them, op. 39.

In the ending, another brief moment of a root-position V9 (circled) is undermined by a chromatic descent and ascent. And a big invitation to what was by the 1870s a cadential cliché--V9/V--lacks its bass and so is another viiº7 (boxed). Brahms sets up the conditions so well that one wonders if the bass players thought they had been given the wrong note.

We'll find the situation somewhat different in the Waltzes, op. 39, but in general Brahms was more conservative than his best-known contemporaries in his treatment of the major dominant ninth and the upper tetrachord of the major key.