Andrew Barker

Little is known about the harmonic theorist Archestratus (probably early 3rd century BC). Our only substantial information comes from Porphyry, who quotes a brief comment by a certain Didymus on his epistemological stance, and seeks to justify it through reflection on a rather startling technical doctrine which Archestratus propounded; and from Philodemus, who comments scathingly on his view of the relation between harmonic theory and philosophy. Neither passage is easy to interpret; this paper tries to make sense of them, and to set them in an intelligible relation to one another. It argues that the doctrine recorded by Porphyry becomes comprehensible when it is placed against the background of Aristoxenus' work in harmonics, and it discusses Porphyry's inferences about the way in which his epistemological position diverged from that of Aristoxenus. It argues that Philodemus' report gives evidence of Archestratus' interest in issues of central concern to philosophy and in particular of an engagement with Aristotelian thought; it tries to identify some specific questions which attracted his attention, and to explain how he seems to have answered them, and why. It suggests that the two reports can be brought together as elements in a single, though fragmentary picture, and finally that Archestratus can be assigned an interesting though minor role in the history of Peripatetic philosophy and science.

For over 40 years, Andrew Barker has been studying the ways in which ancient Greek philosophers, scientists and others analysed and discussed the structures underlying musical compositions; he has focused, in particular, on their methodologies, the conceptual frameworks within which their analyses were formed, and the various philosophical commitments they brought to their work. This volume contains a selection of the essays that Barker has published on these and related topics. The essays are preceded by an English version of his book on 'psychomusicology', previously published only in Italian. It examines Greek writers' diverse and often influential speculations about correlations between musical structures and their counterparts in the soul, speculations which led them to striking conclusions about music's practical value in human affairs, and to recommendations for appropriate ways of employing it in such fields as, for example, moral education, psychotherapy, and the organization and governance of a healthy society.

Porphyry's Commentary, the only surviving ancient commentary on a technical text, is not merely a study of Ptolemy's Harmonics. It includes virtually free-standing philosophical essays on epistemology, metaphysics, scientific methodology, aspects of the Aristotelian categories and the relations between Aristotle's views and Plato's, and a host of briefer comments on other matters of wide philosophical interest. For musicologists it is widely recognised as a treasury of quotations from earlier treatises, many of them otherwise unknown; but Porphyry's own reflections on musical concepts and his snapshots of contemporary music-making have been undeservedly neglected. This volume presents the first English translation and a revised Greek text of the Commentary, with an introduction and notes designed to assist readers in engaging with this important and intricate work.

In his Harmonics, Ptolemy constructs a complex set of theoretically ‘correct’ forms of musical scale, represented as sequences of ratios, on the basis of mathematical principles and reasoning. But he insists that their credentials will not have been established until they have been submitted to the judgement of the ear. They cannot be audibly instantiated with the necessary accuracy without the help of specially designed instruments, which Ptolemy describes in detail, discussing the uses to which each can be put and cataloguing its limitations. The best known of these instruments is the monochord, but there are several more complex devices. This paper discusses one such instrument which is known from no other source, ancient or modern, whose design was prompted by the geometrical construction known as the helikôn. It has several remarkable peculiarities. I examine its design, its purposes, and the merits and shortcomings which Ptolemy attributes to it. An appendix describes an instrument I have built to Ptolemy’s specifications, in an attempt to find out how satisfactorily such a bizarre contraption will work; and it explains how various practical problems can be resolved. Keywords: Ptolemy; Greek harmonics; Scientific instruments; Helikôn; Experiment; Mathematics.