Scientific Method in Ptolemy’s Harmonics

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.

• A full-scale study of the scientific method proposed and exemplified in this crucial text • The book aims to present the treatise as a work of central importance for the understanding of Greek conceptions of science and scientific procedure • Aims to provide students of Greek musicology with alternate perspectives on a fundamental text

Preface; 1. Introduction; 2. Reason and perception; 3. Pitch and quantity; 4. The ratios of the concords: (1) the Pythagoreans; 5. The ratios of the concords: (2) Ptolemy’s hupotheseis; 6. Critique of Aristoxenian principles and conclusions; 7. Ptolemy on the harmonic divisions of his predecessors; 8. Melodic intervals: hupotheseis, derivations and adjustments; 9. Larger systems: modulations in music and in method; 10. The instruments; 11. The tests; 12. Harmonics in a wider perspective; Bibliography; Indexes.

\'Barker has produced an engaging and richly nuanced account of the Harmonics as an argument for understanding Ptolemy as a scientist with a \'method\', a method which demands reliance on both perception and reason. Scientific Method in Ptolemy\'s Harmonics will interest a wide range of readers, particularly those concerned with ancient science, the role of experimentation and the philosophy of mathematics.\'

– British Journal of Philosophy of Science