Generic (Mod-7) Voice-Leading Spaces Journal Article uri icon

Overview

abstract

  • 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.

publication date

  • October 1, 2019

has restriction

  • closed

Date in CU Experts

  • January 18, 2025 9:05 AM

Full Author List

  • Frederick L

author count

  • 1

Other Profiles

International Standard Serial Number (ISSN)

  • 0022-2909

Electronic International Standard Serial Number (EISSN)

  • 1941-7497

Additional Document Info

start page

  • 167

end page

  • 207

volume

  • 63

issue

  • 2