2 papers
math.CO2026
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…
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 …