Chapter 1 of the dissertation is of interest here. It looks at historical attempts to account for various types of additive harmonies, including the major dominant ninth chord. The saga begins with Rameau, whose attempt at constructing a scientific theory of music produced two strong and highly influential results—(1) a reduction of the large catalogue of figured bass chord labels to the three functional categories of tonic, dominant, and subdominant, and (2) the derivation of all chords from the triad and seventh chord—and another decidedly awkward one that follows from (2): chords by sub-position (supposition), that is, tones added below the chord root. The contradiction between chordal generation and analytical usefulness reveals the central issue about additive harmonies—first among them, the dominant ninth—that will persist throughout the 19th century (and, indeed, in textbooks well into the 20th century): "two different derivations of the same chords [expose] a tension in additive harmonic theorizing between, on the one hand, generating modified chord types by using a structural principle consistent with that used to generate the system’s basic chord types, and on the other, having a chord’s identity be defined by how it behaves in context" (2013, p. 19).
Rameau did not permit inversions of additive harmonies but later theorists influenced by him, notably Marpurg, did, in the process stacking thirds and "inventing" the eleventh and thirteenth chords (p. 28). Marpurg only compounded the problem, however, by stacking thirds below the root. His contemporary (and critic) Sorge corrected this by stacking thirds above the root, though he permitted only the dominant ninth as an independent harmony (pp. 30-32). Combined with Kirnberger's distinction between essential (or independent) and non-essential (linearly derived) harmonies, Sorge's method dominated 19th century theory textbooks and treatises, first among them Catel's Traité d'harmonie (see the previous post in this blog) (p. 32).
Thus, we encounter two of the "three distinct strategies for explaining simultaneities that are not triads or seventh chords: adapting basic chord types, identifying non-chord elements, and formulating new basic chord types' (p. 12). The last is a 20th century preoccupation that does not concern us here. Blättler, for the repertoire he studies, is especially concerned with the voicing of chords, which 19th century theorists are inconsistent about: a particular problem with the "extended-triad model is that it inadequately addresses the crucial impact voicing has on the identity of additive chords" (p. 8). Note, for example, that Catel says the fourth inversion of the dominant ninth may not be used because "it is necessary that the ninth above the root be maintained" but he doesn't say why that is the case.
As a final note, here again is Catel's figure introducing the major dominant ninth. The first might be regarded as an essential harmony (Sorge does so), while the latter is linearly derived. It is easy to see why musicians around 1800 would think it is a given that elevenths, thirteenths, and other complex formations would be "non-essential," but equally easy to see why they might equivocate about the dominant ninth.
Reference:
Damian Blättler, "A Voicing-Centered Approach to Additive Harmony Music in France, 1889-1940," PhD dissertation, Yale University, 2013.
Damian Blättler, "A Voicing-Based Model for Additive Harmony, "Music Theory Online 23/3 (2017).
