Ben Folds performs in concert with yMusic at the Royal Opera House in London on Aug. 12. (Goodgroves/REX Shutterstock/Associated Press)

When the rapper Kendrick Lamar performed with the National Symphony Orchestra, it was called a “pops” concert. When Cameron Carpenter, the enfant terrible of the organ, plays with the NSO this week, it counts as “classical.”

But when singer-songwriter Ben Folds comes to the NSO on Friday to perform his piano concerto — yes, his piano concerto — it will be as part of a new series called “Declassified”: an attempt to get beyond these inadequate labels.

The concert will start at 9 p.m. It’s billed as “an interactive multimedia mix of dance-inspired music.” Tickets are a flat $39. You can bring drinks into the hall. A serious “classical” conductor will be on the podium. (On Friday, it will be Sarah Hicks, a principal conductor with the Minnesota Orchestra.) And the music is — sui generis.

Or, well, “proudly derivative,” in Folds’s words. But because it’s a full-blown neo-romantic (in places) piano concerto, although thick with piano-bar-style interleavings, it’s not quite what Folds fans might expect. And with Folds playing — as well as music by Mason Bates and other living composers — it’s not quite the classical music norm, either.

Folds, 49, has made defying categories a part of his artistic identity — playing alt-rock or borderline hokey pop, in hip clubs and mass-market TV shows (he was a judge on NBC’s “The Sing-Off” for several seasons), with people such as Elvis Costello and William Shatner. But when Folds appears with orchestras — pops concerts, he says, make up about one-third of his touring gigs — he writes new arrangements of his songs so that the orchestra isn’t merely backup but serves as his band.

“Rather than making it watered-down pop music,” he says, “why not make it extremely well-thought-out instrumental music that speaks to the time?”

“What interests me is not Mahler and not a pops concert, but a new idea that can only be expressed by the orchestra,” he adds. “That is compelling.”

One motivation: He just likes writing music. Arranging his songs for pops concerts gave him, he said, “a crash course in orchestration,” which sometimes “excites me to the point of jumping up and down like a little kid” — so much so that he’s willing to take a cut in income to do it. (The commission fee for the piano concerto, which was co-commissioned by the Nashville Symphony, the Nashville Ballet and the Minnesota Orchestra, amounted, he said, to “about one night’s work of gig for me.”)

Another motivation: He sincerely wants to win new audiences for orchestras.

“It’s important to me not to do a straight-up pops show,” he says. “If you have a band play with an orchestra, the only thing you notice is the novelty situation. But if the [audience] comes in and discovers something new about my songs, which they already knew, that they feel is greater, there’s a tiny thread for them to grab. Honestly, 2,000 people have made it to this; we might get five people” to buy a ticket to an orchestral concert as a result. Folds says, “I would consider that a success.”

Under Deborah Rutter, the Kennedy Center has been making a big push in artist-led initiatives. Mason Bates, the center’s composer-in-residence, has had free rein to program his new “KC Jukebox” series, which opened with a bang in November (one of his works will be featured on Friday’s “Declassified” program.) Jason Moran, the center’s artistic director for jazz, has been featured in a series of innovative duo performances.

“Declassified” continues the trend — and builds on some of the orchestra’s outreach efforts in its annual “In Your Neighborhood” concerts around the Washington area, including January’s successful foray into the club Echostage. Bates himself will be the centerpiece of the second “Declassified” program, in April; the third, also in April, will feature the singer Storm Large and the male vocal quintet-plus-pianist Hudson Shad.

“The Declassified series was inspired by a moment in our May 2013 concert with guitarist Trey Anastasio,” Nigel Boon, the NSO’s director of artistic planning, said in an e-mail. “He was playing his own long-form music for guitar and orchestra, and it suddenly struck us that the audience (it was sold out, great young demographic) might love the music of the following week’s classical subscription program — Adams, Respighi and Ravel — if only they knew about it.”

“We’re hoping we reach an audience that might not normally come to classical concerts but might be interested in the guest artist or the program,” he adds. “And we’re, of course, hoping that this audience is a younger and broader demographic than that of our regular classical concerts.”

The NSO isn’t alone; plenty of orchestras are making efforts to target new audiences. Hicks, who is conducting some of this week’s NSO programs, is in charge of a wide-ranging series at the Minnesota Orchestra called “Live at Orchestra Hall.” In Zurich, the series tonhalleLATE, at which the concert hall is turned into a kind of club, has been running with success for years. One delicate challenge with such ventures is keeping the focus on the new audience, as plenty of existing subscribers are interested in checking out fresh initiatives themselves. The San Francisco Symphony is deliberately avoiding its regular patrons when publicizing its alternative rehearsal-hall-turned-performance-space, “SoundBox,” which is billed simply as “a new place for people who love music.”

Stripping away preconceptions about orchestra concerts and “classical” music is a challenge. But for Folds, who recorded his latest album, “So There,” with the chamber ensemble yMusic and included his concerto as the last three tracks, it’s an exhilarating one.

“The concerto, within the context of my pop songs, is just another song,” he says. “That’s the biggest success to me. I don’t want it to play into the framework of ‘this kind of music appeals to people over here.’ ”

Since the concerto’s premiere in 2014, Folds has performed it with more than 15 orchestras in the United States, Europe and Australia — meaning it has gotten a lot more play than any comparable concerto by a “classical” composer. He said he hopes that someday it will be performed by other piano soloists. In the meantime, it’s literally in his hands.

“I’m told by classical pianists that my technique looks very real to them,” he says of his piano playing. “I’ve got them fooled. It seems to be working.”

Declassified: In Motion,” the first concert in the National Symphony Orchestra’s new series, will take place at 9 p.m. Friday at the Kennedy Center Concert Hall.