## Mathematics and Music: A Diderot Mathematical ForumGerard Assayag, Hans G. Feichtinger In 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. |

### Contents

Proportions in Ancient and Medieval Music | 1 |

Lagrange Working Mathematician | 4 |

The Latin World | 11 |

LateMedieval France | 18 |

The Decline of Proportional Thinking | 25 |

Introduction | 33 |

3 | 43 |

The Use of Mechanical Devices and Numerical Algorithms | 49 |

Conclusion | 134 |

in the XXth Century | 139 |

References | 145 |

51 | 159 |

Ethnomusicology Ethnomathematics | 161 |

References | 181 |

References | 198 |

References | 211 |

Daniel Strähle | 57 |

on Music Considered as a Source for Science | 65 |

Musical Patterns | 79 |

Inversion | 85 |

Variations on the Logical in Music | 93 |

Mathematics Music and Philosophy | 102 |

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

3 | 119 |

6 | 127 |

Digital Sound | 218 |

Composition of Textures | 224 |

54 | 230 |

The Mathematics of Tuning Musical Instruments | 233 |

References | 240 |

254 | |

References | 284 |

### Other editions - View all

Mathematics and Music: A Diderot Mathematical Forum Gerard Assayag,Hans G. Feichtinger Limited preview - 2013 |

Mathematics and Music: A Diderot Mathematical Forum Gerard Assayag,Hans G. Feichtinger No preview available - 2011 |

Mathematics and Music: A Diderot Mathematical Forum Gerard Assayag,Hans G. Feichtinger No preview available - 2014 |

### Common terms and phrases

acoustic additive synthesis algebraic algorithm analysis approach Aristoxenus arithmetic auditory Babbage Boole calculation called canon century chords cognitive coherence combinations combinatorial composer Computer Music concept considered consonance context corresponding defined denotators equal equal temperament ethnomathematical Eulerian path example expression fifth figures filter formal Frege frequency frequency modulation function geometric harmonic harp formulas idea images inharmonic intervals IRCAM Kircher Lagrange Leibniz listening logic of music mathematical mathematician means melody Mersenne modulation morphism motif music theory musical logic Musical Writings musicians musique notation notes Nzakara objects octave operations parameters Paris pattern perception physical pitch Pitch Class PlayScale polyphony possible prediction predictor presheaf principles problem properties proportions propositions ratio representation rhythmic scale semantic sequence signal processing Simha Arom simulation specific string structure symbols synthesis Tartini theoretical three units timbre tion tone transformation triad University Vanuatu

### References to this book

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