Fractals in Music: Introductory Mathematics for Musical Analysis
Fractals in Music is intended for advanced students of music theory, whether individuals, composers, students, or teachers. It is intelligible to anyone having some knowledge of algebra and trigonometry. The many illustrations clarify such concepts as self-similarity and transforms. Book jacket.
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acoustic feedback amplitudes attractor Bartok bifurcation Brown noise calculate called chaos theory chord close coefficients column correlation cosine data points David Hykes diagram difference dimension discussed Dodge brown music Endnotes to Chapter equal temperament example exponents Fibonacci numbers formula Fourier transform fractal geometry frequency fundamental Gaussian distribution geometric geometric sequence golden mean grid harmonic sequence illustrate impedance instruments inverse iterations Julia set logarithms look mathematics measure melody motion multiphonics multiplying musicians notation notes Notice octave sequence overtone piano piece pink music pink noise pipe proportions random range ratio resonance result rotation sample scale scatter plot Schoenberg Schubert self-similar semi-phrase shear shown in figure shows Sierpinski triangle similar smaller sound space spectrum spiral spreadsheet standard deviation statistics string structural point Table tion tonality tones transposed tuning undertone sequence uniform distribution values variance Voss waveform white noise Xenakis zero