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Book Theft with Schoenberg

Right before I graduated from college, I helped myself to a copy of Schoenberg’s Theory of Harmony from the library. (Yes, I feel bad about it) The section entitled “Chords with six or more tones,” contains some fascinating examples of very complicated polychords and some thoughts about why they sound so rich and harmonious, even consonant, when on paper they would appear to be harshly dissonant.  Schoenberg identifies a few aspects of this phenomenon such as the voicing, instrumentation, and method of resolution. But then he goes on to say, “Why it is that way and why it is correct, I cannot yet explain in any detail...but that it is correct, I firmly believe, and a number of others believe it too.”

I’m sure I looked at this section before in the almost 20 years since I liberated it from its shelf, but it has definitely been some time since I did. Even if I had, I would have had no clue what he was talking about, or how to hear those remarkable harmonies. Now, after years of experience performing, writing, and listening to music, I absolutely agree--those harmonies sound amazing, though I don’t know why. In addition, it’s absolutely true, that, “there is...also an instinctive(possibly exaggerated) aversion to recalling even remotely the traditional chords...they would sound too cold, too dry, expressionless.” This has also become clear to me in my writing and playing experience: it’s incongruous to mix these lush harmonies with simple tonal chords, they lack, as Schoenberg says, “perspective, depth.” Even a “consonant” interval like an octave can sound jarring and out of place when these kinds of harmonies are present.

Theory of Harmony is probably most famous for the way Schoenberg provides an explanation for the almost physical pull of a dominant chord towards its tonic; it has to do with the overtone series, subliminal frequencies that occur every time a tone is sounded. His explanation for how this series of  overtones influences our hearing is so well thought out that I wonder if he also thought to use it to explain why these polychords sound consonant?  Do they also mirror the subtler gravitational attractions of the higher overtones of notes? Their voicing certainly does; wider intervals between lower notes, smaller ones between upper notes.

Schoenberg also writes about the effect of tone color on harmony, which is especially fascinating, as we now know that timbre is actually just a result of the differences in amplitude of the subliminal frequencies of a fundamental pitch. When a violin and a clarinet play an Eb, the fundamental pitch is the same, but the uniqueness of each instrument and its player elicits varying amounts of the higher overtones, thus changing the timbre between one instrument and another. This is how synthesized instruments used to work: generate a fundamental wave at a certain pitch, generate waves at as many of the higher partials as you can, then vary their amplitude to match the sound profile of the instrument you are trying to emulate. Schoenberg (as far as I can tell) didn’t know any of this, yet he seems to predict that further study would eventually lead to an understanding of tone color akin to our modern understanding of harmony: “...if it is possible to create patterns...that are differentiated according to must also be possible to make such progressions out of the tone colors...whose relations with one another work with a kind of logic entirely equivalent to that logic which satisfies us in the melody of pitches.” Schoenberg here appears to not only have presaged the development of his own serial methods but also understood that further analytical investigation of the physical nature of pitch and timbre was inevitable.

He was wrong, however, in one respect: “Tone color is...the main topic, pitch a subdivision.” We know today that pitch is the “main topic”, that in fact tone color or timbre is the result  of pitch. The further analysis into the inner workings of tone color which Schoenberg predicted actually resulted in a deeper understanding of the role of the higher partials in producing specific timbres. Knowing this, can we now convincingly extend his theory of how the overtone series influences the tonic dominant relationship to these more complicated chords?  

As we have pointed out, these harmonies function well when properly voiced and orchestrated.  First of all, the voicings are clearly spaced in a manner at least superficially reminiscent of the overtone series. Second, given that timbre is a by-product of pitch, the fact that a complex harmony works well with a certain combination of instruments and not with others indicates that it is the subliminal frequencies created by these specific instruments that make the harmonies coalesce into a pleasing sound. Orchestrating an eight-note chord for bassoon, oboe, reeds, and trumpet may produce an unpleasant sound, but the same notes played on bass, french horn, and clarinet may sound beautiful. What appears as a change in tone color on the surface is in fact a shift in the subliminal harmonies being created by the instruments, and it is these unheard pitches that determine the quality of the sound. There is no need, then, for a theory of tone color progression; the theory already exists, and was in fact created by Schoenberg himself in the very first chapters of Theory of Harmony.

Most likely this has already been realized by everyone else but me, but in my defense, allow me to quote from Schoenberg himself: “Perhaps I have invented much that was already given; but I invented it and did not learn it from reading.  I found it out for myself...because I experienced it.” If there is anything of benefit to anybody else in these ramblings, I’d be pleased, but I’m most pleased with the fact that I finally perceive a tiny bit of what Schoenberg had discovered. Maybe the twenty odd years it took was punishment for my larceny. Fair enough.