Establishing a new genre of musical analysis, this book goes beyond the usual analysis of chord symbols and period forms to examine such topics as: Fibonacci number and golden mean proportions, Statistics for distinguishing among styles, Self-similarity in form. This second edition includes many new illustrations and concepts, including: Orbit drawings of attractors, Correlation coefficients, Melodic dimensions. It is intended for readers with little mathematical background and requires only algrebra and trigonometry.
A science buff since his teen years, Charles Madden was a physics major until music took over his life. As a starving artist, he frequently had to get work to "support his career." Thus he gained experience in fields as varied as electronics and spreadsheets.
Trained at the universities of Brigham Young, Illinois, and Utah, he taught there, and was a composer and pianist for fifteen years.
For the past several years, he has studied the mathematics of chaos theory and fractal geometry, the result of which is this collection of applications to formal musical analysis.