I can’t listen to music while doing anything that demands my concentration and focus. When I take small breaks I do listen to my favorite songs or calm and relaxing tunes but then when I am back at my trading desk I shut down every external noise.
Not trading but deep focused work, I can't have music running in the background, not even instrumental one (vocal is out of the question since it involuntarily distracts me). What does help concentration however is white noise, from a low-noise electrical fan. I have an electric heater with a fan running on just the fan (heat turned off).
I used to get out of bed at 4.30am with tracks like this. Of course I live in a climate paradise so no cold and pain to work through. And I also like to look for good covers of songs.