Before the foundation of the great philosophical ‘schools’ in the fourth and third centuries, there were no institutions dedicated to scientific or other intellectual pursuits. Some thinkers recorded their ideas in writing, and these writings could travel widely, reaching other individuals at a long distance from their starting point. But no formally constituted community of scholars existed to provide a ready-made audience for the products of ‘academic’ endeavour. Who, then, were these pioneering harmonic scientists, and to whom did they address their work? Did they and their audiences fall into any clearly identifiable group or category, and if so, how were they related to other kinds of technical or intellectual specialist? Are they to be regarded as ‘intellectuals’ at all, comparable, for instance, to mathematicians, philosophers and astronomers? In what settings and for what purposes did they present their ideas? In this chapter I shall suggest two kinds of answer to these questions. They are different but perfectly compatible with one another; some at least of these theorists may very well have marched under both banners at once.

HARMONIC THEORISTS IN THE WORLD OF THE SOPHISTS

There is a small pointer towards my first suggestion in a passage of Aristoxenus which we glanced at in Chapter 2, where he speculates that those harmonikoi who set out their results in a notation did so in order to impress ‘lay persons’, people who were in no sense specialists in the musical sciences, and to give them something on which they could pass judgement (El. harm. 40.29–41.6).