Jason Moran says of Fats Waller: “He needed to talk about depression — personal depression. He needed to talk about love, or loss, or trying to find love again. (Clay Patrick McBride)

“Any time I get a commission, it’s not really to do what the person is asking me to do,” Jason Moran says, a grin glinting through the phone. “It’s actually to think up something that they wouldn’t have considered I would do, and then take that back to them. And, you know, tell them to pay for it.”

When Harlem Stage approached the pianist in 2010 to present a concert honoring Fats Waller, Moran wasn’t just going to re-create a batch of iconic music. Maybe he could turn Waller’s legacy around, use classic tunes like “The Joint Is Jumpin’ ” and “Ain’t Misbehavin’ ” to say something about the present moment in jazz. Forget a concert, how about a dance party?

Moran — a MacArthur Fellows grantee who serves as the Kennedy Center’s artistic director for jazz and is among contemporary music’s leading conceptualists — recruited Meshell Ndegeocello to sing lead vocals and help assemble a band. In the four years since, they have brought the Fats Waller Dance Party to stages across North America. Part funk workout, part cabaret, part improvisational experiment, it represents a creative answer to today’s constant chorus of jazz doomsayers: Go to these shows and you’ll find diverse, relatively young, often unsuspecting audiences listening to a new musical hybrid and dancing with abandon.

So how do you translate something like that onto a record? That’s the question that would seem to greet the arrival of “All Rise: A Joyful Elegy to Fats Waller,” the album released this week under Moran’s name and co-produced by Ndegeocello (she also sings on five of the 12 tracks). But Moran and Ndegeocello never intended for it to be a dance record — by the time they recorded it, they had already moved on to a new idea.

“To say people will hear it as a dance record, that would limit it,” Ndegeocello says, speaking together with Moran via conference call from her home in New York. “I think people are going to be moved [physically], but also moved. I sequenced the record so that it progressed like a New Orleans funeral.”

Meshell Ndegeocello and Jason Moran, wearing the Fats Waller mask, perform in “Fats Waller Dance Party” at the Harlem Gatehouse on May 13 in New York City. (Michael Nagle/Michael Nagle)

Moran chimes in: “There’s many ways to celebrate death in cultures around the world. That’s where this is coming from.”

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“All Rise” is Moran’s ninth album for Blue Note Records, and his first in 14 years without his regular jazz trio, the Bandwagon, at its core. Mostly, it works as an assertion of Waller’s relevance: The virtuoso singer, songwriter and stride pianist is rarely mentioned in the same breath as such other early jazz pioneers as Louis Armstrong and Jelly Roll Morton. Moran and Ndegeocello intend to restore him by tweaking his music.

The record offers a reminder about the fertility of contrasts: Taken together, Moran (musically playful, abstract-minded) and Ndegeocello (insular, coolly earnest) make up a sort of composite foil to Waller, whose persona was ribald and jiving and overt. The further the album drifts away from Waller’s original arrangements and into its own territory, the more it succeeds.

“All Rise” also has plenty of fruitful contrasts within itself, from song to song. At Fats Waller Dance Party shows, the band largely reshapes Waller’s tunes for a hip-hop ear — often by seizing on hidden beats or fleeting riffs from the original recordings and turning them into the foundation for new renditions. That happens some on the record, but things go in more varied directions, too.

There’s a love-struck groove on “Ain’t Misbehavin’,” pulling gently against Ndegeocello’s luminescent vocals; there’s a perked-up, Latin funk feel on “Yacht Club Swing.” Later on, Moran offers a restful, double-keyboard rumination on his “Fats Elegy.”

It can be hard to locate the spiritual center on such a diverse collection, but the undisputable highlight comes on “Ain’t Nobody’s Business.” Tarus Mateen’s droning electric bass moves about with a furrowed brow and ambling limbs — rooted, never restless. Over a clipped funk beat and a slurry trombone line, the song flows forward steadily. Ndegeocello’s vocal line is almost completely unrelated to the spinning melody of the original. “For me, it’s all about color, how watercolors overlap — when they touch, the fault line that happens,” Moran says of the tune. “That’s how I wanted to play.”

What unites the 1922 and 2014 recordings is the lyric, with its uncompromised self-possession. But even there, a difference strikes you: “Ain’t nobody’s business what we do,” Ndegeocello exhales, swapping in the plural first person. All of a sudden the song might be talking about the modern politics of love — it feels contemporary, and its timelessness becomes that much clearer.

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The son of a preacher father and an organist mother, Thomas “Fats” Waller became a star in the early years of commercial radio, back when jazz was pop music. His masterful piano playing and rumbly singing voice helped, but mostly it was the bouncing, hooky tunes he wrote — like “Ain’t Misbehavin’ ” and “Honeysuckle Rose” — and the way he could deliver double entendres with a sly, disarming defiance.

“He was a needed storyteller in the Depression,” Moran says. “For African American people, he needed to say these things. He needed to talk about depression — personal depression. He needed to talk about love, or loss, or trying to find love again.”

Ndegeocello adds, “Although it may have come across as entertainment during his period of time, I really felt he was subversive in his beauty. I try to remind myself of that when I’m onstage — that I want you to dance, and there’s a reason why we all like to dance: to transcend our momentary ills and sufferings.”

Yet Waller has long been a sort of historical problem child. Jazz is largely cast as a tool of upward mobility, a proving ground for black genius, and an implied critique of American capitalism. Certainly it has been all of that. But Waller spoke in a lower-class patois without apology and he talked directly to that stratum. (With “Your Feet’s Too Big” he was a gutbucket comedian; with “Black and Blue,” a commentator on black internal politics.) Besides, Waller was a musical refiner more than an innovator: He can’t be said to have pioneered a new style.

But Moran and Ndegeocello are both accustomed to exploring neglected terrain. Ndegeocello grew up in Washington, studying at the Duke Ellington School of the Arts and playing bass in go-go bands such as Rare Essence before moving on to pursue a national singing career. In the early 1990s, she was already gaining fame for an alchemy of sound that wouldn’t have a name until years later: It was the makings of that slow, raw form of R&B eventually known as neo-soul.

“When I first met my now-wife, there were a few singers that we connected about,” Moran remembers. “She said, ‘Let’s connect over Cassandra Wilson. Let’s connect over Ella Fitzgerald. And let’s connect over Meshell Ndegeocello.’ ”

A member of the hip-hop generation, Moran has lived in Harlem for over a decade and is considered a leader in its burgeoning new-jazz scene. Young jazz musicians living there have been blending what they learn in school, on records and in jam sessions with the popular music of their upbringing, and the greater jazz world has rapidly reshaped itself to reflect this. But while Moran has been an active leader on that front, he’s rarely recorded music under his own name that refers back to funk and golden-era hip-hop as explicitly as many of “All Rise’s” tracks do.

If it seems ironic that a tribute project to an early-20th-century musician is what brought out this side, he’s happy to explain why. “Dance has been a part of society for a long time,” he says. “So some of the rhythms that come out in these songs, I’ve always felt they weren’t new. They were rhythms that were already embedded in Fats Waller’s music, except that I just decided to clip them out and make them a focal point. . . . I don’t really believe in new.”