Bill Charlap, the brilliant pianist and artistic director of the 92nd Street Y’s Jazz in July concert series, is a modest man, almost to a fault. He leans much closer to understatement than to exaggeration. So when he makes a bold, sweeping claim, such as describing the Vanguard Jazz Orchestra, whom he presented in concert on Thursday, as “the foremost large jazz ensemble in the world,” we should be inclined to take him very seriously.

The VJO, which has played at the Village Vanguard nearly every Monday since 1966 (the year Mr. Charlap was born, coincidentally), is the most influential jazz big band of the contemporary era: This is the band in which every student musician dreams of playing, the band that virtually every college jazz orchestra tries to sound like. Nearly every band of the last 40 years is an unabashed spin-off of the VJO, and at least one club in every major metropolitan area has a “Monday night band” that follows the VJO business model. Indeed, it’s a safe bet that a majority of all the big bands in the world right now emulate the VJO, especially since VJO veterans such as Bob Brookmeyer and Mike Abene write for overseas jazz orchestras.

Thursday’s appearance at the 92nd Street Y marked the Vanguard Jazz Orchestra’s most ambitious full-dress concert performance in its home city in a long time. The band also has a new double album, “Monday Night Live at the Village Vanguard” (Planet Arts), in stores. This would be a banner year for the group, except that in March it suffered the irreplaceable loss of one of its most dependable members, Dennis Irwin, the band’s bassist for more than 25 years (both the concert and the album were dedicated to his memory). Perhaps because this is a period of bittersweet memory, the VJO, which rarely looks backward, is concentrating, in both of these current efforts, on works by co-founder Thad Jones, as well as early members Jerry Dodgion and Mr. Brookmeyer.

As such, the band’s primary arranger-composer in residence, Jim McNeely, supplied only one tune apiece for the two current projects: “Don’t Even Ask” in the concert and “Las Cucarachas Entran” on the album. Both are state-of-the-art examples of postmillennial jazz composition, featuring multiple sections, tricky melodies, and rhythmic patterns that refuse to stay in one place. At times one can hear a Latin polyrhythm, at others it’s gone. In the case of the second tune, Mr. McNeely apparently intended to depict the migratory patterns of cockroaches, but both songs display the influence that the VJO has had on younger writers.

It just goes to show how perceptions can change with time: Fifty years ago, when Jones was playing in Count Basie’s trumpet section, he had a hard time getting the Count to play his music. When he did, Basie felt obliged to “dumb” Jones’s music down — he regarded it as too complex for mainstream audiences, especially for dancers, who essentially wanted everything in foot-patting foxtrot tempo. This, naturally, was a big part of what impelled Jones to launch his own big band (in collaboration with the drummer Mel Lewis).

If Jones’s charts seemed radical in their day, when they’re compared with the more deliberately complex and concert-styled works of Mr. McNeely, they now seem amazingly straightforward and swinging. Not that Jones’s charts were simplistic or lacking in intricacy; as Mr. Charlap pointed out, “Little Pixie” is, on the surface, a basic variation on “I Got Rhythm,” but it’s got as much going on as a Stravinsky ballet. The writing is sectional in the best swing-band tradition, with muted, then open-belled trumpets playing off the reeds. Also present is a string of dynamic solos, including the trombonist Louis Bonilla, who wittily quoted Lester Young’s “Rhythm” variation, “Lester Leaps In”; alto saxophonist Billy Drewes, who sounds like Charlie Parker, only with more feathers, and a charging baritone sax solo from Frank Basile, subbing for Gary Smulyan. (Mr. Smulyan more than pulls his weight with a remarkably aggressive reading of “Body and Soul,” as arranged by Jerry Dodgion, on the album.)

Apart from Jones, the composer-arranger who comes off best is Brookmeyer, who is one of the great living masters of large-format jazz. Twice on the album, he takes milestone works of the early jazz canon — W. C. Handy’s “St. Louis Blues” and Fats Waller’s “Willow Tree” — and transforms them into brooding, modern master opuses. His treatment of the Handy blues is a 15-minute epic that is Gershwin-esque in its ambitions yet devoid of concert-hall pretension. Mr. Brookmeyer stretches the melody out with colorful, dissonant chords and tonal painting that are briefly reminiscent of Gil Evans. Postmodern tone clusters abound, yet we are constantly reminded that Mr. Brookmeyer grew up in Kansas City at its musical peak, when the blues of Pete Johnson and Big Joe Turner ran the town. As a writer, Mr. Brookmeyer never gets so avant-garde that he loses track of the basic blues — it’s almost like the further out he gets the further in he goes. Who says you can’t move in two directions at once?

At the 92nd Street Y, band director and trombonist John Mosca favored us with another classic Brookmeyer work: the band’s classic treatment of “Skylark,” which was recorded by the VJO under Mel Lewis’s direction in 1980. The chart is a vehicle for alto saxophonist Dick Oatts and the only number to feature a single soloist all the way through. This is a superior slice of sound painting, whereby the outer context of the arrangement, which is drenched in postmodernism and sounds almost classical, is dynamically contrasted with the centerpiece solo, which is saturated with feeling and incredibly emotional. It’s a rare dessert that’s cool on the outside and hot on the inside, in which the dissonances of postmodernism line up and form a kinship with the rough textures and blue notes of the earliest jazz so that the very old and the very new become indistinguishable. Thank you, Mr. Charlap, for presenting the Vanguard Jazz Orchestra in concert (and even sitting in with them on two numbers) and letting us enjoy them, for once, above ground.

wfriedwald@nysun.com