The band TV on the Radio, from left, Tunde Adebimpe, Gerard Smith, David Sitek, Kyp Malone and Jaleel Bunton, comes to Lupo’s in Providence on Saturday.

AP / JIM COOPER

One day in July a bulldozer mistakenly plowed into the outside wall of Dave Sitek’s Headgear recording studio in Williamsburg, Brooklyn. It’s the studio where the Yeah Yeah Yeahs, Liars and Sitek’s own band, TV on the Radio, made albums that drew international attention to Brooklyn rock just a few years ago.

Those were the indie days, when TV on the Radio was passing out homemade discs at cafes. Over the past five years TV on the Radio, which comes to Lupo’s Heartbreak Hotel in Providence on Saturday, has made its way steadily up the circuit, from independent to major label, from local clubs to international tours, while its music has grown ever more ambitious. Those ambitions are bohemian ones: packing a world of ideas into each song while ignoring both commercial imperatives and ingrown hipster cachet.

Tunde Adebimpe, the singer who started TV on the Radio with Sitek, unabashedly describes its music as art. When the band moved from the independent Touch & Go label to Interscope Records, one of the stipulations of the contract was that “there would be no involvement from the label on the creative end,” Adebimpe said. As the recording business loses its ability to create blockbusters, the band’s self-guided, self-sufficient approach looks like a practical survival strategy.

On Sept. 23 TV on the Radio followed its widely praised 2006 album, Return to Cookie Mountain, with a magnificent third album, Dear Science, (the comma is part of the title). The songs are vertiginous, full of cantilevered rhythms and synthetic sounds, yet openly catchy. Adebimpe and Kyp Malone sing about war and technology, environmental damage and racism, while also invoking pleasure and hope.

The songs are pensive but ultimately joyful. The album starts with “Halfway Home,” an elegy tucked behind a peppy nonsense-syllable chorus, and it ends with “Lover’s Day,” a celebration of sex: “Yes of course there are miracles/Under your sighs and moans.”

Often a song starts with stark, kinetic drumbeats, only to thicken and evolve with layer upon layer of counterpoint. The band’s sound is “representative of the human experience,” Sitek said. “You have your first introduction to sound and hearing, and then you learn a language and then you learn to confuse yourself with that language, and then you’re left with this euphoric, slap-happy, I’ll call it aging twilight consciousness where you’re just befuddled at the human experience and all of the things you’ve accumulated with no direct guideposts or instruction manual.”

In an era of disposable downloads and ring tones Dear Science, is a coherent collection of songs made for repeated listening.

“If you’re going to reach for it, reach all the way for it,” Sitek said. “Albums like Purple Rain and Thriller and those kind of records, you had to reach far above the din of cynicism and modern living to get to that place, against all the odds. The industry used to support that kind of record making, and just because the marketplace of the industry doesn’t support it now doesn’t mean you shouldn’t still try for it.”

But the album was made on a local scale: in Sitek’s studio, with a horn section borrowed from the steady-gigging Brooklyn Afrobeat band Antibalas.

“I think the album as a format is dying,” Sitek said. “To do an album of this magnitude, just in terms of the sheer number of things that had to be done and the amount of musicians involved and the amount of studio hours spent — if we didn’t have my studio, who knows? We could have been really in debt for the rest of our entire beings.”

TV on the Radio has held on to the experimental spirit of what was briefly, before landlords and tourists noticed, a neighborhood of low rents and high creative density. “You could go out on a Saturday night and go to eight different places and see eight different bands, and they would all be interesting — really interesting,” Adebimpe said. There was a feeling, he said, that “I have to keep making stuff that I like so I can keep hanging out with my friends who make stuff that I like.”

Back in 1997 Adebimpe — at the time a filmmaker doing stop-motion animation, with a day job at Film Forum — and Sitek found themselves as roommates in a Williamsburg loft, which led to a musical partnership.

“It just became apparent very quickly that we were going to be friends,” Adebimpe recalled in an interview at the Verb Cafe in Williamsburg, “because his room was full of all this musical equipment with nothing but a mattress, and my room was full of paints and video equipment and nothing but a mattress.”

Soon they took on collaborators: Malone on guitar and vocals, Jaleel Bunton on drums and Gerard Smith on bass. “We bullied everyone else into the band because we didn’t want to go through it alone,” said Sitek, whose main instrument is guitar. All the band members are in their early 30s.

The 4-inch dent in the studio wall is the latest iteration of what’s already an old story: the continuing gentrification of Williamsburg. The members of TV on the Radio all still live in the neighborhood, watching bodegas being replaced by fancy restaurants and boutiques. Early on, TV on the Radio benefited from the talent-spotting and reputation-building of the indie-rock blogosphere. But eventually the band felt typecast. “I’m done with cool,” Malone said. “I’ve been done with cool for years.”

Sitek said: “We always wanted to reach a lot of people. We never wanted to be obscure. I think it was just hard for us to get a handle on how to make the kind of music we make and how to describe it.”