## 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. |

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### 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 | |

### Common terms and phrases

acoustical Adrastus Almagest apodeictic Archytas argument Aristotle Aristox Aristoxenian Aristoxenus arithmetic astronomy attunement auloi Barker bridge positions canonic division chapter chromatic concords construction context deﬁned deﬁnition demonstration Didymus diesis difﬁculty discussion divided Duris eight-stringed enharmonic epimoric epitritic epogdoic equal Eratosthenes evidence ﬁfth ﬁg ﬁnal ﬁnd ﬁrst ﬁve fourth century fragment geometrical Greek mathematics Harm harmonicists helik¯on Hippasus instrument kaª kan¯on kanonik¯e kanonion leimma lettered diagram Locrus mathematical harmonics means mesolabon method monochord musical intervals Netz Nicomachus notes numbers octave octave plus fourth Panaetius perª phaenomena Philolaus pitch Plato Porph Porphyry Porphyry’s postulates pr¼v procedure proof prop propositions Ptol Ptolema¨ıs Ptolemy Ptolemy’s Pythagoras Pythagorean reason and perception scale scientiﬁc Sectio canonis semitone signiﬁcant sound speciﬁcally string lengths t¼n tän tcov tense diatonic tetrachords theorists Thrasyllus Timaeus Locrus toÆv tone toÓ trans treatise Trpos tt]s tt]v tuned