  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.
