turns out the few leading cases tend towards the user.
If there is ~any~ creative involvement by the user and little or no portions of the generating program's copyrighted material in it, then it belongs to the user or the user's employer.
If no user create involvement or the music has significant amounts of copyrighted material from the generating function, then the programmer or his/her employer probably own it.
This is, ofcourse, if no contract specifies.
It's no wonder nobody here knew the answer since this stuff is so new. As a programmer working in computer generated works, I was hoping to avoid a day's worth of research but sometimes you just have to do it yourself.