Hexatonic Cycles

Richard Cohn

in Audacious Euphony

Published in print January 2012 | ISBN: 9780199772698
Published online May 2012 | e-ISBN: 9780199932238 | DOI:

Series: Oxford Studies in Music Theory

Hexatonic Cycles

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Chapter 2 presents the first of two preliminary models of the triadic universe, based on voice-leading proximity, On this conception, the most proximate triads are those whose roots are related by major third, which share membership in a hexatonic cycle. The voice-leading proximity of major-third-related triads is associated with the fact that, in moving between them, they along require that voices move in contrary motion. The chapter argues that this contrary-motion property underlies the oft-observed affiliation of major-third relations with supernatural phenomena in nineteenth-century music. The chapter presents a method for visually representing triaidic voice-leading proximity, based in the 19th-century Tonnetz associated with the writings of Hugo Riemann, and also a method for tracking the individual motions through a cycle, adapting triadic transformations from Riemann via David Lewin. The final part of the chapter asserts that the triad’s capacity for smooth voice leading is unique to it; that this ability is based on its status as minimal perturbation of the perfectly even augmented triad; that the minimal perturbation (near evenness) property generates the characteristic routines of Romantic triadic syntax in the same way that the acoustic perfection property generates the characteristic routines of classical syntax; and that the status of major and minor triads in European music is therefore overdetermined.

Keywords: hexatonic; tonnetz; lewin; triadic transformation; riemann; semitonal displacement; minimal perturbation; near evenness; overdetermination

Chapter.  10521 words.  Illustrated.

Subjects: Music Theory and Analysis

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