Right now, when you turn music off, all music is gone, which includes the meditation music, the spinning wheel and music from music boxes along with the regular background music. If you just want the ambient music gone, you're out of luck.
I think it would be nice if we could turn off the ambient music, while keeping music from these cues around so the game sounds more like the way it was in tests prior to this one. The background music is very cool, but gets tiresome after a while, and I'd like to be able to turn it off and still be able to tell when my meditation has run out.