In New Orleans, there’s a venerated tradition of nicknaming younger, hot-shot musicians “kid” — sort of like Western gunslingers. The name often sticks, which is why it’s no big deal to address an elder statesman as “Kid” in the Crescent City. Two of the best known of these were actually named Edward: the pioneering trombonist Kid Ory (1886-1973) and Kidd Jordan, who is being celebrated this week at the 13th annual Vision Festival at Clemente Soto Velez Cultural Center on the Lower East Side.

In the case of Mr. Jordan, who turned 73 last month, the appellation is somewhat appropriate, since his music continues to convey a childlike sense of wonder. Wednesday was the big night of the six-day Vision Festival XIII, in which the man of the hour played in four different combinations, and a fifth group performed a tribute to him.

I arrived in time to hear the climax of Mr. Jordan’s quartet with the equally sagacious violinist Billy Bang (plus the drummer Hamid Drake and bassist and festival co-founder William Parker). Of course, a free-jazz performance often consists entirely of climax. Messrs. Bang and Jordan are extreme free players, yet they know exactly how much of the traditional elements of jazz to retain. As a result, no matter how explosively chaotic their music gets, one can always hear something that sounds like a regular rhythm, something that sounds like a tempered note, something that sounds like a melody, something that approximates swing, and something that evokes the blues. Owing to Mr. Jordan’s long history in R&B and pop, the tunes and traditions on which the quartet fell back were just as likely to be funk vamps.

Mr. Bang is the latest in a long line of top-tier musicians with whom Mr. Jordan has achieved a remarkable synergy. It’s one thing to achieve that on an agreed-upon pitch in the Western scale, but Messrs. Jordan and Bang coordinated their shrieks to the point that their instruments were yelping precisely the same microtone, as if the violin and the tenor saxophone had somehow been fused into a single mechanism operated by two men.

The next group co-starred Mr. Jordan and the pianist Joel Futterman, and it was planned as an outgrowth of the trio that they have led with the drummer Alvin Fielder (which is represented on the “Southern Extreme” album, from 1997). Sadly, Mr. Fielder was too ill to attend, so the group became a quintet with the inclusion of the prolific drummer Gerald Cleaver, Mr. Parker again on bass, and the trumpeter Clyde Kerr. The highlight here was the interplay between Messrs. Jordan and Futterman; while the bass and drums supplied a foundation of time and a kind of harmony, Mr. Kerr’s trumpet offered a discernible if abstract melody, and the tenor sax and piano departed for parts unknown.

Mr. Futterman’s playing has frequently been compared with that of Cecil Taylor, though it’s hard to imagine how anyone could play free jazz on the piano without sounding like him. Mr. Futterman uses a similar technique of random-sounding pounding on the keyboard — a chaotic swirl of notes and pitches that, in a goofy way, sort of make sense. (Regrettably, Mr. Futterman didn’t double on sopranino saxophone, as he sometimes does on the trio’s recordings.) There were quieter, even lyrical moments, in which Mr. Parker played a skittering arco solo; normally, the use of the bow makes the double bass sound more classical, but Mr. Parker has developed a technique in which his arco playing is even further out than his customary pizzicato. In this music, one relishes every little phrase of conventional melody, much the same way the audience relished every little breeze that wafted through the unventilated theater on Wednesday.

There was a lot of conventional melody in the band consisting of Mr. Jordan’s students and progeny, led by his sons, the trumpeter Marlon Jordan and the floutist Kent Jordan. After years of regularly attending the Vision Festival, I never thought I’d hear a bop-centric set built around jazz standards (“Footprints,” “Impressions”) and the blues. Marlon is a representative member of the power-trumpet school of Freddie Hubbard and Woody Shaw, and Kent soloed eloquently, especially on piccolo, a woodwind rarely heard in improvised music. The quintet was well-propelled by the very versatile Mr. Cleaver on drums, who soloed as if he had been waiting his whole life — or at least the whole evening — to do so. The major disappointment of the set was that Kidd Jordan himself didn’t sit in — he’s never showed New Yorkers any of his facets other than his avant-garde technique, and I would love to hear what he sounds like playing chord-based bebop.

Mr. Jordan has been a regular player at Vision almost since the festival’s origins, but he should have felt right at home at Clemente Soto in another regard: The sweltering heat and heavy humidity in the theater (whatever cooling system they had was decidedly not up to code) must have reminded him of New Orleans. Mind you, this was Wednesday, when the temperature was only in the upper 80s. I can’t even imagine what it must have been like the previous night, when it was 10 degrees hotter. A few hardy attendees (dudes, alas) responded by stripping to the waist. Yet at 73, Mr. Jordan was so robust that he flew from set to set without even pausing to change his sweat-stained T-shirt.

wfriedwald@nysun.com