Why are stutterers fluent when singing/rapping/acting?

Why are stutterers fluent when singing/rapping/acting? I've noticed that I have a much easier time getting words out if I sing them or speak them in a rhythm (tapping my foot as I syllables). Also, I sometimes work as an extra in movies and I've noticed that I don't stutter almost *at all* when I am playing a part or speaking theatrically. Basically, anytime I'm not normally talking and there's an extra layer of some other inflection, I am fluent. Does anybody else experience this? I know it's a common phenomenon, but not sure why.