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.
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.
Includes bibliographical references (p. 270-273) and indexes. Title from publisher's bibliographic system (viewed on 05 Oct 2015).