There are few scraps of Classical Greek music that have come down to us, quite a bit from the early Church (although notation was scanty). You can read all about it in Donald Grout's History of Western Music. That is considered the leading authority.
Ah yes. Grout. What every college music student has been studying Music History from for the last several decades. I remember my sister talking about snoozing thru her 8am Music History class back in the 1970s ;-).