For diehard Mardi Gras traditionalists—those of the rhythm and blues camp, at least, there are but four songs that truly matter: Professor Longhair’s “Go To The Mardi Gras” and “Big Chief” (composed by Earl King), the Hawkettes’ “Mardi Gras Mambo” and Al Johnson’s “Carnival Time.”

Since its recording in 1960, “Carnival Time” has been heard annually on New Orleans radios, jukeboxes and stereos. Like their insatiable appetite for king cake and their ceaseless delight in catching beads, New O...