Last month, Dave Longstreth, the lead singer of the Dirty Projectors, posted a question on Instagram: Had indie rock become “bad and boujee”? His quoting of the rap trio Migos, however ironically, was pointed. Whereas hip-hop could bring joy to the masses while retaining a sense of experimental play, perhaps indie rock had become too “refined and effete,” increasingly detached from “lived, earned experience.” The post, which Longstreth later downplayed as a “jokey riff on fake critical theory language,” inspired a range of responses, most notably from Robin Pecknold, the lead singer of Fleet Foxes, who wondered if “indie” remained a useful distinction at all. What mattered, he contended, was that music, whether aspiring to sound vintage or “progressive,” still possessed the capacity to conjure a “new feeling” in its listeners.

The back-and-forth might have been read as performative navel-gazing. But it was symptomatic of a greater existential worry. The stylistic borders between underground and mainstream, always a bit exaggerated, are barely legible today. Chart-topping pop stars strive to be eclectic and strange; some can even claim to be “indie” by virtue of partnering with streaming services rather than major labels. And while the princes of indie rock in the nineties were the erudite slackers of Pavement or the sensitive members of Sebadoh, many musicians on independent labels now make rock that is stadium-sized and cathartic. These days, artists big and small are often judged by the scale of their ambition—and by how interesting they can make themselves seem. Reinvention and surprise, the capacity to explode orthodox notions of categorization and genre, are ways of making personal and political statements. It can seem a little beside the point to play rock music that aspires to sound like rock music.

The exchange between Longstreth and Pecknold, both of whom have relatively high-profile projects coming out this year, reminded me of the Brooklyn-based band Parquet Courts, whose members have always struck me as reluctant indie-rock stars. The band released its fifth album, “Human Performance,” last April, when the death of Prince and the release of Beyoncé’s “Lemonade” were overshadowing everything else. When I got around to listening to it, I became enamored with the album’s directness and simplicity. There was no mystery as to what the band was trying to do. I listened to the title track over and over, never tiring of the way it just stumbles into being, gently cascading toward the loud parts, as the songwriter and guitarist Andrew Savage sings, “I know I loved you, did I even deserve it, when you returned it?” The album is full of stories recounted through glimpses, many of them about how life changes as you enter your thirties.

Parquet Courts formed in Brooklyn, in 2010, but its members all met in Texas years before. In addition to Savage, the band includes another songwriter and guitarist, Austin Brown, the bassist Sean Yeaton, and Savage’s brother Max on the drums. All of them are thirty-one, except for Max, who is twenty-five. They’ve put out five albums and two E.P.s in a fairly short time, and each successive release has broken them through a bit more than the previous one—but never in a way that changed the settled narrative about who they were: a Brooklyn band indebted to nineties indie rock. The band finds this a little bit frustrating. “If we put out a harsh noise record, people would still describe us in terms of Guided by Voices, Sebadoh, Pavement, and stuff like that,” Savage said. It’s not a tradition he necessarily identifies with. When I asked him what he thought about Longstreth’s “bad and boujee” comments, he had no idea what I was talking about.

The Web site Pitchfork praised “Human Performance” as a “testament to rock’s continued power and relevance,” which is a bit like saying Parquet Courts has mastered an idiom that many, even those who love the band, find old-fashioned. That the album nonetheless appeared on most of the major year-end lists speaks to the quality of the songs as well as the band's attention to craft—the album cover and sleeve notes for “Human Performance” earned a Grammy nomination for Best Recording Package. All of the guys in the band are almost flagrantly ordinary. Savage has the air of a bookish Ph.D. student. His brother Max has the polite deference of an undergraduate waiting for office hours. When Yeaton, the bassist, is not recording or on tour, he is a writer and stay-at-home dad in Philadelphia. “There’s no concept for the band,” Brown, who is affable and goofy—but not extraordinarily so—told me. “It’s really just us. And I think that is difficult for people because there’s no persona, there’s no stagecraft, no tricks. It’s just four guys in a band. We’re writing songs, and these are our songs. We don’t have a thing. It’s just too regular. Does that make sense?”

Last July, I went with Parquet Courts to a taping of “The Late Show with Stephen Colbert.” In a hallway outside the band's dressing room, which was filled with snack trays and people dressed as pirates, Savage was wearing a blazer that resembled a kimono, or vice versa. We wondered if people still discovered new music by hearing bands promote themselves on late-night talk shows. Probably not, we concluded.

The band wasn’t jaded about the opportunity, exactly—but it did want to use it to do something different. So the bandmates invited Bun B, the surviving member of the legendary Houston rap duo U.G.K., to perform with them. It seemed an unlikely collaboration, which maybe was the point. A few minutes before the musicians were to walk onstage, Bun B materialized in the hallway with his manager and a videographer. Brown, whose idea it had been to invite Bun, looked on with hushed reverence as the Texas rap legend delightedly soaked in the scene, staring at a monitor where stagehands were quickly rearranging furniture during a break. Bun knew the Ed Sullivan Theatre as the place where the Beatles and David Letterman had become legends. It seemed odd that Parquet Courts would be the act to finally bring him here.

It was also a reminder that network television remains more hospitable to rock bands than rappers—an indication, perhaps, of just how mainstream and nonthreatening rock music has become. The band played “Captive of the Sun,” a lovely, impressionistic song, and Bun sauntered onstage during the bridge and rapped a verse that echoed Brown’s lyrics about the racket and din of the city. He finished by pointing to the sky and saying, “Trill.” As the crowd applauded, Bun and Colbert wove across the stage, shaking everyone’s hands, playfully punching people on the arms. (Last week, Parquet Courts finally released the remix of “Captive of the Sun” featuring Bun B as a single.)

Afterward, Brown looked teary eyed, as though he couldn’t believe what he had just seen. A bottle of champagne was placed in Bun’s hands, and he gamely popped the cork, asking for someone to bring a stack of Solo cups over. “You did not have to share the stage with me, and for that I am forever grateful.” he said, pouring out celebratory drinks. He looked around to make sure everyone got one, and then he offered a toast. “To Parquet Courts!”