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The ancient science of harmonics investigates the arrangements of pitched sounds which form the basis of musical melody, and the principles which govern them. It was the most important branch of Greek musical theory, studied by philosophers, mathematicians and astronomers as well as by musical specialists. This 2007 book examines its development during the period when its central ideas and rival schools of thought were established, laying the foundations for the speculations of later antiquity, the Middle Ages and the Renaissance. It concentrates particularly on the theorists' methods and purposes and the controversies that their various approaches to the subject provoked. It also seeks to locate the discipline within the broader cultural environment of the period; and it investigates, sometimes with surprising results, the ways in which the theorists' work draws on and in some cases influences that of philosophers and other intellectuals.
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This page intentionally left blank THE SCIENCE OF HARMONICS IN CLASSICAL GREECE The ancient science of harmonics investigates the arrangements of pitched sounds which form the basis of musical melody, and the principles which govern them. It was the most important branch of Greek musical theory, studied by philosophers, mathematicians and astronomers as well as by musical specialists. This book examines its development during the period when its central ideas and rival schools of thought were established, laying the foundations for the speculations of later antiquity, the Middle Ages and the Renaissance. It concentrates particularly on the theorists’ methods and purposes and the controversies that their various approaches to the subject provoked. It also seeks to locate the discipline within the broader cultural environment of the period; and it investigates, sometimes with surprising results, the ways in which the theorists’ work draws on and in some cases influences that of philosophers and other intellectuals. an drew b a rker is Professor of Classics in the Insititute of Archaeology and Antiquity at the University of Birmingham. THE SCIENCE OF HARMONICS IN CLASSICAL GREECE ANDREW BARKER CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521879514 © Andrew Barker 2007 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2007 eBook (EBL) ISBN-13 978-0-511-36650-5 ISBN-10 0-511-36650-7 eBook (EBL) ISBN-13 ISBN-10 hardback 978-0-521-87951-4 hardback 0-521-87951-5 Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. O dear white children, casual as birds, Playing among the ruined languages, So small beside their large confusing words, So gay against the greater silences . . . W. H. Auden, Hymn to Saint Cecilia Contents List of figures Preface page ix xi part i p reliminaries Introduction 3 1 Beginnings, and the problem of measurement 19 part ii em pirical harmonics 2 Empirical harmonics before Aristoxenus 33 3 The early empiricists in their cultural and intellectual contexts 68 4 Interlude on Aristotle’s account of a