The trombone, as composer Hector Berlioz once observed, can musically portray everything from “religious accent, calm and imposing…to wild clamors of the orgy.” New Orleans trombonist Mark Mullins seconds Berlioz’s notion: “Especially that part about the orgy!”

Mullins’ own celebrated career is an orgy of work, touring and recording with fellow Orleanian Harry Connick, Jr.’s big band for the past 15 years, regularly joining Better Than Ezra and the Radiators on stage and recordings, and le...