Fifteen years ago, the bassist Chris Lightcap released an auspicious debut album, “Lay-Up,” involving a nonstandard quartet configuration with two tenor saxophones up front. Mr. Lightcap still hasn’t exhausted that format: “Epicenter” (Clean Feed), due out on Wednesday, is his fourth album to feature it — and by and large his best, which is saying something. It comprises a batch of tunes Mr. Lightcap wrote as a commission, “New York: Lost and Found,” tailored to Bigmouth, his longtime band. The saxophonists are Tony Malaby and Chris Cheek; the rhythm section includes Craig Taborn on acoustic and Wurlitzer pianos and Gerald Cleaver on drums. Mr. Lightcap has a fondness for interlocking parts and a frame of reference that runs from West African music (as in the vamp that slowly materializes in “Stone by Stone”) to the Velvet Underground (as in a potent “All Tomorrow’s Parties,” the lone cover). You could listen to this album and fixate on the contrasting tenor styles: drier and more linear for Mr. Cheek, harder and blurrier for Mr. Malaby. But these musicians all have endless history together, and their total cohesion, with its earthy elasticity, feels like the larger point.