Date of Award
11-21-2008
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
First Advisor
Mariana Montiel - Chair
Second Advisor
Yongwei Yao
Third Advisor
Florian Enescu
Abstract
One goal of music theory is to describe the resources of a pitch system. Traditionally, the study of pitch intervals was done using frequency ratios of the powers of small integers. Modern mathematical music theory offers an independent way of understanding the pitch system by considering intervals as transformations. This thesis takes advantage of the historical emergence of algebraic structures in musicology and, in the spirit of transformational theory, treats operations that form mathematical groups. Aspects of Neo-Riemannian theory are explored and developed, in particular the T/I and PLR groups as dual. Pitch class spaces, such as 12, can also be defined as torsors. In addition to surveying the group theoretical tools for music analysis, this thesis provides detailed proofs of many claims that are proposed but seldom supported.
DOI
https://doi.org/10.57709/1059722
Recommended Citation
du Plessis, Janine, "Transformation Groups and Duality in the Analysis of Musical Structure." Thesis, Georgia State University, 2008.
doi: https://doi.org/10.57709/1059722