Greco-Roman music?

I'm kinda in the mood for something new to listen to, of late, and I was wondering... does anyone here know if music from the greco-roman empires survived? I mean, that culture was renowned for their art, their philosophy, their science... but I don't think I've ever heard an example of their music, despite knowing music/harmonics/tuning-theory to have been an important aspect of their classical system of mathematics (they viewed music as an expression of number in time, much like geometry is an expression of number in space). I've thought of doing a search just for greek music, but I think that would give me much more modern works than I am looking for. Roman might work, though....