Alton “Big Al” Carson is one of the finest vocalists you’ll hear at Jazz Fest, but if you want to hear him in his element, you have to go to Bourbon Street and witness his formidable performances at the Funky Pirate, where he holds court most nights.

Bourbon Street’s heyday as a live music Mecca has passed as legendary clubs have been replaced with T-shirt boutiques, frozen daiquiri stands an...