arXiv Open Access 2016

Hexatonic Systems and Dual Groups in Mathematical Music Theory

Cameron Berry Thomas M. Fiore

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Abstrak

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.

Topik & Kata Kunci

math.GR

Penulis (2)

Cameron Berry

Thomas M. Fiore

Format Sitasi

APA MLA BibTeX

Berry, C., Fiore, T.M. (2016). Hexatonic Systems and Dual Groups in Mathematical Music Theory. https://arxiv.org/abs/1602.02577

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Informasi Jurnal

Tahun Terbit: 2016
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓