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arXiv · 1806.06703

A 5-Dimensional Tonnetz for Nearly Symmetric Hexachords

Vaibhav Mohanty
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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, I present a geometric model for a 5-dimensional Tonnetz for parsimonious voice-leading between nearly symmetric hexachords of the mystic-Wozzeck genus. Cartesian coordinates for points on this discretized grid, generalized coordinate collections for 5-simplices corresponding to mystic and Wozzeck chords, and the geometric nearest-neighbors of a selected chord are derived.

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Vaibhav Mohanty. 2018-06-15. A 5-Dimensional Tonnetz for Nearly Symmetric Hexachords. https://doi.org/10.1080/17459737.2020.1799087

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