François-Joseph Fetis “rejected the leading-tone seventh chord, all types of ninth chords, and the supertonic seventh chords. . . as true chords. Instead these verticalities, as are all other dissonant formations save for the dominant seventh, are explained using the concepts of substitution and/or retardation. Substitution is the replacement of the fifth scale degree in a dominant chord by the sixth scale degree, which produces both the dominant ninth chord and leading-tone seventh chords” (Blättler 2013, 56).See two examples extracted from Blättler’s Figure 1.32 below. Fétis handles inversion by expanding the common argument against the fourth inversion of the ninth chord against all inversions of the chords listed in the quote above (56-57).
Fétis was based in Brussels. During the same period, Siegfried Dehn worked in Berlin as a well-respected teacher, archivist, and editor. Dehn sought a way to include elevenths and thirteenths among the principal harmonies of a key (Hauptaccorde), a broader category than source chords (Stammaccorde), which are triads. (The dominant seventh is among the Hauptaccorde.) Dehn divides his harmony treatise in the conventional way into two parts (Capitel in the original): theoretical and practical, the first part dealing with the generation and derivation of harmonies, the second with their application to composition. The 21st of 25 chapters (§§ in the original) in Part 1 is on the ninth chord (the 22d and 23d are on the eleventh and thirteenth chords, respectively). The corresponding chapters in Part 2 are 24-26 (of 32).
As Blättler describes Dehn's method of derivation,
Ninth chords are generated . . . by placing a third both above and below the diminished triad of a key . . . ; eleventh and thirteenth chords are generated by placing the tonic note beneath the dominant seventh and ninth chords respectively. . . . These chords cannot appear in inversion nor can they sustain omissions of their roots, uppermost tones, or leading tones—restrictions [justified] on practical grounds. The extended triads cannot be inverted because their identity is dependent on a specific voicing [that is, stacks of thirds]. (p. 33)Thus, although Dehn succeeds in placing these among the Hauptaccorde, their practical application [pace his own claims] is quite limited (Blättler, 34-35). In Part 2, chapter 24 "On the treatment of ninth chords," Dehn shows only the major and minor dominant ninths, but he does include secondary dominants. The chapter is primarily concerned with voice-leading. Here is his table of proper (regelmässige) resolutions (Dehn 1860, 215):
The important aspect of this figure is that Dehn sees no problem with a direct resolution of the major dominant ninth chord to the tonic, with its voice-leading of ^6 to ^5. This is certainly more in tune with compositional practice by 1840 than the restriction of harmonies to triads and seventh chords. He even provides a sequence with secondary dominant ninths (boxed):
Alas, when he offers a comprehensive example for all three extended chords, Dehn reverts to a chorale where those chords appear exclusively over dominant basses (boxed), effectively nullifying the ninth chord's status as an independent harmony (Dehn 1860, 219). This ambiguity and uncertainty, I note again, is typical of theoretical treatments through the century.*
* A contributing factor to the confusion is Dehn's unusual sidelining of suspensions—discussion is confined to the final chapter of Part 2, along with other non-harmonic note figures.
Reference:
Damian Blättler, "A Voicing-Centered Approach to Additive Harmony Music in France, 1889-1940," PhD dissertation, Yale University, 2013.
Siegfried Dehn, Theoretisch-praktische Harmonielehre (1840; second edition 1860). The latter was the one available to me. Its source: Digital facsimile from the Bayerische Staatsbibliothek through the Digitale Bibliothek, Münchener DigitalisierungsZentrum.
François-Joseph Fétis, Traité complet de la théorie et de la pratique de l’harmonie (1844).
