To be as clear as I can: the blog is not a primer in ninth-chord types, and the mode of harmonic theory is 19th-century based classical-music theory, not jazz theory. Although there is some overlap in repertoires in the Swing era and in the American musical, jazz theory is primarily aimed at a different, more contemporary repertoire and performance practice, and it wields a different notation system in service of a much wider range of ninth (and other "extended") chords and their voicings. Jazz theory is now well represented in a variety of online resources.
[Note 19 November 2018: I have published an essay titled Dominant Ninth Harmonies in the 19th Century: A Gallery of Simple Examples Drawn from the Dance and Theater Repertoires: link to the essay. Here is the abstract: "In European music, freer treatment of the sixth and seventh scale degrees in the major key encouraged the use of independent V9 chords, which appear already early in the nineteenth century, are common by the mid-1830s, and are important to the process by which the hegemony of eighteenth-century compositional, improvisational, and pedagogical practices were broken down. This essay provides multiple examples of the clearest instances of the V9 as a harmony in direct and indirect resolutions."]The origin of the dominant seventh chord in a passing tone is generally accepted, and there is certainly sufficient evidence in 17th century music to support that. At (a) below are two triads in four voices. At (b), a passing tone connects the notes in the upper voice. At (c), the passing tone is "frozen" and the resulting harmonic entity is a dominant seventh chord. At (d), an alternate voicing allows a complete chord in bar 1.
By analogy, the dominant ninth chord could also be said to arise from a passing tone, as in the series at (e) to (g) below, where the passing tone is within the dominant chord (f), but alternatively connects two chords (g).
We will see examples of these in the repertoire, but it is clear that another derivation is equally prominent (if we judge from the evidence of musical practices in the first quarter of the 19th century rather than from the assumptions of a historical narrative alone). The progression at (h) is modified at (j) with a leap upward—this "one too far" figure is one of the most distinctive and characteristic stylistic identifiers of the Laendler and early waltz repertoire; it is in fact applied to every scale degree, not only to ^6. In this specific case, a potential dominant ninth is formed, although we would have to call it "apparent" because the 9 resolves to 8 (A5 to G5) within the chord. At (k) and (m) are two versions that are less abstract: at (k), the 9 is a neighbor note rather than an appoggiatura; at (m), on the other hand, the expressive intensity of the appoggiatura is heightened with a larger leap (C5 to A5).
At (a) below, the melody of the last example above is shown with the typical Laendler accompaniment. At (b) is the commonplace figure where a two-bar idea over the dominant is repeated (and slightly adjusted) over the tonic. The same notes, A5-G5, are 9-8 over the dominant bass, then 6-5 over the tonic bass. It is not the topic of this blog, but the add6 chord derives in important part historically from these parallel treatments of ^6 over dominant and tonic in the waltz repertoire. At (c) is what I call a direct resolution, where the ninth (A5) moves to the tonic's fifth (G5) without an intervening note. At (d), is an indirect resolution, or what I like to call an "almost direct resolution," where the repetition of the two-bar idea sets up a pattern such that F5 in bar 1 can be heard to resolve to E5 in bar 3 and A5 in bar 2 to G5 in bar 4.
Each of the figures shown above can be found easily in the repertoire, but they do not by any means exhaust the treatment of ^6 or of all the notes in the upper tetrachord. The musicians of this era were creative artists—most of them violinists skilled at improvisation as much as composition or score-compliant performance—and they tested multiple ways to exploit the expressive potential of ^6 and the dominant ninth harmony.
