Involve: A Journal of Mathematics
- Volume 11, Number 2 (2018), 253-270.
Hexatonic systems and dual groups in mathematical music theory
Motivated by the music-theoretical work of Richard Cohn and David Clampitt on late-nineteenth century harmony, we mathematically prove that the -group of a hexatonic cycle is dual (in the sense of Lewin) to its /-stabilizer. Our points of departure are 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 /-group and -group. We also discuss how some ideas in the present paper could be used in the proof of /- duality by Crans, Fiore, and Satyendra (Amer. Math. Monthly 116:6 (2009), 479–495).
Involve, Volume 11, Number 2 (2018), 253-270.
Received: 18 February 2016
Revised: 3 January 2017
Accepted: 24 January 2017
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
mathematical music theory dual groups hexatonic cycle maximally smooth cycle triad transposition inversion simple transitivity centralizer PLR-group neo-Riemannian group transformational analysis Parsifal
Berry, Cameron; Fiore, Thomas M. Hexatonic systems and dual groups in mathematical music theory. Involve 11 (2018), no. 2, 253--270. doi:10.2140/involve.2018.11.253. https://projecteuclid.org/euclid.involve/1513775061