If anyone is interested in ancient Greek music/music theory, the best source is undoubtedly Thomas Mathiesen's Apollo's Lyre (http://www.amazon.com/Apollos-Lyre-Theory-Antiquity-Middle/d...). I had the distinct privilege of taking his ancient music course in his last semester of teaching. The man has literally looked (in person) at every fragment of Greek music or music theory, and translated many of them himself. The book is magnificent, and you will be very unlikely to find any source more well-researched and written.
Edit: If anyone has any questions about Greek music/music theory, I'm happy to try and answer them. It's one of my favorite topics, and while I'm no expert, I probably know a little more than the average Hacker News reader.