They were pretty much the main dig for European culture for over a thousand years of antiquity.
No surviving music? Didn’t they right anything down? Did they have any concept of modern musical theory, such as chords? If not, why? A child playing on a lyre must have eventually hit two strings at once. forming part of a chord, and realized it sounds better than just one.
As far as writing anything down, why should they when oral tradition was sufficient? There was no need to communicate musical arrangements over long distances, and it’s perfectly possible to learn music by ear. Apparently some people did, but for your everyday musician there was no need.
I typed “music in the ancient world” into amazon.com, and found about 40 books on the subject, so I’d say quite a lot is known, either directly or from reconstruction, and “survives” in that sense. (Based on what I see in previews there and on google books, there is plenty of detailed information, including on musical terminology and scales.) The rest survived in the same sense that ancient Greek and Latin survived, gradually changing into the music of the modern Mediterranean world. I’ll wager a musicologist could identify particular shared features of modern Romance-language folk music and ancient Roman music.