MADDEN, Charles

1999

Fractals in Music. Introductory Mathematics for Musical Analysis

United States: High Art Press.

Language(s): English

Keyword(s):

Chaos Theory Fractal Theory Automated Composition Stochastic Music Algorithmic Music

Abstract:

In this book, the author proposes “a new genre of musical analysis”. Madden writes that his text goes “beyond the usual analysis of chord structures and period forms” to focus on topics such as: Fibonacci numbers, the golden mean, statistics and styles, Fourier analysis of melodic structures, chaos theory, fractal theory, self-similarity, attractors and randomicity. In this context, he proposes works by Bach, Beethoven, Bartók, Debussy, Dodge, Schenker, Schillinger, Schoenberg, Schubert, Stockhausen, Stravinsky, Varčse and Xenakis, as examples.

Table of Contents:

1. Introduction
2. Self-Similarity
3. Attractors
4. Fib and Phi
5. Resonance
6. Randomicity
7. Dimension
8. Statistics
9. Transforms