Techniques of Polytempic Polymicrotonal Composition

Techniques of Polytempic Polymicrotonal Composition Compression of Harmony in Polymicrotonality: From Whole-Tone to Polymicrochromatic — Revisited Blog post, 2026 I want to return to an earlier blog (XIIb, June 2025) on harmonic compression in polytempic polymicrotonal composition. Having recently revisited Joseph Straus's post-tonal theory text and Bartók's String Quartet No. 4, I can now name what that blog was demonstrating more precisely than I did at the time. The Existing Device In post-tonal practice, the compression of the whole-tone tetrachord to the chromatic tetrachord functions as a directed harmonic device. The whole-tone tetrachord — four equally spaced pitches, each a whole tone apart — spans a tritone. The chromatic tetrachord compresses this to a minor third, with each interval a semitone. Bartók's String Quartet No. 4 is the concentrated demonstration. His chromatic clusters — four consecutive semitone-adjacent pitches, for example [C, C♯, D, D♯], with int...

  Entropy, Graining, and the Music Nobody Can Hear All At Once A mathematician friend recently sent me a chapter he is writing on mathematical entropy and the arts. His intent was generous: here, he was saying, is a formal framework that might describe what I do. He was right that entropy theory is the right tool, rather than the simplistic calculus integration/differentiation metaphor I had previously considered. What I want to explore here is what happens when that tool is applied rigorously — where it fits my music, polytempic polymicrotonality, where my music strains it, and what new theoretical apparatus my music turns out to require. The Framework The chapter's central argument is elegant: entropy is never simply a property of a signal. It is always a property of a signal relative to a receiver — relative to what the author calls a graining strategy, the set of distinctions a listener is equipped and disposed to make. Two listeners hear the same piece of music; one has spe...