I imagine there's some church music that goes back further than the 16th century. I wouldn't be surprised if many of the cultures you mention maintain some music that's even older. Whether people who are a product of modern sensibilites and Western culture would consider them good tunes is perhaps questionable--by which I mean that most folks have a fondness for what they're familiar with. I could appreciate some of the art of say, American Indian chants or Chinese songs, but I don't think I'd prefer them to songs in English that I can understand, and tunes that don't sound odd to my ear.