ALGORITHMIC MUSIC: USING MATHEMATICAL MODELS IN MUSIC COMPOSITION by GUSTAVO DIAZ-JEREZ Submitted to The Manhattan School of Music in partial fulfillment of the requirements for the degree of Doctor of Musical Arts and approved by August 2000
iiABSTRACT OF THE THESIS Algorithmic Music: Using Mathematical Models in Music Composition by GUSTAVO DIAZ-JEREZ Thesis advisor: Nils Vigeland The intimate connection between music and mathematics has been acknowledged throughout history. This paper is a survey of the most relevant methods employed today in algorithmic composition. It covers stochastic processes (randomness, probability functions, Markov chains); one-, two-, and three-dimensional chaotic systems; fractals; algorithms derived from noise spectra (1/f noise); number theory (Morse-Thue sequence, 3n+1/Hailstone numbers, prime numbers); cellular automata (one- and two-dimensional cellular automata); genetic algorithms; formal grammars (L-systems.) It includes a brief historical survey, an exhaustive list of available computer programs which implement most of the processes discussed, and C++ source code listings of routines valuable for algorithmic composition. Numerous musical examples are provided to demonstrate each process. These examples are included in an accompanying audio CD.