I would say with some sureness that my peoples (Australian Aboriginal) tunes are the oldest surviving (and living) tunes. The sacred Song Cycles of various Dreamings including Honey Ant, Imberombera and others are still observed and as far as we are concerned they have been around since our Ancestor Beings sang the land into being. Considering that Mungo Man and Mungo Woman have been established at near enough to 73,000 years ancient, these tunes have to be at least that old. If you look at the admittedly contested Jimnium sites then they would have to be between 80,000 to 100,000 years old. These tunes aren't "resurrected" - they have always been and still are. America's First People's as well as some of the South America's clans could perhaps also claim tunes that transcend time and still are.