This guy is probably correct as to the oldest recorded music. I am not sure that that would necessarily be the oldest tune handed down.
There is strong evidence that a particular interval (space between notes) exists in all cultures, regardless of the musical system used. This interval is known as the universal plaint, because it is so common. It is the minor third. If you remember the “taunt” that might go, say “na-na, na-na boo, boo!” or “Jan-ey’s got a boy-friend!” the distance between the last two notes is a minor third, the universal interval.
Before writing, when the ancients wanted to pass information from generation to generation, it would have to be in the form of oral tradition. At some point, it was discovered that in order for the tradition to survive generations, it would have to be stylized, in a very specific tone and rhythm. This evolved into songs about tribal history and heroes, as well as love songs, which seem to be the predominate type of song throughout history.