## Mathematics and Music: A Diderot Mathematical ForumIn Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music. |

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### Contents

Proportions in Ancient and Medieval Music | 1 |

LateMedieval France | 18 |

Epilogue | 47 |

Conclusion | 62 |

Lagrange Working Mathematician | 65 |

Musical Patterns | 79 |

Variations on the Logical in Music | 93 |

The Formalization of Logic and the Issue of Meaning | 113 |

Ethnomusicology Ethnomathematics | 161 |

References | 181 |

References | 198 |

References | 211 |

Composition of Textures | 224 |

References | 240 |

254 | |

References | 284 |

### Common terms and phrases

acoustic additive synthesis algebraic algorithm analysis approach arithmetic auditory Boole calculation called canon cellular automaton century chords cognitive coherence combinatorial composer composition Computer Music concept considered consonance corresponding defined denotators elements equal temperament equations ethnomathematical Eulerian path example fifth filter formal Frege frequency modulation frequency ratio function geometric granular synthesis harmonic harp formulas idea images interaction intervals IRCAM Lagrange Leibniz listening major third mathematician Mathematics and Music means melody Mersenne method modulation morphism motif Music Theory musical instruments musical logic musical sound musicians musique non-linear notation notes Nzakara objects octave operations parameters Paris pattern perception performance physical pitch polyphony possible prediction presheaf principles problem properties proportions Pythagorean reasoning representation rhythmic scale semantic sequence signal processing Simha Arom simulation sound synthesis spectral string structure symbols techniques theoretical timbre tion tone transformation triad tuning University Vanuatu vibrating wave

### References to this book

Philosophie et musique contemporaine, ou, le nouvel esprit musical Daniel Parrochia Limited preview - 2006 |