Even people who aren’t sure they’ve heard of Kidd Jordan have probably heard him. Now 73, the tenor saxophonist has been playing since the early 1950s. And since Mr. Jordan’s spirited adolescence coincided with the dawn of rock ‘n’ roll and the explosion of new sounds coming out of New Orleans’s fertile rhythm-and-blues scene, the Crescent City native was at the right place at the right time.

Mr. Jordan was barely out of his teens when he began gigging with the Hawkettes, a band featuring future New Orleans musical royalty Art and Aaron Neville, whose 1954 hit “Mardi Gras Mambo” became a parade anthem. In the half-century since, the avuncular multi-reedist has backed up everyone from Ray Charles to Martha and the Vandellas to Stevie Wonder, worked alongside Professor Longhair and Little Richard, and recorded with Elvis Costello and R.E.M. But for all his session and stage credits, Mr. Jordan has always pursued a parallel path as a jazz avant-gardist of the purest intent. It’s in that role that the saxophonist visits New York this week, headlining a Wednesday night tribute to his career at the 13th annual Vision Festival, the world’s leading free-jazz summit. This year’s edition will present more than 50 events, including music and dance performances, poetry readings, film and visual art projections, and panel discussions.

“It’s like a love-in,” Mr. Jordan said of the festival, where he has performed nearly every year since it was launched in 1996 by the dancer-choreographer Patricia Nicholson Parker and her husband, the bassist and bandleader William Parker. “All the cats that I love are playing. It’s a family thing. You just get up and assert yourself. You play and you do what you do.” Talking by phone from his daughter’s house in New Orleans, Mr. Jordan often displayed an amused regard for the world and for himself. “You know, other than in Chicago, New York, and Europe, people always look at me strange.”

Mr. Jordan is no stranger to the Vision Festival, where his fierce and lyrical style can erupt in whatever impromptu pattern he chooses, without puncturing decorum.

The weeklong lollapalooza first emerged as an alternative to the city’s big-ticket corporate jazz festivals of the mid-1990s, namely the mainstream JVC festival and the long-defunct Bell Atlantic and Verizon festivals organized by former Knitting Factory owner Michael Dorf. Though the Vision Festival has an amorphous relationship to genre — it has hosted artists as non-jazz as Cat Power, and has long fostered an appeal to indie-rock fans — it revels in old-school free improvisation and next-wave jazz exploration. There’s a particular focus on the long tail of influence extending from the revolutionary sounds of such 1960s icons as John Coltrane, Ornette Coleman, and Albert Ayler. It’s a continuum into which Mr. Jordan slips seamlessly, as he will demonstrate when he plays four sets in a variety of combos featuring such favored associates as Mr. Parker, the drummer Hamid Drake, and Chicago tenor saxophonist Fred Anderson, another unsung hero who was previously honored by the festival.

“We’re used to playing together,” Mr. Jordan said of Messrs. Parker and Drake, who are to this kind of music what, say, Sly Dunbar and Robbie Shakespeare were to reggae in the 1970s, and who have collaborated with the saxophonist in various settings during the past decade. Thanks to such a high degree of almost telepathic chemistry, the musicians can move together like a breeze gathering force, capable of radical and unexpected shifts. In the quartet with Mr. Anderson, the rhythm section may become the front line, musically speaking, while the saxophonists create a modulating background of rushing, roiling tones. “They’ll throw different things at you; that’s what I like about improvised music. You don’t get stuck in ruts. You can’t look for nothing!”

A fifth ensemble, formed around two of his musician sons — trumpeter Marlon and flautist Kent — as well as alto saxophonist Donald Harrison, will pay a New Orleans-themed tribute to Mr. Jordan.

It’s appropriate, given that the musician chose to stay in his hometown rather than join a generation of his peers who left for Los Angeles and studio work in the 1960s, or spent most of their time on tour. Instead, Mr. Jordan became an educator, teaching at Southern University in Baton Rouge, running summer music camps for kids, and raising seven children of his own, four of whom are now professional musicians.

“I figured if I always had a job teaching, I could play what I wanted to play,” he said. The only thing that pushed Mr. Jordan out of the city was Hurricane Katrina, which forced him to relocate to Baton Rouge until his home is finally repaired. (“Nobody’s getting nothing done,” he said. “But you got to put up with it. You can’t do nothing about it.”)

While Mr. Jordan became a valued resource in New Orleans, his work as a soulful improviser with a surplus of old-school R&B shout in his heart has filtered out to free-jazz fans through a network of independent labels in America and Europe. As a young man, Mr. Jordan said, he was another horn player copying Charlie Parker’s licks. Then one day, someone played him “Something Else!!!!” a new album by a then little-known musician named Ornette Coleman. “And I said, ‘This is it! I know I’m in the right direction now,'” he said. “Oh, man. When I heard that … Hallelujah!”

As far as lifetime recognition goes, though, Mr. Jordan has no worries. The characteristically self-effacing performer may appear modest, but beneath his New Orleans charm he’s just as tough and singular as Mr. Coleman — and as purely individualistic as any of his now-legendary bandmates from the 1950s and ’60s. As we spoke, he cracked a joke about the time someone was trying to track him down.

“I said, ‘Man! If you want to hear me play then come by my house. As long as I can practice, I don’t care if I play nowhere.'”

The Vision Festival begins today and runs through Sunday at the Clemente Soto Vélez Cultural Center (107 Suffolk St. at Rivington Street, 212-696-6681).