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arXiv · 1602.02577

Hexatonic Systems and Dual Groups in Mathematical Music Theory

Cameron Berry·Thomas M. Fiore
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Abstract

Motivated by the music-theoretical work of Richard Cohn and David Clampitt on late-nineteenth century harmony, we mathematically prove that the PL-group of a hexatonic cycle is dual (in the sense of Lewin) to its T/I-stabilizer. Our point of departure is Cohn's notions of maximal smoothness and hexatonic cycle, and the symmetry group of the 12-gon; we do not make use of the duality between the T/I-group and PLR-group. We also discuss how some ideas in the present paper could be used in the proof of T/I-PLR duality by Crans--Fiore--Satyendra.

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Cameron Berry, Thomas M. Fiore. 2016-02-08. Hexatonic Systems and Dual Groups in Mathematical Music Theory. https://doi.org/10.2140/involve.2018.11.253

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