It’s part of the mission statement of Jazz at Lincoln Center to honor the music’s greatest innovators, and no one jazz icon has received more adulation than Dizzy Gillespie. There have been at least a half dozen formal tributes to him in all; just this month, the Afro-Latin Jazz Orchestra performed a full-length program saluting his contribution to Afro-Cuban jazz.

On Friday and Saturday in the Rose Theater, JALC presented “Bebop Lives,” which wasn’t advertised as a Gillespie tribute, but you can’t play bebop for very long without running smack into Dizzy: Nearly all the frontliners worked with Gillespie at one time, and the show’s star and master of ceremonies, James Moody, was his longest-lasting collaborator. All of the tunes, except a few standard ballad features, were written either by Gillespie or Charlie Parker.

The show could also have been called “Four Generations of Bebop,” since the players ranged in age and experience, beginning with the 81-year-old Mr. Moody, who goes back with Gillespie to the beginning of the bop revolution. The 67-year-old alto saxophonist Charles McPherson kept the flame of classic bebop alive in the ’60s, when most musicians were doing soul jazz and the avant-garde. Surprise guest Paquito D’Rivera, 58, learned the idioms of swing and bop in his native Havana, and though history may remember him as an outstanding Latin-jazz alto saxophonist, today he primarily concentrates on bebop clarinet. The 37-year-old neo-bop trumpeter Roy Hargrove survived the young lion movement of the 1980s and ’90s and is a commanding player who can keep up with the masters. The quartet was backed by Mr. Moody’s working rhythm section —Renee Rosnes on piano, Todd Coolman on bass, and Adam Nussbaum on drums — and all are equally impressive.

The collective’s opening number, Gillespie and Parker’s “Anthropology,” a variation on “I Got Rhythm,” immediately explored the possibilities of four musicians who have a common ideological background and speak a common language: After Mr. Hargrove quoted “All God’s Chillun Got Rhythm” in his solo, Mr. McPherson quoted the same line in his own statement a few minutes later, and then, in her solo, Ms. Rosnes also quoted the same Bronislau Kaper jazz standard. During the blues “Au Private” in the second half of the show, Mr. D’Rivera played a familiar phrase from “One O’clock Jump,” and, shortly after, Mr. Hargrove came back at him with another Count Basie jump, namely “Jumpin’ at the Woodside.”

As the evening progressed, it was clear that all the ensemble numbers were Gillespie-Parker classics and all the solo features were ballads from the Great American Songbook. Mr. McPherson played the first of these, “Embraceable You.” His tone still sounds remarkably like Parker’s, but his solo construction is, if anything, even more baroque. He managed to doubleand quadruple-time the ballad while still maintaining his footing with the rhythm section, no small feat considering he was playing incredibly fast while they were still in ballad time; Ms. Rosnes’s solo here was also especially exquisite. The full unit then played “Woody ‘n’ You,” which, over the years, has grown increasingly Latinate, followed by Mr. Hargrove’s feature, “Speak Low.” Keeping it as simple and direct as possible, he played one beautiful, straightforward chorus on flugelhorn, followed by a lovely coda — which was all that was needed.

Mr. Moody next introduced a guest vocalist, Roberta Gambarini, who made a perfect contribution to the Gillespie program with a scat extravaganza based on the trumpeter’s 1957 recording of “On the Sunny Side of the Street,” in which she sang all three horn solos. (I was equally impressed with Mr. Hargrove, who sang Dizzy’s famous jive-talk variation on Dorothy Fields’s lyric.) After a tremendous ovation, Mr. Gambarini performed Ram Ramirez’s “Lover Man.” Although she is an expert improviser with amazing intonation and technique, Ms. Gambarini’s formidable powers of musicianship do not extend to the ability to personalize or interpret a lyric; she sounds like an electric keyboard with flawless pitch but no dynamics or expression, a lot of pretty notes that don’t add up to anything. For her to invite comparison to Billie Holiday, an artist who was all feeling and, especially in her later years, next to no technique, was a grave miscalculation. Her ballad in the second half, Tadd Dameron’s “If You Could See Me Now,” was an improvement in that it allowed her to show off her bop chops (lyricist Carl Sigman’s line “without my heart behind the smile” seems to describe the singer), but I still resented that she was given three solo features while the formidable Ms. Rosnes didn’t even rate one trio number.

The first half closed with Mr. D’Rivera joining the ensemble on “A Night in Tunisia,” with Ms. Gambarini doing what she does better than anybody, which is fitting her voice into an instrumental ensemble. Here, Messrs. D’Rivera and Hargrove competed for applause, with the former bringing in “Manteca” and “Salt Peanuts,” and the latter surprising everyone with the overture to “The Barber of Seville” (he probably learned it from Bugs Bunny, same as me).

The second half of the show included Gillespie’s “Groovin’ High” (based on “Whispering”), which, as Mr. McPherson informed us, begins with the chords E-flat major, A-minor, then D7 (I’ve never heard a musician do that before). Mr. Moody’s feature was his hit “Moody’s Mood for Love” (another Dorothy Fields variation), which has become more of a comedy number over the years, complete with yodeling and a rap (about soap operas). It even includes singing the piano part in the center in plural, as if he were a gruff-voiced female trio. As always, it was entertaining, but I felt cheated when Mr. Moody didn’t play a tenor ballad.

The full ensemble show closed with “Oop-Pop-a-Da,” with Messrs. McPherson, D’Rivera, and Hargrove fully charged, and with Mr. Moody and Ms. Gambarini scatting the unison vocal. Considering the song’s long heritage of bad intonation — it was co-composed by the notoriously flat Babs Gonzales — it wasn’t surprising when Mr. Moody threw his partner off-pitch. And yet she sang with more spirit and jazz feeling here than at any other point in the show. It’s instances like these, when great musicians capture something inspired by tradition yet created completely in the moment, that bebop truly lives.

wfriedwald@nysun.com