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arXiv · 1301.4255

A Tonnetz Model for pentachords

Luis A. Piovan
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Abstract

This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same $T/I$ class. It is a generalization of the well known Öttingen-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.

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Luis A. Piovan. 2013-01-17. A Tonnetz Model for pentachords. https://arxiv.org/abs/1301.4255

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