All this aside, I have a theory about the bow and arrow. It's usually assumed that the "mouth bow" or "ground bow" (a string and a sapling, sometimes with a drum head somehow attached) came from the bow and arrow. The hunter would like the "thummmmm" of the string and use it (without the arrow) in communal music.
But I think the bow came first, since it's only one thing, and doesn't require the second part (the arrow) to be useful. I think someone came up with the string-and-tensioned stick (the bow) first, and it was used for communal music making. Then one day a bow-player was hitting the string with a stick, and the string caught on a rough spot on the stick, and flung said stick across the campfire into the capacious butt of the shaman. Voila! These bow thingies could "toss" sharp sticks, and thus could be used for hunting. And thus the bow-and-arrow was born.
That's my theory -- music instrument first, hunting apparatus second. Probably within the first week of the invention of the bow, for sure, but still, the bow and its sound came first.