## 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 | 13 |

Music and mathematics through history | 13 |

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

appear approximation Athanasius Kircher beginning bells called century changes channel Chapter close composer composition consonance construction corresponding described developed diagram double effect equal exactly example exchange explain fact fifth Figure five follows four fractal frequency geometrical given gives harmonics hear Helmholtz ideas illustrate integer interest interval involved Kepler kinds known leads length London major mathematical mathematicians means method modulo move movement natural notes obtained octave opening original Oxford pairs particular pattern piano piece pitch Plain plane played points position possible problem produce published Pythagorean range ratio reflection represent result ringing scale sequence shown shows simple single sound space square string structure successive symmetry tempered theory third tion tones transformations transposition tuning University values vibrations whole