It’s said that when John Lennon began learning how to play the guitar in the mid-1950s, he actually detested jazz.

This can be dismissed as an adolescent prejudice. At the time in postwar England, traditional jazz, or “trad” as the Brits called it, was vying with rock ‘n’ roll for the affection of both clubgoers and aspiring musicians. The young Lennon, whose inspirations were Chuck Berry, Little Richard, Buddy Holly, and Elvis Presley, had sworn allegiance to that particular team.

But 10 years later, when Lennon and his wife Yoko Ono began recording albums of avant-garde compositions, they invited some of Europe’s furthest-out free jazz players to participate, not to mention the entire Ornette Coleman Quartet.

I can’t imagine what Lennon would have thought of Beatlejazz, a band masterminded by the pianist Dave Kikoski and the drummer Brian Melvin, who are celebrating the release of their latest album, “All You Need,” this week with a performance at Iridium on Sunday.

Jazz musicians have been playing and singing the music of the Beatles virtually since the Fab Four broke through in 1963–64: Ella Fitzgerald couldn’t buy love, but she bought a lot of groceries with her chart hit on “Can’t Buy Me Love”; Duke Ellington wanted to hold our hand; Buddy Rich gave “Norwegian Wood” an anatomical implication; Wes Montgomery covered “A Day in the Life” and “Eleanor Rigby,” and Count Basie made two entire albums in a Beatle bag.

At that time, the practice of veteran musicians playing contemporary chart hits was viewed as a means of bridging the ever-widening generation gap. Today, when contemporary jazz musicians play the songs of Lennon and Paul McCartney, it’s more about bringing the techniques and crafts they’ve learned to the music they’ve loved since childhood.

That’s certainly true of the brilliant recent interpretation of “Across the Universe” by the bassist Ben Allison, or of “Connie Evingson Sings the Beatles,” a delightful set of swinging treatments by the Minnesota-based jazz singer. Producer Bob Belden’s “Strawberry Fields Forever,” a set of new interpretations by jazz and R&B vocalists, was highlighted by a stunning reimagining of “Tomorrow Never Knows” by Dianne Reeves that made the “Rubber Soul” original seem tepid by comparison.

Still, none of these projects was as ambitious as the Beatlejazz series, which now numbers four volumes:”A Bite of the Apple”(2000), “Another Bite of the Apple” (2001), “With a Little Help From Our Friends” (2003), and the new “All You Need.”

In the parlance of the pop music business, Messrs. Kikoski and Melvin (joined by the bassist Charles Fambrough on the earlier albums, replaced more recently by Larry Grenadier) “cover” the music of Lennon, McCartney, Harrison, and Starr. But these new treatments diverge so markedly from the originals that the term “cover” is best left back where I found it: in the realm of wedding and bar mitzvah bands, and all those dreadful ’70s rock stars who persist in “covering” the Great American Songbook.

Conceptually speaking, Beatlejazz resembles the long series of jazz versions of Broadway shows that flourished in the late 1950s and early ’60s, such as “Jimmy Giuffre Plays ‘The Music Man,'” “Cannonball Adderley Plays ‘Fiddler on the Roof,'” “Louis Prima Plays ‘Marat/Sade,'” and umpteen jazz reconstructions of “Porgy and Bess” and “West Side Story.” The audience, it is reckoned, already knows and loves these songs, so why not stimulate them with imaginative treatments in a separate musical genre?

Messrs. Kikoski and Melvin’s search for creative takes on music they know very well was evident even on the first track of their 2000 debut as Beatlejazz: Paul McCartney’s “Junk” (which he attempted unsuccessfully to record with the Beatles on the “White Album,” but wound up saving for his first solo album in 1970). “A Bite of the Apple” also features a rendition of “Come Together,” which, stripped of its psychedelic lyrics, could be a minor-key boogaloo by Horace Silver.

In some cases, like “I Will,” the trio and various guests take the Beatles’ more lyrical ballads and embellish them with the same touches that jazzmen traditionally give Cole Porter or Richard Rodgers: fresh harmonizations and newer, more swinging rhythms (sometimes in a Latin tempo, as on “It Won’t Be Long”). On other tracks, Beatlejazz seems intent on getting as far away from anything recognizable as possible. “Magical Mystery Tour,” for example, begins with Lennon and Mr. McCartney’s secondary theme, heard only briefly, before launching into a modal waltz that makes it hard to find the song’s main theme — although the tour does travel past “Norwegian Wood.”

On Beatlejazz’s third album, “With a Little Help From Our Friends,” the original trio’s guests were all fusion stars (guitarists John Scofield and Mike Stern, plus trumpeter Randy Brecker and saxist Michael Brecker). All four are excellent players, but not particularly imaginative choices because they’re precisely the kind of musicians who play rock ‘n’ roll tunes all the time. For the new set, though, the guests are more unabashedly out of left field, and include the African bassist and singer Richard Bona (who croons “All You Need is Love”), harmonica virtuoso Toots Thieleman and one of the great sax men working today, the tenor giant Joe Lovano, who is superb on Lennon’s lesser-known “Look at Me.”

The current album, “All You Need,” begins on neutral ground with Mr. Thielemans playing “The Fool on the Hill” (a tune associated with the Brazilian pop star Sergio Mendez as much as the Beatles) along with Messrs. Kikoski and Melvin in an upbeat 3/4, making it clear that Mr. McCartney’s foolish magical mystique is a close cousin of Nat King Cole’s “Nature Boy.” On “The Night Before,” Mr. Kikoski plays an electric keyboard with a Ray Charles-like timbre, and phrases the tune more like Les McCann’s “Compared to What.” He also infuses “I Want You” with a 6/8 Cuban touch.

But the most rewarding track on the album, and perhaps the entire series, is Mr. Lovano’s take on “The Continuing Saga of Bungalow Bill.” This was originally substandard Lennon, a goofy, somewhat malevolently minded comedy bit of a song that nevertheless made it onto the “White Album.” Mr. Lovano, beginning with just drums, makes it even goofier and more playful, alternately rushing and elongating Lennon’s melody, and generally treating it like anything but a sacred text. It is irreverent and inspired, and I’d like to think that John Lennon would have loved it.

wfriedwald@nysun.com

Beatlejazz will perform August 12 at Iridium (1650 Broadway at 51st Street, 212-582-2121).