It’s a spring evening in Brooklyn, New York, and a concert is starting in two minutes, but the queue for beer is huge and twentysomethings in lumberjack shirts and jeans are still surging through the doors, hurtling towards their seats. They will continue to do so until well after the show begins, because fans like these are not used to 8pm ticket times really meaning 8pm: indie rock bands such as Grizzly Bear do not tend to play with the Brooklyn Philharmonic in the orchestra’s own prestigious opera house.

Yet the one-off performance tonight is not such an unlikely collaboration, since Grizzly Bear are in fact part of a new wave of young American bands who place more emphasis on instruments than attitude. Along with Fleet Foxes and Animal Collective (the mammalian nomenclature is obligatory) they have created a camp-fire sort of classical that some have called psych-folk. The music is architecturally deceptive: it sounds gentle, like sweet and intimate folksong, but the instrumentation is densely layered.

Tonight, these songs have been subject to further musical investigation, with the wunderkind composer Nico Muhly (Philip Glass’s protégé) arranging them for the orchestra. And it works, with almost heart-breaking effect. By the time the show ends there’s barely a dry eye in the house. The New Yorker reviews it with great reverence and The New York Times runs a big feature on the band. Since then they have played live on huge American TV shows such as Letterman and come to London to play on Later . . . With Jools Holland. Last month they released their third album, Veckatimest, which went straight into the US Billboard charts at No 7. Robin Pecknold of Fleet Foxes declares it his album of the year. How did Grizzly Bear, who released their first album in 2004 and were always a word-of-mouth phenomenon, get so big?

Ask the band themselves and they are evasive, claiming that there was never a master plan, they’re not part of any scene, musicians have always used things such as four-part male harmonies and they never really expected all this. But they are clearly well-connected New Yorkers who have ploughed their furrow with steely determination. Each of the four members plays various instruments — alongside the usual guitars and keyboards, any Grizzly Bear show might involve an oboe, a flute, recorder, xylophone and an autoharp.

They were ecstatic when Radiohead asked them to tour with them, and to hang out with them. As Edward Droste, the founder of the band, who originally wrote all the music by himself, explains: “We didn’t have much money to eat out on tour so we had this little grill and we were barbecuing every night, just in the parking lot behind the venues. Colin and Jonny Greenwood would be like, what are you guys doing, that’s so American! And we were like, ‘We know! But it’s tasty! Come and have a beer!’ So they came by. And then the next day they were like, ‘Are you gonna grill again?’ And then the day after even more of them would come.”

Paul Simon took an interest in them, turning up to their dressing room before one of their small gigs to announce his presence. What’s he like? “He’s just a little guy in a baseball cap but it scared the living . . . out of us. He’s got his own . . . style of communicating. But he’s very sweet,” says the brooding Daniel Rossen, who was second to join the band. “So we played an impromptu cover of Graceland as an encore. We’d never played it live before and it probably sounded terrible, but he liked it so we played five nights at his Paul Simon and Friends concert. It was thousands of the baby boomer generation, and then us. Quite a big generation gap.”

Ranging in age from 26 to 30, they are an interesting mix of people, from gregarious to deeply serious, but all of them choose their words carefully. The swarthy Droste is socially fluid and charming, not just good at meeting people but good at meeting the right people. A lot of his stories seem to involve “and then we borrowed a friend’s summer house in Long Island”. I speak to another New York musician and ask him if he knows Droste. “I don’t know him,” he sighs. “I’m the only person in Brooklyn who doesn’t know him. I’m the only musician in the whole of New York who doesn’t know Ed from Grizzly Bear.”

Since Manhattan became too expensive, and the artistic talent decamped across the East River, there has been an explosion of successful Brooklyn bands in the past few years — Vampire Weekend, MGMT, TV on the Radio. Natasha Khan of Bat For Lashes even moved there from Brighton to write her second album. But the Grizzlies are a little too knowing to be pinned down. “Oh, you’re trying to ask me about the scene,” Droste says, a little archly, when I begin to approach the subject. Blonde, tattooed Chris Taylor, who trained as a jazz saxophonist, is equally unconvinced. “Vampire Weekend have sold a lot of records but I still run into Ezra [Koenig] from that band just in random bars in Brooklyn. But that’s all it is — we know a lot of those bands, we run into them and talk about what we’re working on, but there isn’t a lot of artistic interaction. Effectively we’re just co-workers who live in the same city. It’s not the Seventies; it’s not like we all go out and take acid together.”

Another band they inevitably get asked about is Fleet Foxes, a group who have made male harmonies their own, and become a surprise hit. Rossen sighs. “You know, with the utmost respect to them, because we love those guys, but we’ve been doing this since before they began.” Indeed, Rossen studied four-part harmonies at music school. Ironically, all of the band except for Droste, its founder, met through music school. They were introduced to Droste through a mutual friend and they liked the sound of what he’d been working on in his bedroom, even though he claims ignorance about music. His grandfather ran Harvard’s music department for 40 years and his mother was a music teacher “but I rebelled against it for so long!” he laughs. He grew up without any modern music in the house, “not even the Beatles, but, aged 12, I managed to get my dad to take me to see a Madonna concert, on that Blonde Ambition tour. She did the whole simulated masturbation on a bed and my dad was like, ‘I don’t know if you should be seeing this, ha-ha.’ I’m so glad I went.”

Meanwhile, the other three spent their teens going to things such as jazz camp. Jazz camp? “We’ll try to make it sound less dorky,” Rossen grins. “It was a ‘summer music programme’,” Taylor explains, “and Chris Bear, who’s now in the band — and yes, we were already called Grizzly Bear when he joined — was in the top jazz group.” Even at 15, the handsome, brown-haired Bear was “so good he was intimidating. I got one chance to jam with him and I was totally freaked out,” smiles Taylor.

It’s amusing to hear a deadpan New Yorker turn to such accomplishments: “I studied saxophone and I sort of play clarinet,” Taylor continues. “I picked up bass clarinet in the last year or so, and I, like, really suck at flute.” Luckily for them, their fans are more assured of their talents. Follow the Bear — it’s going places.

Veckatimest is out now on Warp. The band play Koko in London on August 18

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