3 papers
math.CO2026
Tonnetz Theory, Classical Harmony, and the Combinatorial Geometry of Abstract Musical Resources
Jeffrey R. Boland, Lane P. Hughston
In a previous submission, we established a fundamental relation between tone networks and configurations. It was shown that the Eulerian tonnetz can be represented by a …
math.CO2025
Configurations, Tessellations and Tone Networks
Jeffrey R. Boland, Lane P. Hughston
The tonnetz, which is commonly represented as a tessellation of the plane by a triangular network of tones, can also be represented as a bipartite graph of degree three with twelve…
cs.SD2022
Mathematical Foundations of Complex Tonality
Jeffrey R. Boland, Lane P. Hughston
Equal temperament, in which semitones are tuned in the irrational ratio of , is best seen as a serviceable compromise, sacrificing purity for flexibility. Just intona…