I spoke with the poet/writer Eric Gansworth about this at length when he came to Utica for a reading in 2002. Anyway, Eric's one of the most prolific artists I know. He also does almost all his composition while music is blaring in the background.
I have to say that I also write when there's music going. The music has to be all instrumental, though. There can't be any vocals, otherwise I'm apt to get Earworms. So the music I listen to ranges anywhere from Classical (rarely), to Classical Jazz (most often), to odd-ball instrumental groups like The Dirty Three and The Rachel's.
Still, a lot of writers I know need complete silence. What type of writer are you? Do you need the background noise to compose? Do you utilize the sounds in your environment? Do you need absolute silence when you write?
20 hours ago