Vol. 11, No. 2, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN (electronic): 1944-4184
ISSN (print): 1944-4176
Author index
To appear
Other MSP journals
Hexatonic systems and dual groups in mathematical music theory

Cameron Berry and Thomas M. Fiore

Vol. 11 (2018), No. 2, 253–270

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 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 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, and Satyendra (Amer. Math. Monthly 116:6 (2009), 479–495).

mathematical music theory, dual groups, hexatonic cycle, maximally smooth cycle, triad, transposition, inversion, simple transitivity, centralizer, PLR-group, neo-Riemannian group, transformational analysis, Parsifal
Mathematical Subject Classification 2010
Primary: 20-XX
Received: 18 February 2016
Revised: 3 January 2017
Accepted: 24 January 2017
Published: 17 September 2017

Communicated by Joseph A. Gallian
Cameron Berry
Department of Mathematics
Michigan State University
East Lansing, MI
United States
Thomas M. Fiore
Department of Mathematics and Statistics
University of Michigan-Dearborn
Dearborn, MI
United States
NWF I - Mathematik
Universität Regensburg