The piano is an enduring constant in New Orleans music, and this month’s installation of classic songs features four of the city’s cornerstone keyboardists—six in fact, since the Dr. John track includes Allen Toussaint and Art Neville. Most of these songs went into the standard repertoire: Dr. John’s was a high-water mark for local music on the charts; Booker’s was the miracle moment of a fraught session, Newman’s is a son...