It’s not uncommon for creative people to have more than one outlet for their muse. Musicians as diverse as Felix Mendelssohn, George Gershwin, Tony Bennett and Joni Mitchell could all paint pretty well, for instance.

I know fewer examples of great visual artists who are musically gifted, but Tony Green certainly fits that description. The 41-year-old New Orleans native is one of the city’s better-known painters, and lately his musical star has been rising as well: he’s making his Jazz Fest...