Once, in an interview, Mr. Shorter was asked to account for his pursuit of music above other art forms. He replied that music has an inherent sense of velocity and mystery. It would be hard to find a more concise distillation of his priorities as a bandleader.

“When we go out onstage we always start from nothing,” said Mr. Patitucci by phone from Mr. Pérez’s native Panama, where the quartet headlined a jazz festival last month. “So anybody can spin the wheels in a certain direction, and then we develop those themes.”

What follows isn’t free jazz, exactly, though it uses some of the same tools. “It’s spontaneous composition,” Mr. Patitucci said, “with counterpoint and harmony and lyricism. All of those values are still there. It’s just being pressurized into milliseconds.”

Mr. Shorter framed the idea as an image: “We don’t count how much water there is in a wave when we see the ocean.” He was on the couch of a hotel suite overlooking Central Park South, during one of his recent visits from Los Angeles, where he lives. That evening he would perform at a gala for the David Lynch Foundation, along with the pianist Herbie Hancock, his former partner in the Miles Davis Quintet. He wore dress loafers and a fleece pullover embroidered with the logo of Soka Gakkai International, the Nichiren Buddhist organization to which he and Mr. Hancock belong.

A scheduled interview began with an unscheduled interruption: Ms. Spalding — who won the Grammy for best new artist in 2011, and was also booked at the gala — dropped by with the Argentine pianist Leo Genovese. For all of her success Ms. Spalding still belongs to the demographic that grew up with the notion of Wayne as sage: she and Mr. Genovese were there simply to give him a hug.

Mr. Shorter is a notoriously elliptical conversationalist, prone to cosmic digression and quick-fire allusion. During a spirited two-hour interview he touched on modern art, social politics and science fiction — among the books he produced for inspection was the dystopian “Ready Player One” by Ernest Cline — as well as music and movies, and movie music. “I’m looking at a lot of old silent films now,” he said, “and I listen to the new, hip boy bands. I was checking out some Selena Gomez.” On the subject of jazz, he said pithily, “The word ‘jazz’ to me only means ‘I dare you.’ ”