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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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Introduction to “Contributions toward a Quantitative Theory of Harmony”

Introduction to “Contributions toward a Quantitative Theory of Harmony”


(p.234) Chapter 10 Introduction to “Contributions toward a Quantitative Theory of Harmony”
From Scratch

James Tenney

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

James Tenney presents the introduction to his 1979 essay “Contributions toward a Quantitative Theory of Harmony.” In this introduction, Tenney discusses the history of consonance/dissonance, paying attention to the semantic problem, relations between pitches, qualities of simultaneous aggregates, and contextual as well as operational and functional senses of consonance/dissonance. He also explores the structure of harmonic series aggregates, focusing on harmonic intersection and disjunction, harmonic density, and harmonic distance and pitch mapping. Finally, he considers problems of tonality by analyzing harmonic-melodic roots and the “tonic effect,” along with harmonic (chordal) roots, the “fundamental bass,” and a model of pitch perception in the auditory system. In an epilogue, Tenney describes new harmonic resources as well as prospects and limitations of his contributions.

Keywords:   harmony, James Tenney, quantitative theory, consonance, semantic problem, dissonance, harmonic series aggregates, harmonic distance, tonality, pitch perception

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