There are a number of prominent New Orleans musical families, but the Neville Brothers—Art, Aaron, Charles and Cyril—are the siblings that most perfectly encapsulate the funky, soulful culture of this city. Since the 1950s, jointly and as solo artists, the Nevilles have released innumerable fine recordings, including songs such as “Mardi Gras Mambo,” “Tell It Like It Is” and “Cissy Strut” that are cornerstones of the New Orleans musical canon.

The Neville Bro...