Voice-Leading Spaces

Abstract

This paper studies networks of pitch-classes that model voiceleading-the progression of pitches to form horizontal voices or lines. While tonal voice-leading depends on distinctions between step and leap, consonance and dissonance, chord-tone and embellishment, voice-leading in post-tonal music simply and nonnormatively describes the motions of pitches, one to another. First, I stipulate some limitations on totally free voice-leading and construct a complete taxonomy of voice-leading motions. Then I examine Richard Cohn's explicit coupling of transformation and voice-leading of major and minor triads as represented on Hugo Riemann's tonnetz. The tonnetz is a traditional example of what I have previously called a compositional space; such spaces are outof-time networks of pcs that can underlie compositional or improvisational action. After studying various transformations of the tonnetz, voice-leading is implemented by the use of another type of compositional space, two-partition graphs. These graphs are generalized so that pairs of pcsets connected in the graph need not be disjoint nor form members of only one set class. Any specified voice motions can be stipulated. The result is a collection of voice-leading spaces, a new category of compositional space. Finally, I describe an algorithm that allows one to construct voice-leading spaces of any degree of complexity or closure. This content downloaded from 157.55.39.35 on Mon, 29 Aug 2016 05:57:48 UTC All use subject to http://about.jstor.org/terms

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