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Cambridge University Press 978-0-521-87951-4 - The Science of Harmonics in Classical Greece Andrew Barker Index More information Index of proper names Academy 326 on sound and pitch 27–9, 305–6, 322, 373, Adrastus of Aphrodisias 366n, 388n, 444 419–21 on classes of ratio 342n his theorem on epimoric ratios 272, 303–5, on ratios of pitches 29n, 444n 351, 356, 382 Adrastus (legendary) 89 Arimnestus, and the monochord 81n Aelianus 376n, 381n Aristides Quintilianus 397n, 398n, 400n, 435n, Aetolians, and diatonic music 70, 71 442–3 Agathocles 73, 78, 87–8 on an ‘ancient’ notation 64 Agenor 40n, 52, 55, 78, 81–3 Aristoxenian and Pythagorean elements Akoumenos 89 in 441, 442n Alcidamas 69n on dynamis 184, 188 Alexander Polyhistor 85n on enharmonic 39n Alexanderson, B. 432n on melopoiia 230 Alypius, on notation 61–6 the three ¯eth¯e of 255–6 Anacreon 82 on notes in the pyknon 217n Anaxagoras 327 on the paion¯ epibatos 245n Anaximenes, on ‘dense’ and ‘diffuse’ 25n on pre-systematic harmoniai 45–52, 83, 393, Anderson, W. D. 11n, 47, 47n, 48n, 51n 398, sources and transmission of his Annas, J. 311n evidence 45–8 Apollo 72 on systematised harmoniai 44, 44n Archestratus 437n on tonoi 216n, 225n, 226, 226n, 442n on notes in the pyknon 217n Aristonikos 82, 98n Archilochus 85–6 Aristophanes 6n, 83, 100n, 316n, 324n Archytas 113, 115, 143n, 143–5, 269, 287–307, 311, Aristotle 11, 33, 34n, 46, 114, 328–63, 364, 389n, 321, 327, 329, 332–4, 336–7, 342, 343–4, 390, 409, 414n, 421, 426 361, 364, 375, 390, 409, 440–2 Analytica posteriora 58n, 97, 105–12, 153, 167, and cosmology 305–6, 306n 168, 173, 193n, 193–4, 198, 200, 292n, on the Delian problem 304n 353–61, 364, 377n, 410n, Analytica his divisions of the tetrachord 288, 292–302, priora 106, De anima 28n, 173n, 241n, 352, 403–4 332, 373n, 376n, 429–30, De caelo 271n, and genera 38, 292–302 282, 283n, 286n, 323, Eudemus 329, and mathematical (‘rational’) principles 329n, frag. 47 Rose 329–38, frag. 48 288–307 Rose 332n, De generatione as a mathematician 304 animalium 28n, 184n, 419, De and means and proportions 284, 302–3, 332, generatione et corruptione 340n, 410 Metaphysics 6n, 34n, 193n, 269n, 282n, and musical practice 294–302, 306–7, 443 286, 349–53, 375n, 390n, 424n, personal qualities and achievements 287 Nicomachean Ethics 242n, De and Plato 287, 307, 316n philosophia 329, 329n, Physics 112, 159, Ptolemy on 287–302 379n, Poetics 6n, 235n, Politics 97, 100n, references to instruments 26 234n, 244n, 245n, 248n, 251, 252, 253, 328, 461 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-87951-4 - The Science of Harmonics in Classical Greece Andrew Barker Index More information 462 Index of proper names Aristotle (cont.) piercing of auloi 115n, Praxidamantia 115, 337–8, 393, 433, De sensu 34n, 97n, 289n, Sympotic Miscellanies 115 291n, 338–48, 349–50, 362, 375n, 376n, Elementa harmonica 425n, On the Timaeus and Archytas 333–4 composition and structure of 113–35 and Archytas 329, 332–4, 336–7 as comprising Principles and Elements 116n, on concords and colours 289n, 338–48, 362 130, 134–5, 163, 164, 227 on contemporary musical experts 328 concepts, methods and aims, in on dialektos 241n Book i 136–64, in Book ii 165–96,in on the diesis 349–53, 389n, 424, 425n Book iii 197–228 on dynamis 184, 329 contexts and purposes of 229–59 on ¯ethos 245 digressions in, theoretical and fragment on harmonia 329–38 non-theoretical 125–9, 133, 165, 213–14 its affinities with work of other discussed and quoted by Porphyry 130n, writers 331–3 134–5 analysis of 334–8 incompleteness of, and the missing its contexts in Aristotle and in [Plut.] De portion 115, 197, 200, 207–8, 215–28 musica 329–34 as lectures 122, 123 as expounding Pythagorean theories 333–4 ‘overlapping’ passages of Books i–ii 122, on harmoniai 253, 292, 393 124–34 on harmonics 328–63 programmes of Books i–ii 117–21,of empirical 58n, 97, 104, 168, 292 Book ii 165 mathematical 97, 167, 168, 286, 292, 328, relations between the three books 115–35, 329–48, 410n between Book iii and the others 121–2 mathematical and empirical, relations as remnants of two treatises 116–17, between 353–61 relations between them 121, 123–34 its methods and concepts 328–9, 349–61 as a single treatise 116n its purposes 362 and training for composers 229–33 on the ‘harmony of the spheres’ 283n, 323 and Aristotle’s Lyceum 114, 122, 123, 229, 231 on hierarchies of skills 242n and Aristoxenians, discussed by Ptolema¨ıs and on ‘mixed’ sciences 353–61 Didymus 438–40 on musical ethics 72, 248n on the harmonikoi see Agenor, Eratocles, on music’s social utility 251 Pythagoras of Zakynthos, and General names for ‘harmonics’, ‘metrics’ 6n index s.vv. harmonics (empirical), on nature (physis) 159–60 harmonikoi on Olympus 100n, 245n life and writings 113–15 on percept and concept 173 on mathematical harmonics 143, 166–8, 390–1 on Philoxenus 244n musical writings 115 and Plato’s lecture on the good 251 as a musician 113, 230 on Pythagoreans 263, 282–3, 286, 329–38, 362 his musical conservatism 46, 102, 230, 393 on ratios of concords 289, 291n his names for ‘harmonics’, ‘metrics’, on scientific demonstration 105–12, 168, ‘rhythmics’, ‘organology’ 6n 193–4, 198, 353–61, 377–8 and the nature and goals of harmonics 180–3 silent on genera 38 in Nicomachus 441 on sound and pitch 28n, 373, 417, 419, 429–30 non-musical writings 114–15 use of term harmonikos 37 on percept and concept 173–4 [Aristotle] De audibilibus 367n, 373n, 374n, as a philosopher 113–14, 258–9 429n on his predecessors, see General index s.v. [Aristotle] Problemata 97n, 276n, 291n, 345–6, harmonikoi 348, 375n, 429n, 429–30 his public lectures 231–3 Aristoxenus 12–16, 321, 327, 328–9, 331, 364, 373, and Pythagoreans 113–14, 115, 166–8 377–8, 388n, 390–1, 400, 404–6, 409, contrasts and combinations with 440–2 410, 413, 432n, 434 as source for Aristides Quintilianus 46–8 On auloi 115n, Comparisons 115, Elementa and his students 122, 123, 132–3, 251–2 rhythmica 7n, 115, 238, On and Theophrastus 422–4, 426n, 427–8, 431, instruments 115n, On Music 115, On the 435–6 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-87951-4 - The Science of Harmonics in Classical Greece Andrew Barker Index More information Index of proper names 463 Artemon 74, 82 the three ¯eth¯e of 255–7 Athena 83 on modulation 15n nomos of 179n on notes in the pyknon 217n Athenaeus of Athens (composer) 15n, 100n, quotes Ion 98n 398–9 on tonoi 216n, 217–22, 226n Athenaeus of Naucratis (author) 74, 78n Creese, D. E. 27n, 81n, 306n, 409n, 442n on Lamprocles 83 on Stratonikos 75 Damon 47, 72–3, 73n, 74, 87, 252, 310, 434n Avezzu,` G. 69n Damoxenus 77n Da Rios, R. 185n, 193n, 232n B Club 338n Delian problem 304n Bacchius 400n, 442–3 Delphi 100n, 326, 398–9 on harmoniai 44, 44n Didymus (musical theorist) 288n, 442n on notes in the pyknon 217n on distinctions between ‘schools’ of on types of composition 255n harmonics 438–40 Barbera, A. 366, 366n, 376n, 380–1, 382n, 383n, his divisions of the tetrachord 293n, 296n, 386n, 391–2, 393, 394, 403 438 Barker, A. 7n, 21n, 36n, 48n, 80n, 85n, 97n, and the monochord 438 101n, 145n, 224n, 225n, 232n, 271n, 288n, and Ptolemy 438, 440n, 443–4 291n, 296n, 301n, 306n, 308n, 317n, 325n, Diocles (historian of philosophy) 173n 330n, 342n, 344n, 347n, 350n, 367n, Diocles (Pythagorean) 114 373n, 377n, 392n, 408n, 414n, 430n, Diogenes Laertius 333 434n, 442n, 444n on the ‘last’ Pythagoreans 114 Barker,J.A. 223n, 295n on persons named ‘Pythagoras’ 75n Barnes, J. 106n, 108n, 112, 155n on Theophrastus 411 Belis,´ A. 116n, 117, 119n, 120n, 134, 134n, 296n Dionysius of Halicarnassus 437 Blumenthal, A. 98n Dionysus 72 Blumenthal, H. von 438n Dolopes, and diatonic music 70 Boccadoro, B. 11n Dracon 78 Boethius 382, 398, 437–8 During,¨ I. 217n and Nicomachus 445, 446–7 Duris, on Simos and the monochord 26n, 81n, on Philolaus 271–5, 277–8, 281–2, credentials 409n of his evidence 271 Bolton, R. 106n, 155n Echecrates 114 Bowen, A. C., on Archytas 29n Einarson, B., and P. H. De Lacey 244n, 259n, Bower, C. M. 281n, 382n, 398n, 447n 335n Brancacci, A. 69n Empedocles Burkert, W. 20n, 81n, 263, 304n on colour 142n on Archytas 29n, 269n, 299n on ‘dense’ and ‘diffuse’ 25n on Hippocratics 281n on harmonia 265 on numerology 282, 282n Epicurus, Epicureans 77n, 170, 185n on Philolaus 263n, 264, 271n, 272n, 273, Epigonus 52n, 78, 80, 81, 103 278n, 279n Eratocles 40n, 43–55, 74, 78–9, 83–4, 88, 150, Burnyeat, M. 317n 152–4, 194–5, 223, 224 Byzantium 438 his treatise 54 Eratosthenes 306n, 437n, 438n, 442n, Calcidius 444 445 Callias 74 Erinyes 282n Campbell, D. A. 79n, 80n, 83n Eryximachus 72n, 89, 279n, 280n, 345 Cassin, B. 70n Euclid 107n, 197, 367–8, 384 Cleonides 367n, 397n, 400n, 442–3 [Euclid] Sectio canonis 46, 107n, 358–60, on concords 376n 364–410 on dynamis 184, 188 its aims, sources, strategies and readers 382–4, on harmoniai 44, 44n 406–10 on melopoiia 230 its author 367–8 © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-87951-4 - The Science of Harmonics in Classical Greece Andrew Barker Index More information 464 Index of proper names [Euclid] Sectio canonis (cont.) Heraclides of Pontus (fourth century bc) 46, on concords and their ratios 289–90, 291n, 330, 373n 348, 357–8, 359–60, 372, 375–8, 384–8 Heraclides of Pontus (first century ad) 373n on construction of ditones 93n, 294n, 391–2, Heraclitus 265, 345 409 Hesiod 87 its date, and supposedly later additions 358, Hesychius 333 364–5, 366–70, 391–4, 403–6 Hibeh Papyrus on music 40n, 69–73, 77, 233, and diatonic 276n, 290n, 392, 403–6 292, 393n, 426n and division of the kanon¯ 365–6, 369–70, Hieron I of Syracuse 82 394–408 Hippasus 84–5, 306 and empirical harmonics 359–60, 389–91 Hippias 73, 77 and enharmonic 369, 388–90, 391–4, Hippocrates, Hippocratics 403–6 on abstract principles 104n its introduction 368–9, 370–8 on ‘dense’ and ‘diffuse’ 25n limitations of 409–10 on harmonia and concords in and the kanon¯ 365–6, division of 365–6 embryology 279n, 280–1 necessity and ‘reasonableness’ in 377–8 on ‘imitation’ 53n in Porphyry and Ptolemy 289–90, 366–70, Homer 85, 87 391 Homeric Hymn to Hermes 276n, 316n and Pythagoreans 373, 410 Huffman, C.
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  • The Science of Harmonics in Classical Greece

    The Science of Harmonics in Classical Greece

    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 pro- voked. It also seeks to locate the discipline within the broader cultural environment of the period; and it investigates, sometimes with sur- prising results, the ways in which the theorists’ work draws on and in some cases influences that of philosophers and other intellectuals. andrew barker is Professor of Classics in the Insititute of Archae- ology 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.