Rise and fall of the dominant ninth chord

A one-paragraph historical narrative: 

The major dominant ninth chord ("V9") gradually became a significant stylistic element in European and European-influenced music over the course of the nineteenth century. Early on it appeared in dance-based and song genres—notably, Schubert’s—and from there found its way onto the musical stage by the mid-1830s in both comic and dramatic works, eventually becoming associated with Wagnerian opera. By 1890, the two practices—exemplified by Wagner and Johann Strauss, jr.—were firmly established and can be found in a majority of the music from that point through the first half of the 20th century, including some concert music, but especially in musicals, salon or recital pieces, and commercial song repertoires. Before the end of the 19th century the dominant ninth chord had also established itself as one of the characteristic sounds of contemporary or Impressionist concert music, and, although the style did persist into the 1930s, already by 1920 the dominant ninth sound was considered passé and was often actively avoided.

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Find here an index of essays published on the Texas ScholarWorks platform, with abstracts and links: link. Essays on the dominant ninth are in §2, beginning on p. 10. Within this blog, of course, the search function can be used to locate specific names, titles, etc., and post titles can be browsed in the sidebar.

Altered dominants and the whole-tone scale

  In the entry for 28 October 2018, after explaining that the blog concerns only the major dominant ninth chord--such as C: V9, G9, or A9, etc.--not what I call the minor dominant ninth, or dominant 7th plus b9, or any of the non-dominant ninth chords, I wrote:

Still another exclusion from this blog is the dominant ninth with altered fifth. These chords also begin to appear with some frequency in the 1890s. The version with raised fifth is more common; so, in C major G-B-D-F-A becomes G-B-D#-F-A, which happens to form a whole-tone scale pentachord also: D#-F-G-A-B [see the second example under (d) below]. Less common is the dominant ninth with lowered fifth, so: G-B-Db-F-A  [see the first example under (d) below]. This one, too, can be spelled in scalar form as a whole-tone pentachord: F-G-A-B-Db.

I'm going to take that back a bit, because the derivations of these chords are of historical interest for the familiar story of their connecting the dominant seventh and ninth with the whole-tone scale. Both appear in music first as alterations of V or of V7. 

The dominant seventh with lowered fifth was normally used in second inversion from the 1870s on. The first example under (e) below shows the dominant ninth and its alteration with the lowered fifth first and then the progression with V(b5)7 from which the latter is derived. Two points about it: exploited by Richard Strauss and others influenced by him, V(b5) is sometimes called the "Strauss chord" and normally appeared with the fifth in the bass; although the progression is functionally V(b9)–I, its notes are identical to IV: Fr+6-V. 

The chord with raised fifth, as V(#5)--see "from" in the second example under (e) below--already appears in galant-style music in the second half of the 18th century in the form V7(#5)/IV–IV; it has been associated particularly with Mozart, though he was by no means the only person to use it. The version with the ninth is unlikely before 1890.

Here are two simple (made-up) examples of scalar elaboration, showing the whole-tone scale as a melodic figure. At (f), G9 is first, but the scale is over V(b9) with the lowered fifth in the bass.  At (g), the fifth is missing in the G9; the raised fifth (D#) appears as leading into E6.

Symmetrical 5-chords

Last time I discussed symmetry and introduced the 7 (out of 38) 7-note sets/scales/chords that have it, besides the chromatic set and the major scale. Here are the corresponding 5-note sets, again in the interest of contextualizing the pitch content of 5-34, which is the major dominant ninth chord. 

All are "internally symmetrical" as defined in the previous post, and all are "completely symmetrical" by (1) some single note, or (2) the gap between two adjacent notes, as defined in the previous post. Though it's just another way of conceiving rule 2, a rule (3) makes a "double axis"--two notes at the center. Here are examples: type (1): 5-15 & 5-22; type (2): 5-34; type (3) 5-8.

To expand the contextualizing even more (and, granted, to wander a bit off-topic for this blog), here are some comments on these sets. Traits of most are clear, but a couple are more complex. The diminished triad frames 5-8 and 5Z12. 5Z17 as shown in the first example above is five notes of a C# minor scale (if C4 is B#3), 5-33 is most of the whole-tone scale, and 5-34 is the major dominant ninth. 5-15 has four notes of a whole-tone scale, here C4-D4-F#4-G#4 (if C is B#, this is the "French +6"), but also three chromatic notes and a quartal/quintal chord as G#-C#-F# or F#-C#-G#. 5-22 seems like a mash-up of three triads: C major, c# minor, and C+. And 5Z37 tucks a chromatic fragment D#-E-F into the middle of an augmented triad. The point of interest is that the properties of each of these sheds light on the 7-note complement. I'll explore that in the next post.

Here are two additional ways to think about the 5-note sets: as written, voiced chords, and in brief musical passages. First, the 5-8 below shows something not so obvious in the scalar version: this is a D9 with both 9 and b9.

Using the voicings of the chords above, here are short musical examples incorporating them (and where I can manage it, including V9 chords).

Symmetrical 5-chords and 7-chords

In an earlier "Curiosities" post (link), I discussed the symmetry of the major scale: starting on scale degree ^2, the inversion function, "I", produces all the same notes. Here is the first example again:

Only a small percentage of scales/pitch-sets/pc-sets in the 12-tone equal-tempered system are capable of this. Here are the best known. The chromatic scale is obvious; it has all 12 notes in a half-step sequence: of course, inversion will create the same ones. The whole-tone scale is pretty much the same, but with whole steps. The diminished scale is a little different: it's not symmetrical on a note but between notes. At (d) I have drawn a line between C4 and C#4 and then applied inversion from C4 down and C#4 up. In fact, the diminished scale is so structured that you can do this by drawing a line between any two adjacent notes of the scale.

Thus there are two sorts of scale or set symmetry: (1) from a note, as in the chromatic scale, major scale, and whole-tone scale; (2) from between notes, as in the diminished scale. (The latter can also be understood in terms of note pairs, or C4-C#4 together here.)

For a small number of sets/scales/chords, you can apply these within: I call this "internal symmetry," where you can generate a set/scale/chord from a sequence half its size. It's not common, either, but among the 5-note sets that have it is the major dominant ninth chord:

Btw, you can't find symmetry (1) with the entire V9 chord from its root--if you try it with the G9 above, that is, invert from G4 downward, you'll get an F9 instead, see (a) below. That's because the axis of symmetry is, you guessed it, scale degree ^2, just like the major scale figure at the top of this post--it's D5 at (b) below.

If we take a "scale-size chunk" of seven notes, in this case the pc complement of C: V9--that is, the seven notes in the chromatic scale that aren't in this V9--you can see that the resulting scale is also internally symmetrical. It also happens to be what is often called the "melodic minor scale," here C# minor.

Here are seven additional 7-note sets, beginning with two that have "type 1" symmetry like the major scale. These are followed by five with internal symmetry.

What this table does is to begin to put both 5-34, the pc set of the major dominant ninth, and 7-34, the ascending minor scale and the complement of V9, into a bit more general pitch-design context.

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* The literature on scales and sets is understandably large. As I have explained a number of times, I am retired and don't feel the need to tot up the usual scholarly citations. I can say (a) that very little if anything I've said above is new, but that's not the point--it is to gather and discuss information in terms of the blog's topic; (b) if you want to explore more, the literature on set theory, pitch-class sets, and symmetry or symmetrical relations is the best place to go. Joe Straus's atonal theory textbook is the standard. Of online sites, I particularly like this one: "A Brief Introduction to Pitch-Class Set Analysis" (link) from Mount Alison University in Sackville, New Brunswick. It was made more than 20 years ago but is still available, informative, and easy to use.

Textbooks, update, part 6

My last post added to the series on traditional harmony textbooks (link to first post) discussion of a modern harmony text from the 1950s. Vincent Persichetti doesn't have anything negative to say specifically about the major dominant ninth chord, but as I wrote, he "greatly favors other seventh and ninth chord types over the major dominant ninth, which does appear in a reference example of the same kind of sequential progression that we saw in Mitchell and Ottman, but only once in the chapter's nine composed examples."

Just a few years earlier, Paul Hindemith indirectly offered an explanation: the major dominant harmony (like its close cousin the half-diminished seventh) was too strongly associated with 19th century music. Hindemith was a student in the years before WWI, and matured as a musician and composer in the years immediately following, when the aesthetics and practices of the earlier era, especially anything Wagnerian, were soundly rejected. Thus there is a definite sarcasm in his proposing composition exercises for the harmonium, that "primitive wheezebox": "Is not treasuring such a pitiful instrument like preaching the virtue of poverty and the moral value of asceticism to one living in luxury? The counter-question might be: Why not, if that will further the development of the individual and the general welfare?" (Traditional Harmony, vol. 2, 31, 32) In other words, the argument is a bit like that for writing species counterpoint. . . .

In his conclusion, it's obvious that Hindemith is referring to the major dominant ninth, the ø7, and various altered dominants: 

"In respect to harmony and tonality, our pieces will inevitably sound like so many hundreds of the sentimental genre pieces of the post-Tristan style. . . . What was originally felt to be so 'modern' and to promise so much, turns out to be a technical device that is useful only for the creation of all too limited effects. Nevertheless, it is advisable once, for practice, to wallow thoroughly in this style of writing if only to learn through exaggeration what in the end one wants to avoid."

Like Persichetti's harmony, Leon Dallin's Techniques of Twentieth Century Composition was a very influential text in the 1960s and 1970s (edition I looked at: Techniques of Twentieth Century Composition: A Guide to the Material of Modern Music, 3rd ed., 1974). Dallin makes the same point as Hindemith but very explicitly and with prejudice against "popular" music styles:

"Major and minor ninths can be added to all of the seventh chord structures, both diatonic and altered. The dominant ninth was the first to be incorporated into the harmonic vocabulary, but its value to serious composers is impaired by popular connotations and triteness. The sounds of other less hackneyed ninth chord forms are still capable of pungent expressiveness, even to jaded twentieth-century ears, when used with imagination."

Ouch. Still, for the era, Dallin was undoubtedly right. In a later post, I will write that musicians working in the popular styles he denigrates were equally reticent: the statistics will show that the major dominant ninth appears surprisingly infrequently in songs from the 1920s through the 1980s.