Schoenberg, Harmonielehre (1912/1922)

This continues and completes the series of posts tracing a line from Simon Sechter in the first half of the nineteenth century through his student Bruckner to Schenker and Schoenberg.

If Schenker took Sechter's ideas about scale degrees and chromaticism in one direction, expanding on them to reinterpret but also reinforce a traditional concept of harmony, Schoenberg went exactly the opposite direction from the same starting point. "In such matters as the existence of non-harmonic tones, the duration of harmonic steps and the notion of chords beyond the seventh, Schoenberg and Schenker could not be farther apart" (Wason 1982, 247).

Schoenberg's conversational, often satirical, style is on display in his chapter on the ninth chord, which begins

The 9th-chord is the stepchild of the system. Although it is at least as legitimate as the 7th-chord, it is still generally regarded as doubtful. It is hard to see why. The system begins to become artistic at the moment when it builds the minor triad in imitation of the major. Then, adding the seventh to form a 7th-chord, although not a necessary result of this first arrangement, is still a possible one. But if this is possible, then 9th-chords, 11th-chords, etc. are also possible, which would of course have the advantage that one could continue the system of extension by stacking thirds. (1922, 417; my translation)

He then spends some time poking fun at theorists' inconsistent treatment of inversions. That he accepts them is obvious from this passage near the end:

Of course, [inversions, such as the fourth inversion] no longer bother any serious people today. In [Strauss's] Salome quite a number of different 9-chords occur. . . . The student will easily find examples in the literature. There is no need to set special laws for [the 9th-chord's] treatment. Those who want to be careful can apply the laws that already came into play with the 7th-chords: that is, resolve the dissonance by step downward, make the root leap a fourth upwards. 

Finally, he says that altered forms of the ninth chord are "undeniably" useful as vagrant chords or in progressions involving vagrant chords, and he supplies this example:

Although this might suggest that even the dominant ninth chord type derives from the diatonic tonic ninth by alteration, in a previous example for ninth chords on secondary degrees, Schoenberg shows the dominant ninth chord first, then the others (including I9). In that respect, at least, he follows 19th-century theoretical tradition.

Reference
Arnold Schoenberg, Harmonielehre (1912/1922).   Source: Internet Archive; digital facsimile of a copy of unknown provenance.