English

A Tonnetz Model for pentachords

History and Overview 2013-01-21 v1 Group Theory

Abstract

This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same T/IT/I class. It is a generalization of the well known \"Ottingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.

Keywords

Cite

@article{arxiv.1301.4255,
  title  = {A Tonnetz Model for pentachords},
  author = {Luis A. Piovan},
  journal= {arXiv preprint arXiv:1301.4255},
  year   = {2013}
}

Comments

27 pages, 12 figures

R2 v1 2026-06-21T23:11:32.262Z