A 5-dimensional Tonnetz for nearly symmetric hexachords. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Mohanty, Vaibhav
• Is Part Of: Journal of mathematics and music. Volume 16:Issue 1(2022)
• Page Start: 121
• Page End: 131
• Publication Date: 2022-01-02
• Subjects: Tonnetz -- mystic -- Wozzeck -- voice-leading parsimony -- hexachord; 00A65; Music theory -- Periodicals; Music -- Mathematical models -- Periodicals; Music -- Mathematics -- Periodicals; 781.2
• DOI: 10.1080/17459737.2020.1799087
• Languages: English
• ISSNs: 1745-9737

Abstract

Abstract : The standard 2-dimensional Tonnetz describes parsimonious voice leading connections between major and minor triads as the 3-dimensional Tonnetz does for dominant seventh and half-diminished seventh chords. In this paper, a 5-dimensional Tonnetz is introduced, providing a geometric framework for parsimonious voice leading among nearly symmetric hexachords of the mystic-Wozzeck genus. Cartesian coordinates for points on this discretized grid, generalized coordinate collections for the vertices of the 5-simplices corresponding to mystic and Wozzeck chords, and the geometric nearest-neighbours of a selected chord are derived.