I've just finished reading Andrew Barker's The Science of Harmonics in Classical Greece. While there is probably a bit too much detail here for readers without background in tuning theory, classics, or the history of science, I find this to be really exciting stuff. The book is an account of scholars (and musician-scholars) trying to make sense of real musical practice while developing the set of tools we now recognize as "science". This story is extremely useful for those of us who follow more contemporary music theories, not only because some of the ancient harmonics survives as terminology and structure in modern music theory, but also because the lines of research — the range of those lines as well as the conflicts among them — also surves in contemporary practice. Harmonics was, at once, idealistic, looking toward pythagorean and platonic ideals for the proportions among tones, but it was also observant of musical practice and, chiefly through the figure of Aristoxenus, a nascent science of perception.
Imagining ancient Greek music is a formidable task. We have the difficulty of historical distance and the lack of evidence that accompanies that distance. We have the problem of not re-constructing a single, highly localized, musical culture, but actually a series of cultures extending over the better part of a millenium and stretching throughout the ancient world. We have the problem of unclear degrees of continuity with contemporary practice. From a modern and western European viewpoint, we have the added difficulty of reconstructing an ancient mediterranean culture to which we undoubtedly owe some debt, but our glance backward tells us too little about a culture which looked forward in a number of directions, and the glance towards western Europe was among the most distant.*
But for all that difficulty, it's our fortune to live in a virtual golden age of scholarship about ancient Greek music and the culture around it. In addition to Mr Barker, whose collection of translations of the surviving manuscripts of music theory is also invaluable, Martin L. West and Warren D. Anderson have written very useful summary volumes, Pöhlmann and West have made a useful edition of the surviving examples of notated music, and Stefan Hagel has a great site of reconstructed melodies here.
* Lou Harrison once pointed out to me that the famous missing chapter of Boethius' On Music concerned the division of the fourth into two parts (in contrast to the tetrachordal division into three parts). Lou practically shouted: "It's NOT missing. Someone just wanted to erase the connection between Greece and Africa." While Lou's idea of an intentional erasure is pure conjecture, it is true that trichordal lyre tunings are still practiced in Ethiopia, and these tunings are just one step removed from classical Greek tetrachords.