questions about music in Gangs of New York

In a scene towards the beginning the police officer (John Reilly) picks up a music box then quickly shuts it saying he doesn't care for that tune. Anybody know what tune that is or its significance? Maybe it's something I missed earlier. Also the last half of the closing credits has what sounds like an unaltered field recording from a modern city, presumably NYC. It's not IDed in the credits so does anybody have any details? Thanks, Lang