Sort of on-topic - I disable the music in most first person open world RPGs.
It started with Oblivion. I first disabled it because I didn't like that the combat music is triggered as soon as you're detected by an enemy - it feels like a cheat. But the thing I discovered was that it did wonders for immersion, because suddenly the only sounds I heard were actual in-universe sounds - footsteps, wind, flowing water, animals etc.
After playing like that for a couple of years, I got the urge to listen to the music again, so I re-enabled it. And it was very weird, because I had gotten so used to only hearing in-universe sounds that I kept subconsciously trying to place the music in the world - like there was a symphony orchestra in a forest clearing nearby or something. I had to turn it off and have never turned it back on.
I've never even heard the Skyrim music - I disabled it right from the start.
The only exceptions are game music that actually is in-universe, like the music played over your Pip-Boy in Fallout or over a car radio in GTA.