Saxophonist Tim Green does not have a new record out. In fact, he doesn’t even lead a band, so you’re not likely to find his name in the monthly music calendar. He is a prodigious artist, however, a sideman extraordinaire whose ear-opening sound — emanating from numerous live settings and recording sessions — is seminal to the New Orleans scene.

These days, he’s best known for his blistering tenor work in several of the more outward-bound groups in town, such as <...