Maybe I'm weird, OK, I know I am, but quiet, tranquil music does not put me to sleep. If anything, it annoys me.
For some reason, the only time I can sleep with music on is during the day. And it has to be something I like, and it has to be loud. And on a good system. A shitty system will annoy me with the piss poor sound quality. I think vibrations from the bass must be what soothes this savage beast.
I will usually nap through the short lull between songs, but if the music stops for more than a minute or so, I will wake up.