*****
It is of paramount importance to remember that when I give examples of harmonic continuities in the format of the book - a four voice transformational stratum above a constant root bass part - these are simply proofs of what the series implies is most natural from a purely harmonic standpoint. Sure, this very pure form of harmony can be used in actual composition - some of my musical examples in Appendix I, for example - but it is far more statistically normal for contrapuntal and harmonic elements to be combined in actual compositions: Those elements that I refer to as harmono-contrapuntal effects.
Before Joseph Schillinger codified the transformational logic I use circa 1940, this absolutely pure form of harmony did not even exist, so the great composers of traditional music were not even consciously aware of it: Since traditional harmonic practice grew out of tonal counterpoint - which grew out of the previous modal contrapuntal style - counterpoint was never completely separated from harmony until Schillinger. So, if you analyze Beethoven, for example, with an eye to finding interrupted crosswise transformations during progressive root motions, you won't find them (Or, at least I never have). Ditto every other traditional composer from Bach to Brahms.
The value of understanding on a rational level what the series implies is mechanically most natural for harmonic continuities cannot be understated, however: I'm sure all of "The Three B's" would have loved to have had such information. However, what is most natural is not all that is possible, obviously. Palestrina and Bach were meticulous in their voice leading, following the contrapuntal rules of their times to near perfection: Mozart and Beethoven, not so much. Chopin would be considered positively reckless compared to Beethoven, however, but he was simply exploring some of the less natural possibilities for expressive effect. Nothing wrong with that. By the time you get to the heyday of Jazz music, those less natural possibilities were used to forge an entirely new style of music. Now, from neo-classical to bubble gum pop to heavy metal, those less natural possibilities are being used to forge several different kinds of musical styles. Not that the writers of such music are consciously aware of that, of course.
Schillinger himself pointed out several less natural possibilities for harmonic vioce leading: Constant root, constant third, constant fifth, and constant seventh (For the complete skinny on those, you'll have to consult him: I'm only interested in what is most natural according to what the overtone series implies for this book). By understanding what is and is not natural according to the series' implications, the composer is freed to forge his own style and to get whatever musical effect he wants. The only limit is your imaginaton.
The same holds true for counterpoint: By understanding that there is only one primary law - only imperfect consonances may move together in stepwise parallel motion - one is free to go far beyond the Bachian rule-set to forge a personal contrapuntal style, as I have done (Though I'm still pretty conservative: My main thrust is that I have liberated every inversion of every chord to get some highly colorful and dissonant effects).
By combining the natural/less natural harmonic transformational possibilities with the natural/less natural contrapuntal possibilities, an endless number of personal styles can be created. So, anyone who says that tonal music's resources have been exhausted is an abject, imaginationless idiot in the extreme.
*****
About my relationship with The Schillinger System, and my feelings about it:
Schillinger spends a lot of time in The System arguing that natural, intuitive musical talent is not necessary to compose: That's what the "system" part of it is all about. Ironically, however, he proves otherwise, because he himself had no natural intuitive musical talent: The musical examples in his books are laughably bad (He wrote them), and I've heard some of his compositions. They are lame. So, the bottom line is that Schillinger, though a genius in many respects, had no musical talent, and that's why he tried so desperately to prove that talent wasn't a prerequisite. Sad, really.
Schillinger's lack of insight is never more starkly evident than when he ignores the implications of the series: He got so close to figuring it out - and he provided me with much of the material I used to figure it out - but, no cigar.
The entire history of western art music has been the history of men with natural, intuitive musical talent deducing what the harmonic overtone series implies is possible with music. Generation after generation of these talented men built upon the work of their predecessors until... well... I figured out - and demonstrated - that at the root of it all is the harmonic overtone series (Of course, music theory started with the series, and so it has only come full circle with my work). This evolution of western art music and the technical understanding of it was only possible because western art music is literate: We can write it down and share it with future generations.
Far from the be-all and end-all of music, my work simply proves that the possibilities are endless, and that we've barely even scratched the surface. Schillinger thought he'd done this, but he hadn't. There is a lot of wonderful information in the Schillinger System, but I had to dig through a pig sty's worth of crap to uncover it.
*****
First thing I thought - after I stopped laughing, of course - was, "Man, that old BMW hack job would be worth a lot of money today!" Yes, I have a Beemer of my own.
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