“Don’t be too reverent,” Wynton Marsalis told the crowd in the Allen Room on Monday night, as the Lincoln Center Jazz Orchestra was about to launch into a program of two extended works by Duke Ellington and Count Basie. Don’t be afraid to make some noise – cheer, pat your feet, express encouragement. Even though it’s been more than 60 years since Duke Ellington first appeared at Carnegie, jazz is a music that demands an emotional, demonstrative response.

This was the orchestra’s first appearance – and only one this season – in the Allen Room, a comparatively intimate space with a beautiful view of Columbus Circle (although those reflecting traffic patterns on the glass can be distracting). Its acoustics are even better than the bigger Rose Theater, the sound hotter and more dynamic. And they couldn’t have picked two better works: “The Kansas City Suite” (1959), composed and arranged for Count Basie by Benny Carter, and “Black, Brown, And Beige” (1943) by Duke Ellington.

“Kansas City” is sublime, in part because it doesn’t bite off more than it can chew. Like Tchaikovsky’s “Nutcracker,” this is a suite for both concert and dance purposes, in various terpischorean tempos. It’s part of Carter’s brilliance that the basic orchestral sound is recognizably his own yet still consistent with the rest of Basie’s band book (as arranged by Frank Foster, Ernie Wilkins, and others).”Jackson County Jubilee” could be a sequel to Neil Hefti’s “Whirly Bird,” and – as Mr. Marsalis and trombonist Ron Westray pointed out – “Rompin’ at the Reno” sounds like a response to Dizzy Gillespie’s “Things To Come.”

The pieces vary between fast Lindy hops (“Wiggle Walk”) and slow romantic dances (“Katy Do,” apparently named for the Count’s wife, Catherine), and between Carter’s signature elegance (“Meetin’ Time”) and Basie’s trademark earthy, hard-driving blues (“Blue Five Jive”). Casual as it sounds, this isn’t an easy work: Mr. Westray fumbled a few notes on the ballad “Sunset Glow” but played a flawless solo on “Paseo Promenade.” It was a treat to hear the suite played live: Though Basie commissioned it and made it into a superb album, the Basie band rarely if ever played it all the way through in concert.

In fact, for years the music itself was lost. After Carter’s death last summer his widow, Hilma Carter, located the manuscript and made it available to Lincoln Center; fittingly, she flew in from Los Angeles to attend Monday’s concert. The Lincoln Center Jazz Orchestra required two additional musicians to play it: bass trombonist Max Siegel and guitarist James Chirrillo. Even in this expanded form, the orchestra captured Basie and Carter’s effortless buoyancy.

“Black, Brown, and Beige” is a horse of many different colors. Ellington’s overambitious, sprawling saga – he subtitled it “A Tone Parallel to the History of the American Negro” – attempts to depict the African-American experience from glorifying the labor of slaves (his “Work Song” has “A place to grunt”) to bourgeois Harlemites luxuriating in their Sugar Hill Penthouses. It’s a brilliant but flawed work – one of the most thrilling achievements in all of music.

Ellington’s most famous long-form composition reflects his lifelong phobia of closure. He only performed the entire work once in public, at the famous Carnegie Hall concert of 1943, but tinkered with it for the rest of his life, leaving no definitive score or recording. Both of the well-known recordings, from 1944 and 1956, are vastly incomplete. They’re actually inferior to the CD issued in 1989, 15 years after Ellington’s death, for which a nearly complete version was cobbled together from hitherto-unreleased sessions from the late 1960s. And all the recordings conflict, even on such basic points as how the work should begin and end.

In this work – unlike “Kansas City” and most subsequent extended jazz works (including his own) – Ellington attempted something more complicated than a suite. The work is broken down into three big movements: “Black, ” “Brown,” and “Beige.” Each consists of roughly three subsections. “Black” is the most ambitious, and finds Ellington coming closest to what a classicist would call symphonic form; he introduces one theme, then another and another, then brings back the first. He spends a lot of time weaving elaborate transitions from one theme to the next.

Yet the second movement, “Brown,” is the most successful. Ellington seems to have realized that all that transitioning isn’t necessary, and just goes from one theme to the next: “West Indian Dance” (one of the first jazz calypos – I’d like to hear Sonny Rollins play it), to “Emancipation Celebration” to “The Blues.” Although Ellington later wrote lyrics for “Come Sunday,” and it became the most famous part of this work (he recorded it with Mahalia Jackson),”The Blues” is the only section that had lyrics and a vocal in the original piece. On Monday Paula West, who opened the night after at the Oak Room, gloriously sang “The Blues,” which is neither in traditional 12-bar blues nor 32-bar song form. One would have expected her to slow down and drag it out in her usual sultry style, but she sang it in tempo, exactly as Ellington wrote it.

At the heart of the third movement is a lovely waltz called “Sugar Hill Penthouse,” which evokes Ellington’s partner Billy Strayhorn as well as Glenn Miller. Monday’s version also featured an unaccompanied piano solo, played by Eric Lewis, which was new to me. Ellington originally intended to wind up with a rousingly patriotic climax, but later he changed his mind and never quite found anything to take its place. The result is anticlimactic.

Hearing this piece live was a splendid experience. “Emancipation” has a brass effect I could never figure out from the various recordings; only by watching did I see it’s actually a muted trombone and a muted trumpet yelping in unison. In his verbal description of the opening movement, Ellington depicts black field hands being barred from entering a church and worshipping with white people. I can think of no more appropriate work to play now that Lincoln Center has given jazz lovers a church of our own.