Feb 10, 2013

Those Schillinger Symbols, Explained

Yesterday I received this email from Schillinger historian Louis Pine regarding my post "A Tune-Dex Fakebook and Some Schillinger Symbols." He gives a clear (and authoritative) explanation of the symbols I mentioned in the post. I really appreciate his taking the time to write - thanks, Lou!

Dear Peter,

I just came across your Sept. 30, 2012 post titled “A Tune-Dex Fakebook and Some Schillinger Symbols.” I’m writing to answer your questions about the Schillinger symbols you found in “Dr. K’s” fake book.

You are correct about the first symbol denoting root movement of a major 3rd. The square root of 2 explanation can be found on page 102 of Volume I of The Schillinger System of Musical Composition. It states:

The mathematical expression for this system of tuning [equal temperament] (developed by Andreas Werckmeister in Germany, in 1691) is.
Two expresses the octave ratio of frequencies. i.e., 2 ÷ 1; the exponent 12 expresses the number of the uniform ratios within one octave. The semitones are integers when they express the logarithms to the base of. 
[note: Blogger doesn't seem to provide a better way to get these symbols into the text.]

A footnote that begins on page 101 and continues on page 102 explains further about this topic. If you don’t have Vol. I to see this information, you can read about the twelfth root of two here: http://en.wikipedia.org/wiki/Twelfth_root_of_two.

You are correct that the “S47” symbol denotes a seventh chord. Your idea that the “47” “…was a way of showing that Am6 was really a seventh chord (F#m7b5)…” is also correct. To understand this, let’s look at two charts. The following chart comes from page 388 of Vol. I:

This chart about seventh chords comes from page page 447 of Vol. I:

The generic symbol “S” means a “structure” or chord. Schillinger described the overall structure of a chord by a number that indicates the distance between its outer tones in root position. Thus, an “S5” represents a triad and an “S7” represents a seventh chord. Notice in the first chart, Figure 45, has an “S4(5)” chord, which is a diminished triad. In the second chart, Figure 141, the editors were not consistent in their labeling (or maybe Schillinger wasn’t in his original typescript and the editors didn’t correct it). Be that as it may, IF WE WERE consistent in labeling “S4” in Figure 141, it would be labeled “S4(7).” Thus, Dr. K simply didn’t put the parentheses around the “7” when he wrote “S47.” As you can see, the “S47” signifies a “m7b5,” or a half-diminished seventh, as you surmised.

You are also correct about the third symbol. It indicates “Harmonic continuity as a major generator.”

I hope this clarifies for you the questions you had. For academic purposes, I’d sure like to know more about Randy’s dad.



Louis (Lou) Pine
Historian of Joseph Schillinger's life and work



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