The article presents a generalization of Euler’s tonnetz on a triangulated surface, allowing for more diverse labellings than just notes or pitch-classes. The study introduces the concept of edge labellings, which lead to a plethora of examples related to crystallographic reflection groups. The author also explores the intriguing connection between mathematical Langlands duality and major/minor duality. Additionally, the paper constructs some ‘exotic’ type-A2 examples and a tonnetz on a sphere that encodes all major ninth chords.
Publication date: 28 Jan 2022
Project Page: https://arxiv.org/abs/2401.15692v1
Paper: https://arxiv.org/pdf/2401.15692
