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 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