I don't have anything close to a clear idea of how other musical traditions fit (or don't) into their cultures' mystico-religious thought, unfortunately; and I only have the barest of notions of how other musical traditions actually work from a technical standpoint.

What non-Western musics I am familiar with are, indeed, structured very differently in time, structured around ideas other than the "narrative circle", as it were. What little I know of gamelan music, or Indian classical music, or Japanese theater music, leads me to believe that they treat the flow of time in an extremely different way than Western music.