The roots of the Greek sciences of harmonics and acoustics go back to the fifth century b.c., perhaps even the sixth. No treatises survive from this period, and only one or two short quotations: even these are of questionable authenticity. Later writers, reflecting on the past, offer tantalising hints about pioneering efforts in the field. Some of these, referring to just one of several traditions of enquiry, are collected in my first chapter, and others appear in texts translated elsewhere in the book. It seems likely that these beginnings were fairly unsystematic, and were usually embedded in writings of wider scope. The classification of sciences into distinct domains and their pursuit as autonomous intellectual enterprises are things that were only beginning in the later fifth century, and came into their own in the fourth.

Even for the first three quarters of the fourth century we have very little from the pens of specialists in the musical sciences: our small collection of quotations and paraphrases of the work of Archytas, important though they are, give a pretty thin representation of the work of seventy-five years. Some of them are also included in chapter I. But for these years we have another significant source of information in the writings of the philosophers, especially Plato and Aristotle (chapters 2 and 3). Though neither made the scientific study of music a central part of his own investigations, both found that their reflections in other areas required them to pay these subjects careful attention, and each made contributions to them which exercised a powerful influence on later theorists.