Type of Document Master's Thesis Author du Plessis, Janine Author's Email Address jduplessis1@student.gsu.edu URN etd-11212008-163229 Title TRANSFORMATION GROUPS AND DUALITY IN THE ANALYSIS OF MUSICAL STRUCTURE Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Mariana Montiel Committee Chair Florian Enescu Committee Member Yongwei Yao Committee Member Keywords
- Group theory
- Flat torus
- Torsors
- Mathematical music theory
- Transformational theory
- Duality
- Pitch class set
- Tonnetz
Date of Defense 2008-11-10 Availability unrestricted 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.
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