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Hexatonic systems and dual groups in mathematical music theory

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2018Embargo end date: 01 Jan 2016Publisher:Mathematical Sciences PublishersJournal:Involve, a Journal of Mathematics, volume 11, pages 253-270 (issn: 1944-4176, eissn: 1944-4184,

Authors: Berry, Cameron; Fiore, Thomas M.;

doi: 10.2140/involve.2018.11.253 , 10.48550/arxiv.1602.02577

arXiv: http://arxiv.org/abs/1602.02577

Hexatonic systems and dual groups in mathematical music theory

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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.

16 pages. To appear in Involve: A Journal of Mathematics, published by Mathematical Sciences Publishers

Related Organizations

Michigan State University
United States
University of Michigan–Flint
United States
University of Regensburg
Germany

Keywords

dual groups, triad, 20-XX, PLR-group, 00A65, 20B35 (Primary), 20-01 (Secondary), Group Theory (math.GR), centralizer, maximally smooth cycle, inversion, mathematical music theory, transposition, FOS: Mathematics, Parsifal, neo-Riemannian group, transformational analysis, simple transitivity, Mathematics - Group Theory, hexatonic cycle

15 Research products, page 1 of 2

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