Techniques of Polytempic Polymicrotonal Composition

  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...

There is a contradiction at the heart of the New Complexity movement so glaring that it should have ended careers. It hasn't, because the people who benefit from it control the conversation. This essay is an attempt to change that. The New Complexity — Ferneyhough, Barrett, Dench, the UK network that decides who exists and who doesn't — presents itself as the apex of Western musical thought. Rigorous. Uncompromising. Intellectually serious in ways lesser musics cannot be. Its theoretical self-image draws heavily on Theodor Adorno, whose withering dismissal of jazz as a regressive, pseudo-individualist commodity form remains foundational to the European new music worldview. Jazz, for Adorno, was not serious music. It was administered rebellion — the appearance of freedom within a system designed to prevent it. And yet. The extended technique vocabulary that defines New Complexity on the instrumental level — multiphonics, overblowing, singing while playing, microtonal inflection,...

  Thoegersen vs. Messiaen, Two Objective Views A structural and historical comparison First View: What Messiaen Did That Thoegersen Hasn't Messiaen built a complete, unified compositional language and then demonstrated it at every scale simultaneously — from solo organ miniatures to the Turangalîla Symphony. The system and the catalog were coextensive. He also had institutional reach: the Conservatoire classroom, the published treatises, and the students who became the next generation. His ideas propagated through people, not just texts. His mysticism was also culturally legible. Catholic theology gave him a shared symbolic framework with a broad audience. Thoegersen's mysticism is more philosophically austere — it doesn't have that ready-made audience. What Thoegersen Has Done That Messiaen Didn't Messiaen's polymodality was simultaneous but not structurally independent. The layers in his music share a tempo, a conductor, a single notational fra...

Native MLT Modes in Microtonal Equal Temperaments Modes of limited transposition built from each temperament's own step vocabulary No 12-TET reference. C = chromatic step (smallest interval of the ET). 2C = double chromatic, etc. The Principle Modes of limited transposition exist in any ET where n is not prime. A mode repeats every d steps (its period) across the octave, where d divides n. The fewer transpositions, the more internally symmetric and coloristically concentrated the pitch set. These modes can replace the full-gamut approach for individual layers, yielding a prismatic, Messiaen-like color logic within the polytempic polymicrotonal architecture. Step Size Reference All interval sizes in cents. Each ET's chromatic step (C) and multiples thereof. No 12-TET equivalents named. ET C (1 step) 2C 3C 5C 7C 24-TE...