I sometimes wear my headphones with no music, just in noise-canceling mode. Just like you, I think music can be distracting or tiring after a while. My Sony headphones have such powerful noise canceling that it silences even the slightest hum, sort of a anechoic chamber. It helps me concentrate and I like keeping my ears warm. If I'm in the mood, I also put some white noise sounds on (youtube has plenty of it) including rain, beach waves and train rides.

And I work in my own private corner office.