Scientific Method in Ptolemy's Harmonics

This book examines, for the first time, the scientific procedures devised by Ptolemy (second century AD) for investigating the structures underlying musical melody, a project that he conceived as closely related to astronomy. Ptolemy's account of his methods is unusually explicit, and he pursues them faithfully. By providing an analysis of Ptolemy's sophisticated theoretical apparatus, his strategies for integrating theory with observation, and his meticulous instructions for the design and conduct of experimental tests, the book offers historians of science a new starting-point for wider studies of ancient scientific method.

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.

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.

This book examines Ptolemy's scientific procedures for investigating the structures underlying musical melody. By providing an analysis of Ptolemy's theoretical apparatus, his strategies for integrating theory with observation, and his instructions for the design and conduct of experiments, the book offers a starting point for studying ancient scientific method.