Ptolemy's reputation as one of the outstanding scientists of the ancient world rests mainly on his epoch-making treatise in astronomy, the Mathematike Syntaxis (usually known as the Almagest). Modern students of the ancient sciences know him also for his writings on optics, geography and astrology; but with a few honourable exceptions they have shown rather little interest in his Harmonics. Those who have examined it in detail have not, for the most part, been historians of science. Either they have been concerned less with the text in its original setting than with its afterlife in Renaissance musicology, or else they are dedicated (even fanatical) specialists in ancient musical theory; and we are rather few. But even if the subject it addresses continues to languish (as it should not) in a cobwebby corner of our gallery of the Greek sciences, the Harmonics itself deserves much wider attention.

It is in the first place a work of real intellectual distinction, and its skilfully mustered arguments, despite their technical intricacies, are presented with a flair and panache that should commend it to any connoisseur of scientific writing. Secondly, it is quite unusually explicit and self-conscious about its own methodology and procedures. In this respect it has a good deal more to offer than the Syntaxis, whose overt reflections on the general features of the science are relatively brief and less directly methodological, and play a notably less prominent role in the development of the subsequent argument.