Ascending resolutions of the ninth

 One feature of practices with the major dominant ninth—and one that applies to eleventh and thirteenth chords as well—is the upward resolution of the characteristic note. Instances of the ninth ascending as in (a) start in repertoire as early as Schubert waltzes from around 1820 (link 1; link 2). By 1850, these were well integrated into practice, especially in the dance repertoires and in music for stage that made use of dance genres. After about 1860, a stationary resolution to ^6 in Iadd6 (not shown) was also an option. After about 1890, resolutions such as the one at the right, V9 to I7, became possible, too.

The examples in (b1)-(b3) are sequences with paired roots in thirds, (b1) with a chromatic line in the upper voice, (b2) with a diatonic line (as if beginning in C major), and (b3) with ascending thirds and all chords as dominant ninths. Note that these are not traditional ascending resolutions: the first is stationary, and the second descends by a half-step. It's only if you extend "resolution" to include parallelism of function that A4 could go to C#5 and E5 to G5.  At (b4) are two smooth resolutions that take the ninth to #11 in the subsequent chord.

At (c), both upper voice and bass move by seconds in contrary motion. The second chords carry a #11, like (b4) above. Under "Chabrier" the voices are in parallel motion. More about this example below, as also for (d), where the bass changes at the tritone.

The chord pair shown above is from Emmanuel Chabrier's opera Le Roi malgré lui (1887). The example is from Lenormand's chapter on ninth chords (Study of Modern Harmony (Eng. trans 1915; French original 1912)).

The entr'acte between Acts II & III does not focus on the ninth--it is a pastoral Andantino that mostly uses the traditional progressions involving dominant and diminished seventh types. Here is the simple ii–V–I cadence (bars 25-28) followed by what sounds like a coda extension of the tonic via a pedal point.

This passage beginning at 29, however, breaks into further development, in course of which the parallel dominant ninth chords appear. It is only at bar 44 that a coda proper starts, entirely over a tonic pedal. The three chords in Lenormand's example are clear, and note that there is a fourth one, as well.

Here is Lenormand's example with the tritone resolution, from Florent Schmitt's piano quintet (published 1908). The slow movement is very long, the heart of the piece, really, and the quoted passage occurs relatively early, around bar 35 and the first change of key signature (from no sharps or flats to 5 flats—it turns out that Db major is the primary key).

As it happens, Lenormand doesn't quite get the chords right, as the first one is G9 with a flat 5--see the box below. Furthermore, the ninth is not at all so prominent as the example suggests--see the circled notes: second violin and viola abandon their A-natural or B-double flat, the cello actually resolves down, not up, and it's the piano that takes A3 to Bb3, but in the middle of its arpeggiations.

Here are some other examples with ascending resolutions. 

to c:

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:

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.

New publications: Dominant Ninth, 1900-1924, Parts 1 & 2

I have published The Dominant Ninth in Music from 1900 to 1924 on the Texas ScholarWorks platform. Part 1: link.   Part 2: link.

Abstract for Part 1:

By about 1890, the major dominant ninth harmony had become firmly established in compositional and improvisational practice. After 1900, this harmony was routinely used in many musical genres. The two parts of this essay sample a few of these occurrences in repertoires ranging from those that are surprisingly conservative (American marches and ragtime) to those that are remarkably adventurous (French Impressionists and the English and American musicians influenced by them). Composers represented in Part 1 include Costa Nogueras, Friml, Hageman, Herbert, Joplin, Kern, Lehar, Lincke, MacDowell, and Sousa.

Abstract for Part 2:

This continues the study of the major dominant ninth harmony in European and European-influenced music after 1900. Composers represented in Part 2 are Claude Debussy, Lili Boulanger, and Charles Griffes. Scholarship by Taylor Greer, Keith Waters, and Deborah Williamson is summarized and discussed. Composers whose stage works are discussed in the introduction are Herbert, Lehar, Mozart and Wagner.

Foote and Spalding, Modern Harmony (1905) (3)

Here are more of Foote and Spalding's repertoire examples for the dominant ninth chord. These are from p. 160.

The Chopin example comes from the first movement, the second theme in the recapitulation—see the boxes in the third and fourth systems. It is indeed a proper major dominant ninth with a direct resolution (although with octave change). It is also an isolated instance, as nowhere else in the movement, or in the sonata, does the ninth chord play any role. In this theme, the far more prominent feature is the 13th (see arrows), which is a melodic rather than harmonic element but contributes a distinctive sound to the theme and so illustrates that characteristically uncertain positioning of the extended chords between harmonic and linear processes.

Incidentally, the ninth in the example above is not in the second theme in its initial presentation during the exposition:

George W. Chadwick's "Lovely Rosabelle" sets a short ballad from Sir Walter Scott's Lay of the Last Minstrel.  The form is that of a melodrama—like an operatic szena, alternating dramatic recitative with more formal sections of air or chorus melody. The example comes from near the end, where the chorus repeats several times text including "a dirge for lovely Rosabelle" (who has drowned).

The example isn't very convincing as a ninth chord. There are several better ones earlier in the piece. Throughout the 19th century, the major dominant ninth chord as a harmonic entity was more likely to appear in lyrical, sentimental, or even pastoral movements or passages, as here, with "soft" and "sad." Note especially the contrast between the vigorous, minor-key, martial music and this passage.

Here are two good textbook examples that Foote and Spalding might have used to better effect. Note the direct resolution of the ninth C5 in the soprano.

The ^6-^8 figure in the cadence was a common Scots-Irish touch. We have encountered it before in Macdowell's "To a Wild Rose": link to the blog post.

Reference:
Arthur Foote and Walter Spalding, Modern Harmony in its Theory and Practice (1905). Source: Internet Archive; digital facsimile of a copy in the UCLA library.

Foote and Spalding, Modern Harmony (1905) (2)

Foote and Spalding's chapter on the ninth chords is distinctive for its generous number of examples from the repertoire, examples that show clearly the range and character of their own stylistic sources and assumptions.* One can see this already in their first page (p. 158). In Lohengrin below, G5 is strongly emphasized by position and duration, achieving the same kind of "climax coloration" that we found in American songs of the same period (see my essay Dominant Ninth Harmonies in American Songs around 1900: link). As with Wagner, Schubert moves the ninth (but ascending) over a stable dominant bass. The two brief excerpts from Beethoven are common instances from the era of the minor dominant ninth.

The next three examples are also concerned with the minor dominant ninth chord.

Amy (Mrs. H. H. A.) Beach's "Fireflies," no. 4 from Four Sketches, op. 15 (1892), has many dominant ninths, both major and minor. This short passage comes less than twenty bars from the end. Something of the flavor of the whole can be gotten by a slightly larger excerpt (see below). "Walküre" is a striking resolution of the minor dominant ninth, with ninth in the alto and fifth moving upward chromatically. "Parsifal" is a passing major ninth within a wedge shape: F-F#-G in the top voice, F-E-Eb in the bass.

Further comment on Amy (Mrs. H. H. A.) Beach, op. 15n4. Below is a slightly larger excerpt (bars -18 to -10). The passage quoted by Foote and Spalding is boxed; instances of the dominant ninth are circled: all but the last are understood as major dominant ninth chords, but see my final comments and the figure below the score. For the moment, notice the strongly marked direct resolution of the ninth in bars -11 to-10. The tonic reached in bar -10 is the final chord, prolonged by figuration to the end.

Here is a reduced view of the harmony and voice leading:

Obviously, this reduction isn't as good as it could be, since the move major-dominant-ninth to minor-triad is problematic. The composer "sneaks in" a minor ninth just before the chord change, and thus it would have been better to notate the entire example as follows:

Beach's "Fireflies" is one of those rare compositions before 1900 in which the dominant ninth is strongly motivic. Here is the opening, the ninth chords marked (minor in bars 1-2, 8; major in 5-6).

And here is a reduction of the harmony and voice leading:

More of Foote and Spalding's repertoire examples will appear in a subsequent post.

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* Such generosity was not typical earlier in the 19th century, but I should point out that by the end of the century multiple examples from the repertoire were commonly used, either for practical compositional or analytical purposes, as with Foote and Spalding, or as examples of historical practices.

Reference:
Arthur Foote and Walter Spalding, Modern Harmony in its Theory and Practice (1905). Source: Internet Archive; digital facsimile of a copy in the UCLA library.