Configurations, tessellations and tone networks
Abstract
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 vertices denoting major triads and twelve vertices denoting minor triads. We show that this Levi graph can be realized geometrically as a system of twelve points and twelve lines in R2 with the property that three points lie on each line and three lines pass through each point, in a configuration {123} of Daublebsky von Sterneck type D222. This tonnetz configuration, alongside various generalizations thereof, can be used as a new basis for the composition and analysis of music.
Fields of Study & Subjects
Musicology and Musical Analysis
Quasicrystal Structures and Properties
History and Theory of Mathematics
Publication details
- Journal / source
- Journal of Mathematics and Music
- Publisher
- Informa UK Limited
- Pages
- 1–33
- Publication date
- 24 July 2026
- Language
- EN