This. I don't want the game alerting me via a musical soundtrack. That would totally blow immersion.
my game music is off most of the time, in both Oblivion and Skyrim. The only time I turn it on is if my character is in a rich person's house, or in the Blue Palace...somewhere opulent. And even then, I'll only put music on its very lowest setting. I figure they
could have some musicians hidden off in a room somewhere, or even a magical device that plays tunes or something like that.
Instead of music, I usually open up the glass door that leads into my room. There's forest back there, with birds singing, wind blowing, rain falling at times. In the summer there's also crickets and katydids making lots of noise at night. The way it works, sometimes it's hard to know where the in-game birds and wind and insects stop, and real-life noises behind my home begin.

.
Music is not the only alert.
Enemies will speak, threaten, grunt and/or scream the moment you get near.
You would have to be in successful sneak mode the entire game to rarely hear a programmed alert.
Also, when enemies are attacking you, they always make their presence known in the same fashion. There are no silent stalkers.
I suppose all of that can be turned off too, via console command.
I wouldn't know. I am on 360.