Mine was doing this--I thought randomly-- after I installed an app (sorry, don't remember which one.). Only it wasn't just music, it was the fifth sorrowful mystery of the rosary. Sort of freaky in the middle of the night.
Anyway, I did notice that it started at 4:53 am once, and when I checked my email the next day, I had gotten an email at that time. I checked the notification sound, and guess what?
Something in whatever app just assigned random sound files to the email notification.
I would check that first.