## Music and Mathematics: From Pythagoras to FractalsJohn Fauvel, Senior Lecturer in Mathematics John Fauvel, Raymond Flood, Robin J. Wilson, Gresham Professor of Geometry Raymond Flood From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional and analytical relationships between mathematics and music are unfolded and explored with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques. |

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### Contents

an overview | 1 |

Music and mathematics through history | 11 |

Tuning and temperament closing the spiral | 13 |

Musical cosmology Kepler and his readers | 29 |

The mathematics of musical sound | 45 |

The science of musical sound | 47 |

Faggots fretful fiasco | 61 |

Helmholtz combinational tones and consonance | 77 |

Ringing the changes bells and mathematics | 113 |

Composing with numbers sets rows and magic squares | 131 |

The composer speaks | 147 |

Microtones and projective planes | 149 |

Composing with fractals | 163 |

Notes on contributors | 173 |

Notes references and further reading | 177 |

Acknowledgments | 183 |

### Other editions - View all

Music and Mathematics: From Pythagoras to Fractals John Fauvel,Raymond Flood,Robin J. Wilson Limited preview - 2006 |

### Common terms and phrases

acoustics angle approximation called century change ringing channel Chapter clarinet combinational tones composer composition consonance construction corresponding cosmology cyclic design diagram difference set modulo double exchange dual plane equally tempered equally tempered system example Fano plane Figure finite projective plane five bells fractal frequency ratios frets frieze pattern geometrical graph Greek guitar harmonics Helmholtz Iannis Xenakis ideas instruments integers interval Kepler Kircher London magic square major third mathematicians mathematics and music Mersenne Mersenne's method motif music theory musical space musicians natural notation notes octave oscillograph trace Oxford pairs perfect fifth permutations Peter Maxwell Davies piano piece pitch pitch classes Plain Bob Minimus plain hunting played points problem produce Pythagorean scale ringers Robert Sherlaw Johnson rung Schoenberg science of music semitone sequence sounds Stråhle's string structure symmetry syntonic comma tion transformations transposition tuning twelve-note University vibrations violin Xenakis