I stumbled across this Vintage News article about the h.6 stone tablet a while back, along with one of several interpretations of how the hymn might have sounded. The article has more info, so if you like the music, check it out.
The Hurrian songs are a group of stone tablets with music inscribed in the cuneiform writing system. These were unearthed from the ancient Amorite city of Ugarit and date to approximately 1400 BC.
One of these tablets (h.6), contains the Hurrian hymn to Nikkal, making it the earliest markedly entire piece of composed music in the world. On some of the broken pieces, the composers’ names are inscribed, but h.6 is an anonymous work.The hymn is played by Michael Levy on the lyre.
The lyrics of the h.6 tablet are a hymn to Nikkal, a Semitic goddess of orchards. It also contains inscribed directions for a singer playing a nine-stringed sammûm, a type of harp or, more likely, a lyre. Instructions for how to tune the harp are also contained on some of the tablets.