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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.