This article constructs generic voice-leading spaces by combining geometric approaches to voice leading with diatonic set theory. Unlike the continuous mod-12 spaces developed by Callender, Quinn, and Tymoczko, these mod-7 spaces are fundamentally discrete. The mathematical properties of these spaces derive from the properties of diatonic pitch-class sets and generic pitch spaces developed by Clough and Hook. After presenting the construction of these voice-leading spaces and defining the OPTIC relations in mod-7 space, this article presents the mod-7 OPTIC-, OPTI-, OPT-, and OP-spaces of two- and three-note chords. The final section of the study shows that, although the discrete mod-7 versions of these lattices appear quite different from their continuous mod-12 counterparts, the topological space underlying each of these graphs depends solely on the number of notes in the chords and the particular OPTIC relations applied.
Research Article| October 01 2019
Generic (Mod-7) Voice-Leading Spaces
Journal of Music Theory (2019) 63 (2): 167–207.
Leah Frederick; Generic (Mod-7) Voice-Leading Spaces. Journal of Music Theory 1 October 2019; 63 (2): 167–207. doi: https://doi.org/10.1215/00222909-7795257
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