There's quite a bit of ye olde Greek music on Spotify. Just search for ancient or classical Greek.
There seems to be quite a lot around which
claims to be ancient Greek, and there is one song (mentioned in the second video I posted) which seems to have been known for quite a long time. But this appears to be the first academically robust reconstruction of melody, rhythm and instrumentation together in a performable form - even if the singers are a bit Oxford choral tradition (he says with fond memories of near-sight-reading of difficult choral music in Oxford 25 years ago). Apart from anything else, the instruments used were only made in the last year or so, based on very recent investigations into archaeological artifacts.
(Oh, and for the real pedants, "ye" is a misunderstanding of the Old English letter thorn, and "olde" is a 19th-century affectation.)