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From ScratchWritings in Music Theory$
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James Tenney, Larry Polansky, and Lauren Pratt

Print publication date: 2015

Print ISBN-13: 9780252038723

Published to Illinois Scholarship Online: April 2017

DOI: 10.5406/illinois/9780252038723.001.0001

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The Structure of Harmonic Series Aggregates

The Structure of Harmonic Series Aggregates


(p.240) Chapter 11 The Structure of Harmonic Series Aggregates
From Scratch

James Tenney

, Larry Polansky, Lauren Pratt, Robert Wannamaker, Michael Winter
University of Illinois Press

James Tenney discusses the structure of harmonic series aggregates and provides a detailed explanation of the genesis of his HD function. He describes, through first principles (perception, simple mathematics), what happens when “two or more compound tones are sounded simultaneously.” Using simple properties of relatively prime (reduced) ratios, the harmonic series, and least common multiples and greatest common divisors, Tenney approaches harmony in the way he had suggested some thirty years earlier: “to start if possible at the very beginning, to clear the mind of loose ends whose origins are forgotten; loose ends and means become habits.” After exploring harmonic intersection and disjunction, Tenney concludes with an analysis of harmonic distance and pitch distance.

Keywords:   harmony, James Tenney, harmonic distance, tone, harmonic series, harmonic intersection, harmonic disjunction, pitch distance, HD function

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