What word can I use for unclear music?

It depends on the actual nature of the sounds you are hearing.

Music that is tough to make out because the sounds aren't as sharp and crisp as they should be is called "muddy" (or sometimes "undermodulated").

Music that is tough to make out because of overlaid noise is... well noisy. However, sound folks have all kinds of different names for different kinds of noise. There's hiss and hum and pops. Tapes can exhibit a certian kinds of noise called wow and flutter. Bad radio reception (as Mitch mentioned in the comments) contains static.

The signal is poor, the music is hazy, indistinct.

I don't know if there's a good technical term, but I often hear people describe such radio signals as "choppy" or "staticky" (meaning there is a lot of noise in the signal that sounds like static).

You could also call it "noisy" (as in "this is a noisy transmission") to mean the signal-to-noise is low, but I suspect many people would be confused as calling a sound "noisy" also has a more common meaning that the sounds has a very loud volume (even if signal is very clear).

Maybe interference is the word you are looking for? "The music had a lot of interference."