Almost Difference Sets in Transformational Music Theory
Document Type
Conference Proceeding
Publication Date
1-1-2017
Abstract
The combinatorial theory of difference sets has prior applications in the field of mathematical music theory. The theory of almost difference sets, however, has not received similar attention from music scholars. Nevertheless, these types of structures also have significant musical applications. For instance, the well known all-interval tetrachords of pitch-class set theory are almost difference sets. To that end, we investigate the various categories of almost difference sets (cyclic, abelian, and non-abelian) in terms of their representations in Lewinian music-transformational groups.
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
63
Last Page
75
Recommended Citation
Peck, R. (2017). Almost Difference Sets in Transformational Music Theory. Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, 10527 LNAI, 63-75. https://doi.org/10.1007/978-3-319-71827-9_6