William Parry touched on this in his book about the Valsalva Mechanism. Stuttering overwhelmingly happens as a result of the interruption of *phonation*. Put your hands to your throat and speak normally. You'll feel your larynx buzzing with phonation. Now, with your hands still on your throat, simply whisper. Notice how your larynx doesn't move at all, because you aren't phonating when you whisper. I'm not sure how singing fits into this paradigm, but most people seem to agree it has something to do with activating a different part of your brain than normal speech does.