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:

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.