Klein-Bottle Tonnetze
Robert W. Peck
KEYWORDS: transformation, generalized interval systems, Klumpenhouwer networks, Lewin, group theory, neo-Riemannian theory
ABSTRACT: Departing from the toroidal Tonnetz of neo-Riemannian theory, we construct a generalized Klein-bottle Tonnetz. Further, we examine associated transformational graphs and analytical contexts, using operators from the cyclic T group, the dihedral T/I group, and a generalized quaternion T/M subgroup. In the T/I example, corresponding regions within a Tonnetz are related by various Klumpenhouwer network isographies. Finally, we consider relationships among entire Klein-bottle Tonnetze, and place them into recursive supernetworks.
Copyright © 2003 Society for Music Theory
Published as PDF only, available here
Robert W. Peck
Louisiana State University
rpeck@lsu.edu
Copyright Statement
Copyright © 2003 by the Society for Music Theory. All rights reserved.
[1] Copyrights for individual items published in Music Theory Online (MTO) are held by their authors. Items appearing in MTO may be saved and stored in electronic or paper form, and may be shared among individuals for purposes of scholarly research or discussion, but may not be republished in any form, electronic or print, without prior, written permission from the author(s), and advance notification of the editors of MTO.
[2] Any redistributed form of items published in MTO must include the following information in a form appropriate to the medium in which the items are to appear:
This item appeared in Music Theory Online in [VOLUME #, ISSUE #] on [DAY/MONTH/YEAR]. It was authored by [FULL NAME, EMAIL ADDRESS], with whose written permission it is reprinted here.
[3] Libraries may archive issues of MTO in electronic or paper form for public access so long as each issue is stored in its entirety, and no access fee is charged. Exceptions to these requirements must be approved in writing by the editors of MTO, who will act in accordance with the decisions of the Society for Music Theory.
This document and all portions thereof are protected by U.S. and international copyright laws. Material contained herein may be copied and/or distributed for research purposes only.
Prepared by Brent Yorgason, Managing Editor and Tahirih Motazedian, Editorial Assistant