^ This is the correct answer. To add/overly simplify brain function: In normal speakers, only one portion of the brain increases activity when speaking. In stutterers, additional areas of the brain increase activity (which is hypothesized to be a large cause of disfluency). Coincidentally, the additional areas are ones that are used when engaging with music (like singing, keeping rhythm, matching pitch, etc.). Thus, the stutter goes away when singing. Another great stuttering artist is Scatman John. "Scatman," his popular hit that launched his global career, is even about his stutter.