Charles L. Seeger, jr., and Edward G. Stricklen, [Outline of a Course in] Harmonic Structure and Elementary Composition (Berkeley, CA: [self-published], 1916). A copy sent by Seeger to the Harvard College Library is available through the Internet Archive.
Seeger was the spouse of Ruth Crawford Seeger. He is well-known for strong musicological and ethno-musicological interests. He was born in 1886, graduated from Harvard in 1908, and after study in Germany took up a position at the University of California at Berkeley; he was dismissed in 1916 for his public opposition to U.S. entry into World War I. (Information from Wikipedia.) Stricklen was a long-time instructor at the University, beginning as a Reader under Seeger but then becoming chair of the music department after Seeger left. He was skilled as a pianist and composer but never attended college. (Information from University of California In Memoriam [1957]: link.)
The title page makes clear what was obvious anyway, that these are course materials--the subtitle is "An outline of a course in practical musical invention"--and that Stricklen did the editorial work and revision. Seeger's grandiloquent introduction has little to do with the actual content; it ends with modern ideas going "upward and onward in true Hegelian fashion, to higher, more complete and more comprehensive forms, not forsaking the old, but reaffirming transcending and embellishing it as each new fragment of dissonant chaos is conquered and found beautiful to the eyes of a more universal consciousness" [4]. This is interesting with respect to extended and other complex chords but the real work of the book is mostly traditional diatonic writing in four voices. The theory is dualist but that has little impact on instruction. Chord symbols are inconsistent but generally are figures or scale-degree-theory capital letters with figures added where needed.
There are two parts: diatonic consonances and diatonic dissonances. Each has 15 chapters. Stricklen's preface [5] announces a "Chromatic Harmony" but that was apparently never written. In Part 2, chapters 16-27 are on seventh chords, beginning with the dominant seventh but also giving considerable attention to other diatonic seventh chords. Chapters 28 & 29 are on ninth chords, and chapter 30 presents 11th & 13ths.
The dualist theory relies on overtones and undertones, and so the dominant ninth-chord is derived from the harmonic series (46). "On account of its natural origin, it is the only primary ninth chord in the diatonic key scheme" (47). Seeger and Stricklen require the seventh to be present in all positions, and like most others they reject the fourth inversion. The major-key vii°7 is the dominant ninth without root (a very old idea but consistent with derivation from the harmonic series). The chapter is 4 pages; other ninth chords get 2 pages (50-51), and elevenths and thirteenths another 4 pages (52-55). The other ninths are accepted--see an example below. There are no repertoire examples but "the student is recommended to the study of the works of Grieg in which may be found fine examples of the treatment of these chords" (51).
In the end, the dualist superstructure gives way to traditional instruction, but it is to be noted that the extended chords are accepted as usable.
Howard E. Parkhurst, A Complete System of Harmony (New York: Carl Fischer, 2d ed. 1908)
Parkhurst was born in Ashland, Massachusetts in 1848. I don't have information about his training but I assume it was in Boston. He spent his entire career as an organist in New York; he died in 1916. Parkhurst composed a number of religious pieces. A Complete System is his only book on music theory.
The most conservative of the volumes examined in this new series, it uses figured bass and has no Roman numeral labels. Parkhurst does not recognize the dominant ninth chord (in fact, never mentions it).
Because of the focus on figured bass, the figure "9" does occur fairly often. Under "suspension of the ninth" an internal resolution appears.
Under "passing chords" a decidedly unconvincing reading makes a V11-V9 neighbor pair subordinate to an unaccented triad.
An equally plausible reading gives even more prominence to V9 in a direct resolution:
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