The ancient science of harmonics investigates the arrangements of pitched sounds which form the basis of musical melody, and the principles which govern them. It was the most important branch of Greek musical theory, studied by philosophers, mathematicians and astronomers as well as by musical specialists. This 2007 book examines its development during the period when its central ideas and rival schools of thought were established, laying the foundations for the speculations of later antiquity, the Middle Ages and the Renaissance. It concentrates particularly on the theorists' methods and purposes and the controversies that their various approaches to the subject provoked. It also seeks to locate the discipline within the broader cultural environment of the period; and it investigates, sometimes with surprising results, the ways in which the theorists' work draws on and in some cases influences that of philosophers and other intellectuals.
I have to admit that Barker is the preeminent writer on Ancient Greek music theory. I can't fault this book on technical grounds, or really on any of the content. And if someone told me they really wanted to know all they could about how Ancient Greeks thought about musical pitch, I'd probably point them here.
However, my ranking is lowered because of its incomprehensible density and dryness. As much as I'm used to dense academic texts, even this was a slog.