On the face of it, Roussel's Divertissement would seem to be a good companion for the small company of pieces that make the dominant ninth chord integral to large-scale harmonic design. I've written about one on this blog: Marion Bauer's "Epitaph of a Butterfly" and another—Charles Griffes's White Peacock—in an essay published on the Texas Scholarworks platform: The Dominant Ninth in Music from 1900 to 1924, Part 1: you can check this blog post for an abstract and link: 2020 June 5.
As it happens, however, although Roussel gives a prominent place to a D9 chord as G:V9 at the beginning, (1) unlike the pieces named above, it doesn't hold that place in overall design amongst a rich play of harmonies and tonal regions; (2) it doesn't really even sound like a dominant ninth.
Here is the figure with which the piano opens:
I listened to the excellent commercial recording accessed from the IMSLP page for this piece (one may need to subscribe to hear this--I'm not sure) and, although the notes are all there, to my ear the sound isn't anything like the traditional V9. Voicing (distribution of the notes) is key: the ninth isn't at the top (instead there's the seventh and even the octave on each second beat) and a cluster at the bottom has E4 in the middle of it.
To make things worse—that is, to undermine the V9 sound more—once the quintet members enter, the clarinet (in A) plays A3, which more than hints at a complex chord based on A, with E as its fifth and its third C at the top. See at the first arrow. The theme is in the oboe.
Here is a simplified version of the opening, with annotations.
The second arrow in the original score above points to a downward shift in the piano's left-hand figure. This effectively negates any possible V9 function and in fact now offers a clear Am7. The left hand keeps descending and offers just a passing hint of the opening sonority (boxed) before reaching I7, which relaxes to Iadd6 very briefly (the tempo is fast) before Am7 reasserts itself at |1|.
As just one example of the kaleidoscope of harmonies that ensues, here is the next entrance of the theme. The persistent G4 does more than suggest B7/b13.
Two more themes are mixed in, both of them easily heard as derivatives of the main theme, but then the tempo suddenly turns slow (Lent) and we hear a section in the orientalist style at which Roussel excelled. Then fast again, slow again, and the transition into a final fast section brings this:
. . . followed by
Here are a few ways to look at this progression:Figure (a) shows what might have happened to the F7 in a traditional progression--such chromatic movements of the bass (here F-F#-G) were common already in the early 18th century; the assumed key is either Bb major or G minor. Figure (b) tries to account, again in traditional terms, for the change from F7 to Fm7, but going that way one ends up in Eb major. Figures (c) & (d) show simplified close voiceleading for the chord sequence in the score, (c) with the traditional resolution of the 7th Eb down, (d) exchanging the outer voices (Eb5 becomes Eb4; F4 becomes F5) so that one can arrive on D9. Neither of these is exactly what Roussel does, as you can see from looking again at the score excerpt above.
The troublesome A3 reappears, now in the bassoon, and the flute's E5 is solid confirmation of A as root. The long notes D4 in clarinet and horn make for an overall effect of Am(sus4) until the bassoon lands on D3 (circled in the last bar of the first system).
The insertion of IV between the V & I of the closing cadence is a fairly common device in French music by about 1890. Below is a simplified version of the passage above.
