I tend to play better (blitz and bullet) with music too.
I think it's because it increases your confidence / improves your mood. It can also become background noise to help you focus on what you're doing.
But it can also be distracting. I prefer silence for long games.
Maybe play with both and try to figure out how it helps you, and try to make those adjustments on your own during the games without music. Honestly music vs no music may not matter much for your long games, but paying attention to your attitude and the effectiveness of how you're playing can only help.
I have recently begun starting to listen to music and the results are interesting. My rating is going up. I want to know ways I can break this habit as at tournaments it will eventually feel awkward playing without music. It is good for my online chess but probably bad for my long term OTB rating.
I listen to (The Sun Is Shining, Mu Getsu, and Ha-doh) from the Ki-Oku playlist and the Wii Shop Channel song.