There’s an emblematic photograph of Herbie Hancock on the back cover of his album Sunlight, which he began recording 40 years ago this month. He’s depicted against a red backdrop with a Sennheiser vocoder headset on his cranium, which is bowed in deep focus.

He’s also totally boxed in by his keyboards. The LP insert sleeve includes a diagram to help identify them by name: Oberheim Polyphonic Synthesizer, Sequential Circuits Prophet Synthesizer, ARP 2600, ARP Odyssey, Micro-Moog, Mini-Moog, Poly-Moog. (This is not a complete tally.)

At the time, Hancock had already proven his ability to work in a few divergent modes: taut acoustic postbop, of the sort he’d refined in the Miles Davis Quintet; coloristic chamber-jazz, on albums including Speak Like a Child; and earthy jazz-funk, in and out of his spectacularly successful band The Headhunters. But Sunlight opened yet another door to pop crossover, pushing even some admiring listeners to their limit.

Dave Tompkins chronicles one such reaction in his 2011 book How to Wreck a Nice Beach: The Vocoder from World War II to Hip-Hop, The Machine Speaks. “What’s gotten into Herbie Hancock?” writes a disgruntled fan after a Boston concert, in a letter published in the July 1979 issue of Musician. “Where does he think he’s going with that ridiculous vocoder? That thing isn’t just a waste of time, it’s a complete waste of taste.”

The music endured by this affronted concertgoer probably sounded much like it does in the clip below. Filmed in London on April 4, 1979, it features a performance of “I Thought It Was You,” Sunlight‘s opening track, a radiant vocal number that set the mold for the more recent neo-disco alloy of Daft Punk.

The clip shows Hancock, slightly out of breath, prefacing the song with an endorsement of the vocoder: “With this device, even a keyboard player like Herbie Hancock can sing.” The performance that follows is hardly seamless in its execution, but Hancock, a former electrical engineering major, never looks less than delighted (if also a little harried).

Like the Sunlight photograph, this footage captures a spirit of obsessive musical technophilia that Hancock still wears like a scout badge. At 77, he has stayed in the game long enough to embrace technologies barely imaginable back when Sunlight first saw daylight, in 1978.

All of which is worth keeping in mind as Hancock — pianist, composer, NEA Jazz Master, UNESCO Goodwill Ambassador, 14-time Grammy winner, unabashed keytar assassin — forges onward with his current world tour. (Its North American leg begins on Sunday, at the Count Basie Theater in Red Bank, N.J. Then come the Beacon Theater in New York City on Monday and the Kennedy Center in Washington, D.C. on Tuesday, followed by points west.)

Hancock thankfully travels lighter now than he did in the frontier age of analog synthesizers. “I have memory sticks that have my sounds on them, so I didn’t have to actually bring my keyboards on tour,” he said by phone last week. “I can use what’s provided, and put my sounds in them.”

Speaking from a tour bus during a 700-kilometer trek from St. Moritz, Switzerland to Marseille, France, Hancock touched on the evolution of his working band, the state of his hotly anticipated new album and the grinding exhaustion of the road.

“This is one of the hardest tours I’ve done, just because of the scheduling,” he said. “In six weeks of this European tour, there were only two days where we weren’t either playing a concert or traveling.” (During one of those off days, about 48 hours before our conversation, he’d dashed by private plane to Paris for the premiere of the intergalactic sci-fi movie Valerian and the City of a Thousand Planets, in which he has a cameo.)

“We did, at one point, five concerts in five days in five different countries,” Hancock added. “It wasn’t easy, but you have no choice. So you commit to it, and say: ‘I’m going to give my all, no matter what.’ And you know what? Those were some of the best concerts that we did.”

Hancock’s band mainly consists of brilliantly adaptable musicians who have worked with him for years, like drummer Vinnie Colaiuta, bassist James Genus and guitarist Lionel Loueke. But it also features a newer arrival: Terrace Martin, the alto saxophonist, keyboardist and producer best known for his body of work on record with rappers Snoop Dogg and Kendrick Lamar.

Last summer Hancock and a close facsimile of this group appeared on the Celebrate Brooklyn! series, at Prospect Park Bandshell. The concert was filmed by Jazz Night in America, and the video captures both the charged interplay and gear-shifting ingenuity of the band.

When I asked Hancock how the sound of the band might have changed since, he responded at first in macro terms. “The very concept of how the band works means that it’s different every day,” he said. “Because the concept is that open. It can go from avant-garde to completely funky stuff. So the spirit of what happened in Brooklyn, we’re fine-tuning that more.”

But he also offered a concrete example of the band’s recombinant strategies, pointing to “Cantaloupe Island,” a loping funk confection that he first recorded in 1964. (It has been covered or sampled countless times, most famously in the early ’90s by Us3.) In its present form on tour, “Cantaloupe Island” comes spliced with a Lionel Loueke invention called “Flying,” featuring a tricky sequence of metric stutter-steps.

“The concerts are going way better than expected,” Hancock said, returning to a more general frame. “We’re constantly creating new ways of treating the material that we have. And the flow of the concerts is different than other tours I’ve done before.”

There’s another way in which Hancock has lurched away from his usual protocols, and it can be traced to his home in West Hollywood. There, in a basement studio that calls to mind a state-of-the-art successor to Hancock’s old synth barricade, he has been working on another style-blending album, the details of which have been a subject of hungry scrutiny.

Hancock’s main partner in the studio has been Terrace Martin, who was born about six months after Sunlight was released, and has internalized its canny balance of live-band spark and high-gloss sheen. Martin belongs to a generation that grew up devouring Hancock’s pop hits, no less than his postbop innovations — and he understands how integral that crossover music, with its meld of brisk syncopation and emulsified texture, was to foundation of G-Funk.

In other words, Martin isn’t predisposed to regard Hancock’s synth-and-vocoder experiments as “a waste of taste,” or even an aberration. Rather, he sees it as part of a holistic expression, one that can still give up the occasional secret.

But this alert emulation isn’t a one-way street, as Hancock was quick to acknowledge. “I hear elements coming from Terrace, because of his generation, that I can add to my toolbox,” he said. “I don’t mean necessarily the songs, but the approach. How he approaches the process of producing my record is totally new for me; it’s not like anything I’ve been used to in the past.”

Martin travels in a vibrant creative orbit: He just released an album by a Los Angeles R&B collective he calls The Pollyseeds, and has collaborated with his fellow saxophonist Kamasi Washington, the electric bassist and vocalist Thundercat, and the electronic producer Flying Lotus, among others. One of Martin’s peer mentors is pianist and producer Robert Glasper, who has bridged much of the aesthetic and audience divide between hip-hop, R&B and modern jazz.

Every artist just mentioned is a member of Team Herbie, in one way or another. Flying Lotus featured Hancock’s playing on a recent track; Glasper covered a Hancock tune, complete with vocoder, on a Robert Glasper Experiment album last year. By way of Martin, Glasper and Thundercat, there are moments on Kendrick Lamar’s epic To Pimp a Butterfly that clearly evoke Hancockian precedent.

Lamar will reportedly make an appearance on Hancock’s new album. Hancock said Snoop Dogg has recorded a track, and Common has agreed to contribute. “Then we also have a track that Pharrell [Williams] wrote, and we kind of put it together in the studio,” he added. But it might not be accurate to suggest Herbie Hancock is making a hip-hop album, per se; he’s making a Herbie Hancock album, with parameters set to include some notable rappers.

Whatever the case, the goal is to have some music ready for release by early next year. “It’s coming a lot closer,” Hancock said. “We have some real melodies that we’ve come up with, instead of just building blocks.”

He paused, as if catching himself. “You know, it gets a little tricky when it’s taking years to put this together,” he said, laughing. “People can’t wait. If I let everything out in the press too soon, people will lose interest after a while. But it still seems to be building. Word is getting around.”

For all of his deftness as an early adopter, Hancock has also learned by experience to adopt the long view: It took years before Sunlight, for example, was widely regarded as a success. In concert, he now receives applause for the album’s second track, “Come Running to Me,” which was memorably sampled by J Dilla for Slum Village. (Glasper recently unpacked that sample, among others, in a Jazz Night in America video short.)

Hancock has composed more enduring jazz standards, to be sure, and had bigger breakout hits. When people talk about Afrofuturism, rightly placing him in its vanguard, they often fixate on the sci-fi imagery of an album like Thrust, or the landmark hip-hop synergies of “Rockit.”

Still, that image on the back cover of Sunlight frames the idea in beguilingly practical terms, as if Hancock were a magician producing all his cards for inspection. Not that seeing the cards, fanned out on the table, does anything to disarm the sleight of hand.

Describing the episodic, quick-fire digression of his show, Hancock chuckled. “The reaction I see from people is that they’re on the edge of their seat,” he said, “not knowing what we’re going to do next.”

Herbie Hancock appears at the Count Basie Theater in Red Bank, N.J. on Sunday; the Beacon Theater in New York City on Monday; and the Kennedy Center in Washington, D.C. on Tuesday. For more tour dates and other information, visit herbiehancock.com.

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