There has never been a musician more “New Orleans” than Jelly Roll Morton.

Many have been more financially successful (Fats Domino, Allen Toussaint) and certainly Louis Armstrong has been a greater overall influence.

But who captures the essence more than Morton? Start with the knickname, “Jelly Roll,” like “jazz,” a euphemism for things sexual. Has a more famous New Orleans neighborhood than Storyville ever existed? Well, Jelly Roll is the greatest musician to have played there regular...