Probably not very precisely. Unless your character has studied music theory, I'd steer clear of jargon, beyond perhaps commonplace words like "beat" or "rhythm".
I think you'd be best off describing how the character responds to the music emotionally rather than attempting to describe the sound. How does it make him feel?
Oh, and positive slang words in use from around that period include "hep", "choice", "sharp", "sweet", "smooth", "a lulu" and "a gas".
edited 22nd Sep '11 9:50:22 AM by BobbyG