To celebrate his first solo album, singer-saxophonist James Martin made a unique display of filial piety. “I released the album in coordination with my ancestor Francois Martin’s marriage to Marguerite Denes in the St. Louis Cathedral, 250 years prior to the date,” he explains.

In a city where family ties stretch back centuries, you’d be hard pressed to find a musician with deeper New Orleans roots than Martin, who counts a streetcar driver and a comrade...