While not a couple three thousand years old, one might take a look at The Ancient Music of Ireland, by Edward Bunting, published in 1840. He was asked to notate all the tunes & songs played by the old style itinerant harpers at the last of the old Belfast Harp Festivals which was held in 1792. The book was a treatise on those tunes & other Harp & Pipe Music, but the tunes were arranged for Piano--presumably because by then the Piano was much more in vogue than Harp or Pipes.
   The "very ancient" air, Eileen a Roone, is one tune which I have heard with lyrics in various languages. I wonder how old it is, and how it meandered to other countries. We will likely never know.
    It makes me wonder . . .if one is sitting in 1792 and a tune is described as being "very, very ancient," just how old is that?