Nth roots of pitch-class inversion
Document Type
Conference Proceeding
Publication Date
6-30-2011
Abstract
In this study, we investigate the square, cubic, and other nth roots of inversion in discrete pitch-class spaces. We examine the group-theoretical structures that they inhabit, as well as various multi-dimensional regular polytopes whose symmetries model those structures. Moreover, we determine which nth roots of inversion occur in pitch-class spaces of various sizes, and their multiplicities. Because of their relevance to the majority of music in the Western canon, as well as to the transformational theories that engage this repertoire, we focus largely on inversions and their nth roots in mod-7 diatonic space and in mod-12 chromatic space. Our objective is to further the understanding of pitch-class inversion as a gesture, through an exploration of its nth roots in discrete transformational music theory. © 2011 Springer-Verlag.
Publication Source (Journal or Book title)
Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics
First Page
196
Last Page
206
Recommended Citation
Peck, R. (2011). Nth roots of pitch-class inversion. Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 6726 LNAI, 196-206. https://doi.org/10.1007/978-3-642-21590-2_15