Greek Musical Writings: Volume 2, Harmonic and Acoustic Theory (Cambridge Readings in the Literature of Music)

589 Pages·1990·11.52 MB·English

by  Andrew Barker

CAMBRIDGE READINGS IN
THE LITERATURE OF MUSIC
General Editors: John Stevens and Peter le Huray
Greek Musical Writings II
CAMBRIDGE READINGS IN
THE LITERATURE OF MUSIC
Cambridge Readings in the Literature of Music is a series of source
materials (original documents in English translation) for students of
the history of music. Many of the quotations in the volumes will be
substantial, and introductory material will place the passages in
context. The period covered will be from antiquity to the present day,
with particular emphasis on the nineteenth and twentieth centuries.
Already published :
Andrew Barker, Greek Musical Writings, Volume I: The Musician
and his Art
James McKinnon, Music in Early Christian Literature
Peter le Huray and James Day, Music and Aesthetics in the Eighteenth
and Early-Nineteenth Centuries
Bojan Bujic, Music in European Thought 1851-1912
Greek Musical Writings
Volume II
Harmonic and Acoustic Theory
Edited by
Andrew Barker
Senior Lecturer in Philosophy
University of Warwick
The right of the
University of Cambridge
to print and sell
all manner of books
was granted by
Henry VIII in 1534.
The University has printed
and published continuously
since 1584.
Cambridge University Press
Cambridge
New York Fort Chester
Melbourne Sydney
PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE
The Pitt Building, Trumpington Street, Cambridge, United Kingdom
CAMBRIDGE UNIVERSITY PRESS
The Edinburgh Building, Cambridge CB2 2RU, UK
40 West 20th Street, New York NY 10011-4211, USA
477 Williamstown Road, Port Melbourne, VIC 3207, Australia
Ruiz de Alarcon 13, 28014 Madrid, Spain
Dock House, The Waterfront, Cape Town 8001, South Africa
http://www.cambridge.org
© Cambridge University Press 1989
This book is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.
First published 1989
First paperback edition 2004
A catalogue record for this book is available from the British Library
Library of Congress cataloguing in publication data
Greek musical writings.
(Cambridge readings in the literature of music)
Includes bibliographies and indexes.
Contents: The musician and his art — v. 2. Harmonic
and acoustic theory.
I. Music, Greek and Roman - Sources. 2. Music - To
500 - Sources. I. Barker, Andrew, 1943—
II. Series.
HL167.G73 1984 781.738 83-20924
ISBN 0 521 38911 9 volume 1 paperback
ISBN 0 521 61697 2 volume 2 paperback
Contents
Acknowledgements page vi
Abbreviations, texts and typographic conventions vii
Introduction i
1 Pythagoras and early Pythagoreanism 28
Appendix: the scalar division of Archytas 46
2 Plato 53
3 Aristotle 66
4 The Aristotelian Problemata 85
5 The Peripatetic De Audibilibus 98
6 Theophrastus no
7 Aristoxenus 119
Elementa Harmonica 126
Book 1 126
Book 11 148
Book in 170
Appendix: Aristoxenus' Elementa Rhythmica Book 11 185
8 The Euclidean Sectio Canonis 190
9 Minor authors quoted by Theon and Porphyry 209
Passages from Theon of Smyrna 209
Passages from Porphyry 229
10 Nicomachus 245
Enchiridion 247
n Ptolemy 270
Harmonics 275
Book 1 275
Book 11 314
Appendix to Book 11 357
Book HI 361
12 Aristides Quintilianus 392
De Musica 399
Book 1 399
Book 11 457
Book in 494
Bibliography of works by modern authors 536
Index of words and topics 545
Index of proper names 572
Acknowledgements
I should like to record my thanks once again to the University of Warwick for
various periods of sabbatical leave, to the many scholars on both sides of the
Atlantic who have discussed and encouraged my work, to the students who
have insisted that I talk about it, and to the staff of Cambridge University Press,
especially Penny Souster and Andrea Smith, for their unfailing help and
patience.
In this volume even more than in its predecessor, I owe a particular debt to
Professor Winnington-Ingram, especially for his generosity in allowing me to
see his manuscript translation of Aristides Quintilianus, De Musica, together
with detailed notes on some of its early chapters. My work on that difficult
treatise would otherwise have been even more imperfect than it is: he is not to
be blamed for my errors and confusions.
Writing a book is an absorbing activity, but one that gets inextricably
entangled with others. I should like to dedicate this volume compendiously to
my wife Jill, my family and my friends, without whom it would all have been
very different. It is also a little offering in memory of Derek Macnutt, at whose
feet I first learned the rudiments of the translator's art, and whose shade even
now, between exertions on the Elysian fairways, still notes our mistakes with
an unerring eye, and smiles benignly on our small successes.
VI
Abbreviations, texts
and typographic conventions
In citing ancient and modern works I have used only a few esoteric
abbreviations:
DK H. Diels and W. Kranz, Die Fragmente der Vorsokratiker, 8th
edition, Berlin, 1956-9
GMW vol. 1 A. Barker, Greek Musical Writings, vol. 1, Cambridge, 1984
MSG C. von Jan, Musici scriptores graeci, Leipzig, 1895
SVF H. von Arnim, Stoicorum veterwn fragmenta, 4 vols., Leipzig,
1905-24.
Most other references to modern writings are by author's name and date. Full
details of works indicated in this way will be found in the Bibliography.
The translations are based on the following editions (cases where I have
preferred a different reading of the texts are mentioned in the notes):
Chapter 1 The text of the second passage is from vol. 4 of the edition by
R. G. Bury, London, 1961 (Loeb Classical Library). Extracts from
authors translated more fully elsewhere in the volume are taken
from the editions mentioned below. For the remainder I have used
the texts printed in DK
Chapter 2 Plato: texts from editions printed in the Oxford Classical Texts
Chapter 3 Aristotle: texts from editions printed in the Oxford Classical Texts
Chapter 4 Texts from Aristotle, Problems I-XXI, ed. W. S. Hett, London,
1970 (Aristotle, vol. 15, Loeb Classical Library)
Chapter 5 The Peripatetic De Audibilibus: from Porphyry, Commentary on
Ptolemy's Harmonics, ed. I. During, Goteborg, 1932
Chapter 6 Theophrastus, frag. 89: from During (1932), as above
Chapter 7 Aristoxenus, Elementa Harmonica, ed. R. da Rios, Rome, 1954.
Appendix to ch. 7, Aristoxenus, Elementa Rhythmica Book 11, from
Aristoxenus von Tarent: Melik und Rhythmik des Classischen
Hellenenthums, ed. R. Westphal, vol. 2, Leipzig, 1893 (reprinted
Hildesheim, 1965); see also Pighi (1969).
Chapter 8 The Euclidean Sectio Canonis: text from MSG
Vll
viii Abbreviations, texts and typographic conventions
Chapter 9 Passages of Theon Smyrnaeus, Expositio return mathematicarum
ad legendum Platonem utilium: from the text of E. Hiller, Leipzig,
1878; passages of Porphyry from During (1932)
Chapter 10 Nicomachus, Enchiridion : text from MSG
Chapter 11 Ptolemy, Harmonics, ed. I. During, Goteborg, 1930
Chapter 12 Aristides Quintilianus, De Musica, ed. R. P. Winnington-Ingram,
Leipzig, 1963
Other musicological works frequently mentioned include:
(a) The three treatises each entitled Eisagoge Harmonike by Bacchius,
Cleonides and Gaudentius: texts are in MSG, as are the selections
entitled Excerpta ex Nicomacho; Cleonides is translated in Strunk
(1952), Bacchius in Steinmayer (1985)
(b) The group of short works whose familiar title I abbreviate as Anon.
Bell., the Anonyma de musica scripta Bellermanniana, ed. D. Najock,
Leipzig, 1975; see also Najock (1972)
(c) Philodemus, De Musica, ed. J. Kemke, Leipzig, 1884; see also Rispoli
(1969)
(d) The Plutarchian De Musica: text and translation in Plutarch's Moralia,
vol.14, ed. B. Einarson and P. H. De Lacy, London, 1967 (Loeb Classical
Library); other important editions, both with French translation and
substantial commentary, are Plutarque: de la musique, ed. H. Weil and
T. Reinach, Paris, 1900, and Plutarque de la musique, ed. F. Lasserre,
Olten and Lausanne, 1954; English translation also in GMW vol. 1
In referring to passages translated in this volume, I have generally used the
systems of numbering that stem from canonical printed editions of the texts:
these are indicated in the left-hand margin beside the translations. The names
of author and work are preceded by bold numerals indicating where they occur
in this book. In cases where a chapter contains a single passage or treatise, the
numeral is the chapter number; where it contains several passages, the first
numeral is the chapter number, and the second identifies the position of the
passage in its chapter. Thus a reference to line 8 of Meibom's page 16 of
Aristoxenus' Elementa Harmonica, which occupies the whole of chapter 7, will
appear as 7 Aristox. EL Harm. 16.8. A reference to Plato, Republic 531a, which
occurs in the first passage of chapter 2, will appear as 2.1 Plato Rep. 531a.
Introduction
Preliminaries
The roots of the Greek sciences of harmonics and acoustics go back to the fifth
century B.C., perhaps even the sixth. No treatises survive from this period, and
only one or two short quotations: even these are of questionable authenticity.
Later writers, reflecting on the past, offer tantalising hints about pioneering
efforts in the field. Some of these, referring to just one of several traditions of
enquiry, are collected in my first chapter, and others appear in texts translated
elsewhere in the book. It seems likely that these beginnings were fairly
unsystematic, and were usually embedded in writings of wider scope. The
classification of sciences into distinct domains and their pursuit as autonomous
intellectual enterprises £re things that were only beginning in the later fifth
century, and came into their own in the fourth.
Even for the first three quarters of the fourth century we have very little from
the pens of specialists in the musical sciences: our small collection of
quotations and paraphrases of the work of Archytas, important though they
are, give a pretty thin representation of the work of seventy-five years. Some of
them are also included in chapter i. But for these years we have another
significant source of information in the writings of the philosophers, especially
Plato and Aristotle (chapters 2 and 3). Though neither made the scientific study
of music a central part of his own investigations, both found that their
reflections in other areas required them to pay these subjects careful attention,
and each made contributions to them which exercised a powerful influence on
later theorists. Both also give us valuable information about the work of their
contemporaries and predecessors.
Among the sciences which Aristotelian methods of classification identified as
independent enquiries was physical acoustics; and from the years after
Aristotle's death there survives a compilation, made within his * school', the
Lyceum, of problems that arise in that field, together with suggested solutions.
In the same collection is a comparable set of puzzles relating to music more
generally, some of which bear on harmonics. Selections from both are given in
chapter 4. Something approaching the status of a complete treatise is translated
in chapter 5: parts of it are certainly missing, but even as it stands it is a
substantial essay in acoustics, still within the Aristotelian or 'Peripatetic'
tradition. A long fragment by another philosopher in this school, Aristotle's
successor Theophrastus, occupies chapter 6. It reviews, very critically, the
assumptions and procedures of all theorists up to that time who had conceived
2 Greek Musical Writings
the study of music, from any point of view, as a quantitative or mathematical
discipline.
So far, all that we know of specialist writings in harmonics comes either
indirectly, in the reports and comments of others, or in the form of fragmentary
quotations, torn from their context. But from the end of the fourth century we
have two impressive works, the Elementa Harmonica of Aristoxenus (chapter
7), and the Sectio Canonis attributed to Euclid (chapter 8). The former is
incomplete, and as we have it is probably the remains of more than one treatise,
edited into a continuous piece at a later date, but its importance for the history
of the subject can hardly be exaggerated. Subsequent theorists treated
Aristoxenus' writings both as the foundation stone of one major tradition in
Greek harmonics, and as the pinnacle of its achievements. The Sectio Canonis
is dated only uncertainly to this period, but it represents neatly and
systematically, and perhaps in almost its complete and original form, a
rounded exposition of harmonic theory in a quite different style from that of
Aristoxenus, one based in mathematics and physics rather than in musical
experience. It is an illuminating specimen of the tradition that may roughly be
called 'Pythagorean' or 'Platonist', in the more scientific and rigorous of its
various guises.
The enterprises of theoretical harmonics, under the banners of two principal
schools of thought (loose confederations of interests and approaches, each
internally divided in significant ways), were now well under way. Disappoint-
ingly, very little remains of writings in either tradition over the next three
hundred years. From the time when our direct evidence begins to resurface, in
the first century A.D., we can put together a tolerable amount of material
representing contemporary ideas, and giving some notion of their relation to
their fourth-century precursors: relevant passages from two major sources are
assembled in chapter 9. My remaining chapters contain three complete
treatises, those of Nicomachus, from about the end of the first century (chapter
10), Ptolemy in the second century (chapter 11), and Aristides Quintilianus,
whose date is uncertain, but perhaps belongs to the third century or fourth
(chapter 12). Of the three, those of Ptolemy and Aristides are of great intrinsic
value: Ptolemy's for his intellectual rigour, his compelling and original method,
his detailed critiques of previous theories and his independent development of
new ones; Aristides' for its impressive (if only fitfully successful) attempt at the
extraordinary project to which its author set himself with such enthusiasm,
that of bringing everything that could be said about music into a compendious
scheme embracing all human life, the cosmic order and God. Both convey a
mass of information about musical practice, and about the ideas of earlier
writers, much of it unknown elsewhere. The work of Nicomachus, though
slighter than the others, is significant as our earliest complete specimen of the
genre from which Aristides' much wider vision developed, the 'Pythagorean'
essay in musical metaphysics. Like the other two, it must also be treated as a
landmark in musicological history for the influence it came to exert on theorists
of post-classical times.