The Science of Harmonics in Classical Greece

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.

Part I. Preliminaries: Introduction; 1. Beginnings, and the problem of measurement; Part II. Empirical Harmonics: 2. Empirical harmonics before Aristoxenus; 3. The early empiricists in their cultural and intellectual contexts; 4. Interlude on Aristotle's account of a science and its methods; 5. Aristoxenus: the composition of the Elementa harmonica; 6. Aristoxenus: concepts and methods in Elementa harmonica Book 1; 7. Elementa harmonica Books 2-3: the science reconsidered; 8. Elementa harmonica Book 3 and its missing sequel; 9. Contexts and purposes of Aristoxenus' harmonics; Part III. Mathematical Harmonics: 10. Pythagorean harmonics in the fifth century: Philolaus; 11. Developments in Pythagorean harmonics: Archytas; 12. Plato; 13. Aristotle on the harmonic sciences; 14. Systematising mathematical harmonics: the Sectio canonis; 15. Quantification under attack: Theophrastus' critique; Postscript: The later centuries.

Harmonics was the most important branch of Greek musical theory, and its ideas were still vigorously debated in the Renaissance. This 2007 book, written by a leading specialist on ancient music, concentrates particularly on the theorists' methods and purposes and the controversies that their various approaches to the subject provoked.