We have a number of written forms of music, from Ancient Greek, to Cuniform, and many others, but the problem with these forms is that we DON'T know what any of them sound like. There are lots of people who have tried to interpret them, but with any interpretation, they're unlikely to be really correct. We also have numerous interpretations of the same piece, that are all very different.

However, there are many, many folk music traditions throughout the world that were NOT ever written down, and many were passed down by rote. While this creates a problem of knowing whether the pieces we hear now are unaltered in the intervening centuries and millenia, they give us a unique glimpse into the music of the region. Unlike the spoken word, which is a little more subject to the "telephone game" problem of changes as it's passed down, music tends to be learned more precisely, so there's a good change that what we hear in folk music is pretty similar to what was being played hundreds, or thousands of years ago.