## The Monochord in Ancient Greek Harmonic ScienceAmong the many instruments devised by students of mathematical sciences in ancient Greece, the monochord provides one of the best opportunities to examine the methodologies of those who employed it in their investigations. Consisting of a single string which could be divided at measured points by means of movable bridges, it was used to demonstrate theorems about the arithmetical relationships between pitched sounds in music. This book traces the history of the monochord and its multiple uses down to Ptolemy, bringing together all the relevant evidence in one comprehensive study. By comparing the monochord with a number of other ancient scientific instruments and their uses, David Creese shows how the investigation of music in ancient Greece not only shares in the patterns of demonstrative and argumentative instrument use common to other sciences, but also goes beyond them in offering the possibility of a rigorous empiricism unparalleled in Greek science. |

### Contents

The Geometry of Sound | 1 |

The role of instruments and diagrams in greek harmonic science | 22 |

2 Mathematical harmonics before the monochord | 81 |

3 The monochord in context | 131 |

4 Eratosthenes | 178 |

5 Canonic theory | 210 |

6 Ptolems canonics | 283 |

Conclusion | 356 |

Bibliography | 360 |

374 | |

388 | |

### Other editions - View all

### Common terms and phrases

according acoustical Adrastus already appears approach Archytas argument Aristoxenus arithmetic attempt attunement Barker bridge called canonic division century chapter chromatic clear concern concords construction context demonstration diagram diatonic Didymus discussion distance divided equal Eratosthenes evidence example fact ﬁfth ﬁrst fourth fragment geometrical given gives greater Greek half Harm harmonicists harmonics important included instrument intervals introduced kaª kan¯on later length lines mathematical means measure method monochord musical Nicomachus notes numbers objects octave offers passage perception Philolaus pitch position possible practical presentation problem procedure proof prop propositions Ptol Ptolema¨ıs Ptolemy Ptolemy’s Pythagoras Pythagorean question quoted ratios reason reference represent requires scale scientiﬁc Sectio semitone sense similar simply sound string suggest tables taken tän tcov tetrachords theorists theory things Thrasyllus Timaeus tone toÓ trans treatise tuned units