Applications of Dynamical Systems to Music Composition

McAlpine, Kenneth B (1999) Applications of Dynamical Systems to Music Composition. PhD thesis, University of Glasgow.

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Abstract

Mathematics and music have long enjoyed a close working relationship: mathematicians have frequently taken an interest in the organisational principles used in music, while musicians often utilise mathematical formalisms and structures in their works. This relationship has thrived in recent years, particularly since the advent of the computer, which has allowed mathematicians and musicians alike to explore the creative aspects of various mathematical structures quickly and easily. One class of mathematical structure that is of particular interest to the technologically-minded musician is the class of dynamical systems - those that change some feature with time. This class includes fractal zooms, evolutionary computing techniques and cellular automata, each of which holds some potential as the basis of a composition algorithm. The studies that comprise this thesis were undertaken in order to further examine the relationship between mathematics and music. In particular we explore the notion that music can essentially be thought of as a type of pattern propagation: we begin with initial themes and motifs - the musical patterns - which, during the course of the composition, are subjected to certain transformations and developments according to the rules dictated by the composer or the musical form. This is exactly analogous to the process which occurs within a cellular automaton: initial configurations of cells are transformed and developed according to a set of evolution rules. We begin our study by describing the development of the CAMUS v2.0 composition software, which was based on an earlier system by Dr. Eduardo Miranda, and discuss how best to use the system to compose new musical works. The next step in our study is concerned with highlighting the limitations of CAMUS as it currently stands, and suggesting techniques for improving the capabilities of the system. We then chart the development of CAMUS 3D. At each stage we justify the changes made to the system using both aesthetic and technical arguments. We also provide a composition example, which illustrates not only the changes in operation, but also in interface. The system is then re-evaluated, and further developments are suggested.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Additional Information: Adviser: Edwardo Miranda
Keywords: Applied mathematics, Music
Date of Award: 1999
Depositing User: Enlighten Team
Unique ID: glathesis:1999-76461
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 19 Nov 2019 14:19
Last Modified: 19 Nov 2019 14:19
URI: http://theses.gla.ac.uk/id/eprint/76461

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