A 5-dimensional Tonnetz for Nearly Symmetric Hexachords
Paper published in Journal of Mathematics and Music (2020)
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. Read here.
Dodecatonic Cycles and Parsimonious Voice-Leading in the Mystic-Wozzeck Genus
This paper develops a unified voice-leading model for the genus of mystic and Wozzeck chords. These voice-leading regions are constructed by perturbing symmetric partitions of the octave, and new Neo-Riemannian transformations between nearly symmetric hexachords are defined. The behaviors of these transformations are shown within visual representations of the voice-leading regions for the mystic-Wozzeck genus. Read here.
Recent Music Research Talks
The Music Society at Temple (themus) Conference | Philadelphia, USA | April 3, 2021
Virtual conference, Temple University [Website]
Talk title: The Final Piece of the Neo-Riemannian Puzzle: Dodecatonic Cycles and a 5-dimensional Tonnetz for Nearly Symmetric Hexachords.
McGill Music Graduate Symposium | Montreal, Canada | March 12-14, 2021
Virtual conference, McGill University [Website | Facebook]
Talk title: The Final Piece of the Neo-Riemannian Puzzle: Dodecatonic Cycles and a 5-dimensional Tonnetz for Nearly Symmetric Hexachords. Presentation on March 13, 2021. Abstract here.