Few books have more splendidly informative titles than Theon of Smyrna's Mathematics useful for reading Plato. A title modelled on his, perhaps Harmonic theory useful for reading classical Greek philosophy and other things would have given a fair impression of my agenda here. But that's a little cumbersome; and for accuracy's sake, I would have had to tack the phrase ‘and indications of the converse’ onto the Theonian title, since I shall be trying to show not only how harmonics can be ‘useful’ to students of other fields, but also how the preoccupations of Greek writers who tilled those fields can shed light on the development of harmonics itself, and can help us to understand its methods and priorities. More importantly, this hypothetical title would have been dangerously hubristic; it has the air of presupposing a positive answer to one of the book's most serious questions. Leaving one or two exceptional passages aside (the construction of the World-Soul in Plato's Timaeus, for example), does a knowledge of the specialised science of harmonics, and of its historical development, really give much help in the interpretation of texts more central to the scientific and philosophical tradition, or in understanding the colourful environment inhabited by real Greek musicians and their audiences, or indeed in connection with anything else at all? Can such knowledge be ‘useful’, and if so, in which contexts, and how? I intend to argue that it can, though not always in the places where one would most naturally expect it.