If f you study with Banu Gibson at her New Orleans Traditional Jazz Camp, one of the first things she’ll do is march you around the French Quarter with your axe. To her, learning the notes is easy, but learning the feel is a little harder—and a lot more important. And sometimes the simplest lessons are the crucial ones, starting with learning not to play too damn fast.

“One of the first things you notice as you listen to the traditional jazz repertoire over the years is that it just got fa...