A Generalized Dual of the Tonnetz for Seventh Chords: Mathematical, Computational and Compositional Aspects

Year: 2018 Authors: Sonia Cannas; Moreno Andreatta

Core claim

A generalized dual Tonnetz for seventh chords preserves geometric-musical correspondences and yields compositional tools via Hamiltonian cycles and paths.

Topics

Tonnetz, seventh chords, Hamiltonian cycles, voice leading, computational music theory

Domains

graph theory, simplicial complexes, group actions, Hamiltonian paths, modular arithmetic, music visualization, music composition, educational design

Methods

algebraic modeling, graph construction, computational analysis, compositional examples, voice-leading analysis

Media

OpenMusic, HexaChord, graph representations, circular chord diagrams, Hamiltonian path traces

Source status

This page publishes metadata and extracted analytical signals only. Raw PDF and full OCR text are kept local for now.