## Fractals in Music: Introductory Mathematics for Musical AnalysisFractals 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Introduction | 1 |

Conclusion | 17 |

SelfSimilarity in the Harmonic Sequence | 31 |

Application to Atonality | 47 |

Organicism | 61 |

Resonance | 77 |

Randomicity | 97 |

Conclusions | 117 |

Conclusions | 136 |

Correlation | 151 |

Transforms | 163 |

191 | |

205 | |

### Other editions - View all

Fractals in Music: Introductory Mathematics for Musical Analysis Charles Madden,Charles B. Madden No preview available - 1999 |

Fractals in Music: Introductory Mathematics for Musical Analysis Charles B. Madden No preview available - 2007 |

### Common terms and phrases

acoustic feedback amplitudes attractor Bartók bifurcation boxes brown music Brown noise calculate called chaos theory chord close coefficients column correlation cosine data points David Hykes diagram difference dimension discussed 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 Mandelbrot mathematical measure melody motion multiphonics musicians notation notes Notice octave sequence overtone piano piece pink noise pipe pitches proportions random range ratio resonance result rotation sample scale scatter plot Schoenberg Schubert self-similarity shear shown in figure shows Sierpinski triangle similar sound space spectrum spiral spreadsheet standard deviation Statistics string structural point Table tion tonality tones transposed tuning undertone sequence uniform distribution values Voss Voss's waveform white music white noise Xenakis zero

### References to this book

Fractals in Music: Introductory Mathematics for Musical Analysis Charles B. Madden No preview available - 1999 |