I put a music disc into a jukebox, went into the menu and changed the audio level (Sound). The music stopped playing, even as I exited the menu. Other gamesounds (punching, walking, etc) were still there. To play it again, I had to remove the disc and put it back in. That was on a 1.6.2 vanilla server.

I recreated the same offline in creative and survival mode.
These things trigger this event, when i play music and go into sound settings: (state before, action)

1) Music is OFF, change sound volume
2) Music is ON, set music volume to OFF, then back to ON
3) Sound is OFF, turn sound OR Music ON (no music at all)