Andrew Barker

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.

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.

Many ‘Introductions’ give the impression of standing aloof from the battle which they describe, of surveying the field with lofty impartiality from above. Often this apparent lack of involvement is misleading: even when it is not it may trivialise the subject by lending an atmosphere of pointlessness to the whole disputation. Dr Theobald, however, is plainly down there in the thick of it, and has written a book which not only makes an excellent introduction to the philosophy of science, but also constitutes a stimulating and at times overtly polemical contribution to the subject.

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

The science called 'harmonics' was one of the major intellectual enterprises of Greek antiquity. Ptolemy's treatise seeks to invest it with new scientific rigour; its consistently sophisticated procedural self-awareness marks it as a key text in the history of science. This book is a sustained methodological exploration of Ptolemy's project. After an analysis of his explicit pronouncements on the science's aims and the methods appropriate to it, it examines Ptolemy's conduct of his investigation in detail, concluding that despite occasional uncertainties, the declared procedure is followed with remarkable fidelity. Ptolemy pursues tenaciously his novel objective of integrating closely the project's theoretical and empirical phases and shows astonishing mastery of the concept, the design and the conduct of controlled experimental tests. By opening up this neglected text to historians of science, the book aims to provide a point of departure for wider studies of Greek scientific method.