Some musical auteurs keep each of their feet in different aesthetic worlds; Herbie Hancock does this with his hands. At this week’s JVC Jazz Festival concert at Carnegie Hall, he had a smaller electronic keyboard mounted on top of his Fazioli F278 concert grand (as well as a fuller-sized electric piano), and he often played the electric in the treble clef with his right hand while keeping his left on the acoustic instrument in the bass clef.

Mr. Hancock is a man in two worlds at once, and, at 68, he is only getting better at it. Two years ago at JVC, he gave a major concert at Carnegie in which he performed with expected brilliance in several different acoustic settings — trios, duos, quartets. But he sabotaged his own concert by performing with, at one point, a mediocre all-electric band of young, pop-styled players half his age. Yet with his 2007 album “River: The Joni Letters,” Mr. Hancock found a way to bring both halves of his musical career onto the stage at the same time, making pop music and jazz that satisfied both strata of fans.

Currently in the midst of what he calls his “River of Possibilities Tour” (referring also to his previous album, “Possibilities”), Mr. Hancock continues to intermingle the elements of electronically driven pop and adventurous, hard-edged jazz, with the two elements complementing rather than distracting each other. He reinterprets widely known songs by Joni Mitchell in such a way that her fans will recognize them without feeling as though he is merely paying lip service to them. But at the same time, he reinvests these songs with brilliant new chords as well as astute improvisations.

“River” was so prized by the pop music industry that it was awarded the Grammy, for Album of the Year. When I was half-watching the telecast in February (while reading the latest issue of “Simpsons Comics”), and I saw Mr. Hancock stroll onstage to collect his statuette, I assumed he had merely won the jazz award. I didn’t realize until the next morning that he had snatched the top prize of the evening, a victory for jazz in general.

At Carnegie this week, nearly every performance featured elements of both jazz and pop, electric and acoustic playing, improvising and rocking out: The first number, “Actual Proof,” used the electric rhythm section in the opening, but shifted to an acoustic improvisation in the center, courtesy of Mr. Hancock and the monstrously talented tenor saxophonist Chris Potter. The two numbers that followed spotlighted a pair of female vocalists. Sonya Kitchell, who sounds like a folk-tinged singer-songwriter, and is sonically compatible with Norah Jones and Joni Mitchell herself, sang “River.” Then Amy Keys, who is more of a straight-ahead soul singer, took the lead on “When Love Comes to Town” (written by U2), although both ladies performed on both tunes in a way that reminded me momentarily of Sergio Mendes.

The highlight for the hard-core jazz fans in the house was the middle section of the set, which began with Mr. Hancock introducing the bassist Dave Holland, and then leaving the stage. Mr. Holland, who was playing a smaller-than-usual upright acoustic instrument (called a Czech-Ease Road Bass), launched into an understated, unaccompanied solo, which turned out to be an introduction for Mr. Hancock, who returned to the Fazioli and delivered the evening’s nicest moment: a long and rewarding, completely unaccompanied and abstract meditation on his own most famous composition, “Maiden Voyage.” For the rest of the evening, when other instruments were playing, the Fazioli was somehow miked to sound completely lifeless and free of resonance, like a toy Casio keyboard. But when heard only by itself, the Fazioli sounded glorious.

There were other highlights, but the high point had been reached: Mr. Hancock played “All I Want,” a Joni Mitchell song not on the album, Leon Russell’s contempo-pop standard “A Song for You” (vocal by Ms. Keys), and two of his own standards in different fields, the modal jazz “Cantaloupe Island” and the funk “Chameleon.” He played the latter as an encore, with a big drum solo by Vinnie Colaiuta. It’s been said that you can’t please everybody. Mr. Hancock may just be the first.

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On Sunday and Tuesday, two other artists gave one-act recitals at Carnegie that also straddled the worlds of jazz and pop. First, the Brazilian guitarist and singer João Gilberto, one of the creators of bossa nova, celebrated the 50th anniversary of that movement. It was easy to take, with his mellow voice and simple, soft-on-the-ear picking. However, 100 minutes of Mr. Gilberto singing in a mid-tempo monotone got to be a bit much; someone else doing a Gilberto song, or perhaps Mr. Gilberto working with a guest artist or a band, would have provided a little variety. I couldn’t argue with his two choices of encore: his blockbuster hit “Desafinado” and Irving Berlin’s “God Bless America,” sung in Portuguese.

The trumpeter Chris Botti, the only jazz musician whom one wouldn’t be surprised to see on “American Idol,” played a 100-minute set on Tuesday. He, too, walks down the middle, refusing to be classified as another robotic, smooth-jazz player; his band is full of hard-core players, such as the guitarist Mark Whitfield and the Hancock-influenced pianist Billy Childs.

But at the same time, Mr. Botti has caught the ear of the big pop audience. Early in the program, he showed that he’s quite capable of playing extended, harmonically based bop-style improvisations (and I wouldn’t have minded a few more of those) in the middle of rhapsodizing over melodies from the pop (and even classical) world. Mr. Botti paid homage to Miles Davis with “Flamenco Sketches” — not one of the late trumpet guru’s easier compositions — as well as two tunes by Leonard Cohen (“Hallelujah” and “A Thousand Kisses Deep”). He then shared an anecdote about dropping out of college to play with Frank Sinatra in 1984 before closing with the Sinatra saloon anthem “One for My Baby,” which he delivered with the warm, vibrato-tinged timbre of Bobby Hackett or Ruby Braff. Which goes to show you that the cutting edge of jazz and pop can sometimes lean back to the old school.

wfriedwald@nysun.com