Extending downward: A curiosity

The usual method of extending triads to make 7, 9, 11, and 13 chords is to go above. (And I point out yet once more that's a theoretical and pedagogical convenience, not a historical narrative.) But we can also play with going the opposite direction. Here's an example, where (at a) the top note remains the same (just like the root would do if we were building upward) and the bass moves down by thirds. At (b) I've isolated the fifth movements that get us to Db#11.

This generates a surprisingly large percentage of basic chord types--and also a good sounding progression! 

Satie, "Je te veux” (1902)

This song was mentioned at the end of the previous post. Here is that text again, expanded and with additional examples. 

"Je te veux" is one of the better known among Satie’s cabaret songs, where we would definitely expect dominant ninth harmonies. (Satie began working as a pianist at the Parisian cabaret Chat noir in the later 1880s.) One appears immediately in the introduction (box). In the Refrain (the overall design is RCRCR, where R is the Refrain, and C is a couplet [same music but different text]), the major dominant ninth appears in the early or middle part of a period, as is more typical of popular song, and not near the cadence, as we find commonly in “art song.” The circled notes point to the free treatment of degrees in the upper tetrachord in relation to harmony—a heritage of mid-19th century waltz practices.

Thanks to repetition of the opening phrase, V9 is a characteristic sound of the couplets.

Satie, Sarabandes and songs

Erik Satie's distinctive styles--whether the early one of the Trois Gymnopédies or the later one of Parade--make very little use of the major dominant ninth harmony, but to show that he was no stranger to it, at least in his earlier years, here are examples from four stylistically varied pieces, three of them written around the same time as the Gymnopédies.

The 3 Sarabandes (1887) provide an extreme. This is the opening of no. 1. I almost feel I should apologize for the absurd welter of accidentals, in particular the three Bbb9s (enharmonic A9).

Here is a version that I hope is easier to read: it's a transposition up a half step and I've added chord labels.

And the beginning of no. 3. The Db9 becomes a recurring motto chord.

From the 3 Mélodies (1886), the opening of no. 3, "Sylvie." The treatment of sonority and texture is a bit reminiscent of the Gymnopédies. Unlike in the sarabandes, this V9 is an isolated instance.

Finally, from a decade or more later, "Je te veux," one of the better known cabaret songs, where we would definitely expect dominant ninth harmonies. (We should mention that Satie began working as a cabaret pianist in the later 1880s.)

Inversions, part 3

 Last, the fourth inversion. I have very little to offer here. From the trio to James Scott's Grace and Beauty Rag is this (circled), but the Bb in the right hand resolves internally and the Bb in the bass is easily heard as a passing tone within the Ab7 harmony.

I decided to look at René Lenormand's Study of Modern Harmony (Eng. trans 1915; French original 1912), which is distinguished by its very large number of musical examples. Even he had trouble locating fourth inversions. This one from a ballet by Florent Schmitt (Study, 31) reminds us of the difficulties that can attend the definition of complex chords (Lenormand himself says of ninth chords that "In all the [examples] that follow, the disposition of the parts is very important" [27]). I've written the boxed chords again at the right; to my ear, the second of them is more convincing as a D9. It's the fourth E3-A3 at the bottom of the first chord that gets in the way (and the C4 even makes an A minor triad), where the "cluster" of ninth and third (E3-F#3) in the second chord, combined with the pairing of seventh and root above it (C4-D4), definitely sounds like a chord built on a D root.

Inversions, part 2

This continues discussion of inversions of the major dominant ninth chord.

Apologies for the overlapping boxes in this graphic of the opening of Franck's Violin Sonata. Boxes 1 and 2 include the second inversion of A: V9, each sandwiched between root position chords. The third "clears out" the chord momentarily by reducing it to a root position B minor triad.

Here is a passage from later on. The sounds over C#3 vary, with C#9 briefly touched in the third bar, though against a dissonant passing tone in the violin. The fourth bar gives us a#ø7, which becomes the upper part of the F#9 a bar later.

Now a secondary dominant ninth in its second inversion (MacDowell, To a Wild Rose). I've added the slurs in the bass to bring out the pattern in the harmonies: consonance to dissonance over the same bass in bars 1-2 & 3-4, then the reverse in bars 5-6 & 7-8.

And two examples of the unfolding bass figure: Sousa, Hail to the Spirit of Liberty, trio; James Scott, Broadway Rag. In the latter the boxes and arrows point to the common parallelism in a figure over V9, then over Iadd6.

For the third inversion, a waltz by Alexis Castillon and the introduction to An der Elbe, op. 477, Johann Strauss, jr.'s last published waltz set. There is expressive emphasis in Castillon's version, but as a harmony it is undercut by its middle position in a dominant.

In the second box below, a clever parallelism with a reversed harmonic progression, because of which the ninth (G5) resolves internally.

The best example for the third inversion, though, is in the "Serenade of the Doll" from Debussy's Children's Corner. Here is the second of three divisions of the B-section; it is made entirely of major dominant ninth chords, 15 of them, 9 of which are third inversions (indicated by asterisks (*)).

By way of a postscript: in the third division of the B-section, the F#9 returns to initiate a traditional cadence progression: E: V9/V drops the sharp to become ii13, then follow V7 and Iadd6:

Inversions, part 1

Discussion of inversions of the major dominant ninth chord typically stall on Arnold Schoenberg's famous needling of detractors about a fourth inversion chord in his Verklärte Nacht (see my post on several authors' analyses of the passage: link). But now that I am done with that ritual notice, let's move on.

Looking at examples from posts to this blog and from essays published on the TexasScholarworks platform, I found 25 instances, considerably more than I expected, though as we will see I have included a particular type that some readers may not accept as a proper inversion. The numbers were: first inversion 5; second inversion 17; third inversion 2; fourth inversion a questionable 1.

In the graphic below, I have shown G7 and inversions with simple voicing, then the same for G9, whose inversions are labeled a-d.

A weakness of the first inversion is the likelihood of its collapsing into the most commonly used inversion of V7: see (a1) below; a standard resolution to the tonic is at (a2). At (b1) the loss of the root turns the second inversion into viiø6/5. The standard resolution is at (b2) in five voices, at (b3) in four voices; it must be to I6 in order to avoid parallel fifths between the bass and the voice carrying the ninth of the chord. The "particular type" I mentioned earlier is at (b4). Before you complain--as some certainly will--that this doesn't excuse the parallels, let me remind us all of a very common dodge used in Renaissance-era counterpoint: 5-3-5-3, as at (b5). 

The figure at (b4) is of course a schematic form of the ubiquitous oom-pah bass. Its resolution nicely balances line and bass function; Schenkerians often represent this as shown below.

The third inversion--at (c1) and (c2)--has the smoothest voiceleading of the lot, with a pleasant pair of tenths between the bass and the voice carrying the ninth. At (d1) the fourth inversion collapses into V7; (d2) shows that this inversion leads to I6/4, (d3) that one can avoid the 6/4 with a mediant, but iii is the weakest of the major key's three minor triads and to make things worse is often used functionally as a dominant, which would make the ninth chord resolve internally.

 We begin with the first inversion. Here is an excerpt from the third waltz in Johann Strauss, jr.'s Künstlerleben [Artist's Life], op. 316:

And here is nearly the same in the trio from his father's Damen-Souvenir Polka, op. 236:

Again from Strauss Vater, in the trio of his best-known piece, the Radetzky March:

My added unfolding symbols give you the essence of the "particular type": it is ^5 (E2) that moves directly to ^1 (A2) in the bass, but ^7 (G#2) is given such emphasis that it will still be heard as resolving to ^8 (A2). The balance between line and function is perfect.

A march by Sousa, "The White Plume":

And finally another from Johann Strauss, sr., the second strain of the second number from Die Sorgenbrecher, op. 230, the most often played (or, at least, recorded) of his waltzes:

I will take up the second inversion examples in another post.

Update/Administrative

I have placed a file called "Index to V9 blog and essays" on my Google Drive. The document's title is "On the Dominant Ninth Chord: (1) List of posts to the blog; (2) List of essays published on the Texas ScholarWorks platform; (3) Repertoire list for the essays." Link.

Here also is the complete text of an administrative post I put up on 11 February 2019:

[Blog introduction]  In the introductory post to this blog, I wrote that in studying cadence figures in the upper tetrachord of the scale, "I noticed the variety of treatments of scale degree ^6 as the ninth of a dominant ninth chord. This blog is intended to document some of those, especially in the essential 19th century European repertoires of the musical stage and music for dance." Link to the introduction.

[Types of the dominant ninth]  A subsequent post looked more closely at the different melodic and harmonic treatments of the dominant ninth: link to "On seven types of the dominant ninth."

[Gallery]  I also announced publication of an essay, Dominant Ninth Harmonies in the 19th Century: link to the post. Link to the essay on Texas ScholarWorks. This is intended as a gallery of simple (clear) examples from the repertoire.

Originally I said the blog would be limited to the major dominant ninth chord. I am focused now on music in the first quarter of the 20th century and, not surprisingly for the period, am finding the forms with lowered or raised fifth more often. That being the case, I will be including those forms occasionally if their presentations are of interest, even while continuing primarily to document the unaltered major dominant ninth chord. Cases in point are two of the songs by Marion Bauer discussed in recent posts: V9#5 in "Only of Thee and Me" (link to Part 2) and V9b5 in "Gold of the Day and Night" (link to Part 4).

The four ninth chord types are shown under (a) below. Under (b) I have repeated them with a traditional altered form (without root; for the major and minor dominant ninths) or a common voicing (for the raised or lowered fifth).

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.

Eight songs by Marion Bauer, part 4

The last three of the eight songs, all published in 1921, are "Gold of the Day and Night," "Night in the Woods," and "Thoughts."

"Gold of the Day and Night": A point of interest is the CM7 at the beginning (circled). Another of the many cases in music after 1890 where much attention is given to a particularly voiced if traditionally dissonant sonority--observe that the CM7 is promptly repeated--but where one can, if one insists, hear a triad resolution (on the fourth eighth note of bar 1 in this case, at which point the 7 is gone). The parallel instance--a possible CM13 (second circle)--is pushed off more quickly by the chromatic voiceleading (D# making a V#5), but the repetition in bar 4 definitely sounds independent.

The first section ends with a clear cadence using V9b5 (boxed).

After that, a major dominant ninth chord appears once, but as part of a descending bass progression, once the bass begins to move down the section's Ab pedal.

"Night in the Woods": A contemplative song with stronger presence of classically voiced major and minor triads, diatonic dissonances, and wavering tonal center (Phrygian at the outset, possibly A minor or A Dorian in the section below, ending in/on D major). There are three sections: this is the second half and ending of the first section.

This is the parallel place in the close to the second section.

"Thoughts": Much more traditional than "Night," with a V9 to begin the piano's introduction. The dotted box shows that V7, not V9, is the presence just as the voice enters.

Here is the parallel place ending the first section and overlapping into the second. In bar 21, the same "throw-away" ninth (F4; arrow) that we saw in "Only of Thee and Me" renders the resolution an almost proper V9.

Eight songs by Marion Bauer, part 3

Here are two more of the songs published in 1921: "A Parable" and "Roses Breathe in the Night." 

As a dramatic song in a minor key, "A Parable" does not offer much of an opening for the major dominant ninth. In fact, this is the best we can do:

Someone *might* construe the climax chord as a ninth with flat 5 (dotted boxes), but honestly I don't think so. I don't trust chords in the middle of a pedal point passage (and in any case the ninth is immediately lost, both times).

Things are really not much better in "Roses Breathe in the Night." The motivic middle-voice half-step play (see the accented notes B-A# in the opening) does not invite anything like the open sound of the ninth chord, but we get at least this in bars 6 & 7: a V9, then a raised fifth (and seventh)--as A#4 and C#4) and continued movement up to B4 and D4.

At the end of the first section, the climax chord is not a V9 but A: iiø7 (circled); V9 does appear in the cadence (boxed) but then the mode promptly shifts to minor with the tonic, erasing any subsequent influence.