Can this really be the fifth season of Jazz at Lincoln Center at Rose Hall? Already there are young people filling seats at the Rose Theater who probably feel that JaLC has been around forever, and even take it for granted. They’d probably be amazed to hear that listeners in the 1940s thought it was a big deal whenever jazz made it to one of the major concert halls, like Carnegie or Town Hall, and probably couldn’t imagine a world in which American music was accorded the same respect as symphonies and chamber works. (It had only been a few generations since ragtime was condemned by the pope and jazz itself was officially denounced by the city of New Orleans, where it was created.) So if young fans want to act as though Rose Hall — the only jazz-specific multiplex in the country, if not the world — is no big deal, then that’s a good thing, an illustration of how far we’ve come.

Last year, JaLC kicked off the fourth season at Rose with two of the best shows in its 20-year history in programs devoted to Benny Carter and Gil Evans. This year, it began equally auspiciously with a program on Thursday night built around the iconic pianist Ahmad Jamal. On paper, the idea looked dauntingly complicated: Getting Mr. Jamal’s famous trio to interact with the full Jazz at Lincoln Center Orchestra, led by artistic director Wynton Marsalis, would not be not an easy undertaking. Then again, there is a whole repertoire of modern jazz concertos (and concerto grossos) out there, from Sonny Rollins’s 1958 “Big Brass,” with charts by Ernie Wilkins, to George Russell’s “Living Time” (1972) for Bill Evans.

In performance, the presentation turned out to be refreshingly simple. Mr. Jamal and his ensemble — a quartet, actually, with James Cammack on bass, James Johnson on drums, and Manolo Badrena on Latin percussion — held the stage for the first half of the evening, playing a condensed version of the sets they play in jazz clubs all over the world, beginning with his customary opener “Wild Is the Wind” and building to his signature hit, “Poinciana.” Mr. Jamal is more of an interpreter than a composer: Few of his own originals have caught on with other performers, but his touch at the piano and the sound of his augmented trio is so distinctive that he can make any melody sound like his own.

“Poinciana” is the archetype of the Jamal orchestration (which is not to say that his treatments of other songs follow it like a formula). He essentially downplays the original Brazilian melody and emphasizes a complex foundation of interlocking polyrhythms and an original, undulating vamp, which would make the song sound exotic even if it weren’t South American. Mr. Jamal gives the actual melody of “Poinciana” less screen time than “I’m Glad There Is You,” another 1940s pop standard that the pianist quotes throughout “Poinciana.” Not only does the vamp get more attention, but Mr. Jamal stresses it so much that it eventually goes into business for itself and becomes the arrangement’s central melody, rendering the “Poinciana” tune a fading counterpoint to itself.

Fifty years ago, when “Poinciana” was first heard on a live album recorded in Chicago’s Pershing Room, it catapulted Mr. Jamal to the top of a food chain already rich with powerhouse pianists showcasing sheer chops (Oscar Peterson), sheer swing (Erroll Garner), and sheer style (George Shearing). Mr. Jamal was offering a thick yet translucent style in which levels upon levels of melody and countermelody ran in and out of one another on top of multiple levels of rhythm, transforming the familiar into the exotic and vice versa.

Elsewhere in the first set on Thursday, Mr. Jamal played a melancholy original, “Papillon,” which reflected his Francophile tendencies. (For the last decade or so, he’s recorded for the French label Dreyfus Records.) “Melodrama,” by friend Jimmy Heath, began with Havanese block chords and featured passages in which Mr. Jamal played on top of the rhythm section, rather like a horn soloist, and others in which he was completely integrated into it.

The second half of the performance consisted of three Jamal originals, arranged to include both his quartet and the 13 horns of the JaLC Orchestra. The orchestrations, by Byron Rooker and Trevor Kuprel, achieved the difficult task of integrating the big band into the quartet on Mr. Jamal’s terms. After the first half of the show, when four men became a full orchestra, the second half saw an orchestra sublimate itself into a quartet. The first piece, “The Aftermath,” set the pattern: Most big-band numbers begin with the full ensemble before breaking into individual solos. These Jamal works began with one of the pianist’s characteristic introductions, which led into the trio playing the central melody or “head.” The big band then stated its version of the melody in full force, which in turn introduced the individual horn soloists from the band. Finally, Mr. Jamal neatly concluded the works himself.

The meeting of the quartet and the horns seemed entirely natural and unforced, and the orchestra seemed like a direct, organic extension of the leader’s piano, much the same way that the big bands of Duke Ellington and Count Basie seemed like extensions of their leaders’ piano styles. The four trumpets, four trombones, and five saxophones introduced a world of new musical colors into a style that was already far from monochromatic.

The second orchestral piece, “Should I,” had no connection to the standard of that title, but was nonetheless a reference to vintage song styles: Set in ¾ time, it combined the feel of a premodern jazz waltz, such as Fats Waller’s “The Jitterbug Waltz,” with a postmodern waltz, such as Miles Davis’s “All Blues” (and reminded us that there are virtually no bebop-era waltzes). The final announced piece, “The Devil’s in My Den,” was a funk number dedicated to the late Stanley Turrentine (who recorded this song with Mr. Jamal in 1997), in which the horns swirled around Mr. Jamal like raging winds in a hurricane.

Commendably, the soloists, starting with Mr. Marsalis on “The Aftermath,” absorbed Mr. Jamal’s approach into their playing; the most notable part of alto saxophonist Sherman Irby’s improvisation was his repetition of a simple phrase, varying only the most minute nuances of it, like a saxophonic equivalent of one of Mr. Jamal’s piano vamps. The trumpeter Sean Jones played a Harmon-muted solo in which the motive seemed to be to leave as much space between the notes as possible, which again mirrored what Mr. Jamal would have played on his piano.

After a standing ovation from the sold-out opening-night crowd on Thursday, the quartet left the stage and returned to play the bouncy “You Can See,” by the Jamaican pianist Monty Alexander, who was also in the house.

Although Mr. Jamal has not yet recorded these works, he and his quartet have performed them with the Chicago Jazz Orchestra and the Columbus (Ohio) Jazz Society Orchestra. The existence of a circuit of JaLC-like jazz orchestras around the world may be the best news of all. Younger jazz fans may take such things for granted, but I can’t.

wfriedwald@nysun.com