During the opening riff to Dizzy Gillespie’s classic composition “Manteca,” the legendary trumpeter-composer usually had the members of his band chant “I’ll never go back to Georgia” over and over. It was an extraordinary thing that the single most important figure in the development of the medium now known as Latin jazz was not Latin himself but rather a black man from the American South; it was as if the creator of Viennese waltzes had come from Shanghai or the originator of the Argentine tango had been born in New Jersey.

Gillespie’s contributions to the medium were the subject of a tribute concert Friday and Saturday night at Rose Theater by the Afro-Latin Jazz Orchestra, which is the Latin wing of Jazz at Lincoln Center. Titled “Cubana Be, Cubana Bop,” after one of the Gillespie band’s breakthrough works, the concert was directed by the pianist Arturo O’Farrill. Mr. O’Farrill is the son of the late Chico O’Farrill, one of the most distinguished composerarranger-bandleaders in all of Latin jazz and, not coincidentally, one of Gillespie’s closest collaborators.

Although this second Lincoln Center Jazz Orchestra is beginning just its fourth season, it is somewhat larger than its older brother; for most of the evening, the ALJO sported a full retinue of 20 musicians: five trumpets, four trombones (including bass trombone), five reeds, and the standard three-piece big band rhythm section, plus an additional three Latin percussionists and some additional guest stars.

Mr. O’Farrill began with “Tanga,” a composition frequently cited as the first true work in the nascent Latin jazz idiom, composed for the bandleader Machito by the trumpeter Mario Bauzáá. The song had a profound influence on Gillespie, who put his own Latin pieces together in the late 1940s, adding Latin elements to his big band while encouraging a new wave of Latin bandleaders to add jazz soloists to theirs. Latin jazz was Gillespie’s next step following his crucial role in the bebop revolution. By fusing Cuban music and bop, he created a new medium that was, in a move largely new to both of its predecessors, equally at home in concert halls and dance clubs.

And Gillespie created a remarkable body of music for them to play. Dizzy’s Latin tunes are perhaps the most exciting part of his large body of compositions. The second tune performed Saturday was Gillespie’s lovely “Con Alma,” played by a three-horn frontline featuring two guest trumpeters: Jon Faddis (Gillespie’s most famous protegé) and Sean Jones (of the Jazz at Lincoln Center Orchestra), plus ALJO tenor saxophonist Mario Rivera. For the third piece, Mr. O’Farrill called on one of the most famous works in the Gillespie catalogue, the concert’s title tune, “Cubana Be, Cubana Bop,” written for the Gillespie band by George Russell. Here, Gillespie did for Latin-Bop what Benny Goodman had done for swing with “Sing, Sing, Sing,” at Carnegie Hall a decade earlier: It’s a two-sided concert work that dramatically builds to an episode of trumpet and drums. The chanting section at the climax, in which the band recites the title, has always, to me, foreshadowed the similar moment in Coltrane’s “A Love Supreme,” except that here, the second time the four notes are stated, the last one goes up instead of down.

One might have thought Mr. O’- Farrill had overplayed his hand by dealing one of his most powerful cards so early in the game, but he had a lot of cards up his sleeve. He proceeded with his father’s expanded version of “Tanga,” the highlights of which, as in much of Chico O’Farrill’s music, were often the slow sections: The opener featured clarinet over percussion and the third section featured two trombones in a pas de duex, one playing smooth and pretty à la Lawrence Brown, the other rough and scrappy à la Joe Nanton.

After intermission, Mr. O’Farrill announced that the evening’s performance was dedicated to the great saxophonist Michael Brecker, who died Saturday morning at 57 of leukemia. By apparent coincidence, the next work he called was the evening’s original commission, “Goodbye From the Heart,” by the ALJO’s youngest member, the alto saxophonist Erica Von Kleist. This was a pretty piece that featured its composer at the beginning and end and also gave the conductor his best spot at the piano, playing first in an idiom that seemed equal parts Ravel and Ellington, then leaping into a Cuban montuno.

The central piece of the evening, though, was Chico O’Farrill’s “Second Afro-Cuban Jazz Suite” of 1951, a brilliant work that is obscured in favor of its predecessor, the famous original suite from three years earlier that featured Charlie Parker — and also because, perhaps, the composer didn’t bother to give it a more memorable title. The 1951 suite is striking in its use of classical elements, opening as it does with a mixture of oboe, flute, and bass clarinet over congas (from a time when those instruments were rarely used in jazz), and also including a remarkable, non-Latin interlude that seemed inspired by Woody Herman’s “Four Brothers.”

Mr. O’Farrill had planned to end the concert with “Manteca” as a rousing finale, and it certainly was rousing — oppressively so. This was the fourth long, Latin suite of the evening, and it was one too many. The audience’s collective ears were worn out after a long, rewarding evening with a lot of trumpet blasting. Mr. O’Farrill might have considered closing with the simpler, shorter original 1947 arrangement, rather than the expanded “Manteca Suite.” Instead, the band finally closed with the biggest blaster of them all, an erupting six-trumpet competition in which Mr. Faddis, as expected, out-blasted his five contenders, including the formidable Mr. Jones and Michael Phillip Mossman. My ears may never recover.

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Saturday night had to be the most multicultural in the short history of Jazz at Lincoln Center’s Rose Hall: At Dizzy’s Club Coca-Cola, the amazing drummer Lewis Nash and his quintet offered quintessential, basic bebop. Across the hall in the big Rose Theater, the Afro-Latins were offering their Pan-American version of the same. Around the corner in the Allen Room, there was a remarkable meeting of two idioms in a program of blues by the country music legend Willie Nelson with JALC artistic director Wynton Marsalis (the portion that I heard was so outstanding that I hope it will be reprised soon).

As if that wasn’t enough, having left Messrs. Marsalis and Nelson in the Allen Room, I ran into a power trio in the hallway, namely Tony Bennett, his longtime companion Susan Crow, and Bill Charlap. They too were hopping from one show to the next in what has become the world’s first jazz multiplex.

wfriedwald@nysun.com