This is a great question and it would be great to be able to find out who created something so beautiful. However, when it comes to the origins of things, it is impossible to find out facts precisely, because so much has been lost. Think about it. Things written even 500 years ago are debated.
With this said, from a biblical perspective, it says that the sons of Jubal in Genesis 4:21 created music. According to the biblical account, Jubal's sons made pipes and played them. From the perspective of Genesis, this is only a few generations removed from Adam and Eve.
While many will not accept this as historical, it is perhaps the best we can do in view of the lack of evidence. Basically we can take the lack of any evidence to mean that music originated organically instead of from anyone in particular, and that it hs probably been in existence for as long as humans have.