Sigur Ros - Takk that! Iceland's chilly minimalists blow back in

We've all heard hours of Sigur Ros's atmospheric washes, even if we didn't realise, across acres of TV. The band tell Nick Hasted about their new album

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Sigur Ros vanished four years ago. In their absence the band who are, after Bjork, Iceland's biggest musical export, saw their atmospheric music, with singer Jonsi Birgisson's unearthly falsetto at the apex of every soaring chorus, remain an emotion-pumping fixture on British TV, from Planet Earth to The X Factor. Their last two studio albums, Takk (2005) and With a Buzz In Our Ears We Play Endlessly (2008), sold half a million each, honing the sort of prettily emotive formula which has served Coldplay so well.

Their much delayed 10th album's title, Valtari, means "Steamroller" in Icelandic, and a planet-crushing comeback would seem on the cards. Except that Sigur Ros have abandoned music which was turning blandly acceptable for more challenging terrain.

"It feels like the last two albums are more upbeat," Birgisson tells me. "Too joyous, too festive! Maybe it became too easy. It's time for us to take a left turn and do something more experimental. It feels like a new beginning."

Sitting in his Covent Garden hotel room, Birgisson is a boyishly petite 37-year-old who slaps his thigh when he laughs, his only bluffly Viking trait. For all the prog-rock-style grandiosity of their gigs (caught on last year's stopgap live release Inni), the chasm between Sigur Ros and rock norms is visible in their modest singer. The title of new song "Dauoalogn" means, he tells me, "dead calm – it's about peace and quiet." Bassist Georg Holm, who I meet separately, dubs the new album "introverted". Painstakingly pieced together last year from songs abandoned in their time off, it feels fascinatingly unfinished, haunted by static and surface noise. The Billie Holiday songs Birgisson has on as we talk suggest a model for its intimate warmth

"I like having her in the background," he tells me. "Billie Holiday's the only thing I have on my phone. Modern-day recording sounds really shitty. But this sounds warm and cosy and camp-firey. We are trying in our music to be timeless, and make it sound organic like that. It was so amazing in those days, they were just in a room playing music around one microphone..." Have Sigur Ros tried it that way?

"No, we are not that good. We could never do it! They're musicians. We're more like noodlers... and I never saw myself as a singer. I started singing because somebody had to. Of course, over time you get better..."

The mystique fans see in Birgisson, which he doggedly pricks with such statements, springs from his ethereal, unworldly stage presence. So it's a shock when he mentions his previous job working for his dad, usually described as a sylvan-sounding blacksmith. But Birgisson the frail imp of myth was forged in a blunter, working-class, reality.

"I worked at my father's steel factory on ships that came to harbour," he remembers, "and that was dark, oily, cold. I was working with these old guys, and they were all depressed. It was freezing and snowing, everything was rust and cold steel. You had to saw steel pipes into a hundred pieces, and you went out of your body and thought about nicer things. Actually, I had a lot of good ideas there."

Amidst such hellish workdays, Sigur Ros formed in 1994 – long before Damon Albarn made Reykjavik his cosmopolitan playground, and the country's cultural (and fictive economic) renaissance became globally known. Back then, only Bjork's band the Sugarcubes had made it away.

"When we were growing up, Iceland was much more isolated," Birgisson says. "We never, ever dreamt of being able to play music somewhere else. We just did it because making music with your friends was the best thing in the world. It was only about having fun. And with that comes your original voice."

That originality is fundamental to Sigur Ros. But to its members, it goes deeper than Valtari's stripped back, organic arrangements, residing instead in the almost sacred atmosphere of new songs such as "Dauoalogn". The look Birgisson gives as he squeezes his eyes shut on stage and sings also suggests what he's doing is precious, that the mystique he dispels in interviews rests in something real. The band find spiritual transcendence not in religion, but in their music.

"I do some hiking up mountains in Iceland," Holm says, "and when you're tired and you get to the top, you can see forever, and you can hear the blood pumping inside your ears. I've felt that playing music sometimes. In our old studio I used to like to go into my little bass room, and close the door, and just play. I've always wanted to make myself fall asleep playing the bass," he confesses hesitantly. "You get this feeling with the vibration of it, that takes you somewhere else. And to me that's more important than being a good musician. We're terrible musicians..."

"He's weird," Birgisson laughs. "But sometimes I do just close my eyes and open them up at the end of the show, and don't remember what happened... I do look at myself as a spiritual person. If you're true to yourself and do things with an open heart, that's what good music is about, or everything is about. It's important to follow your instincts. We're just four people who meet and have fun. If it gets like a chore, or not as free, we stop." Even the vegetarian singer's long-time penchant for eating only raw food (he has recently relented) suggests a man in search of something pure, clean. "Of course, it all connects," he says.

"When music is very honest," adds Holm, " it will always sound pure. It always has to happen naturally." In their four years away, Birgisson made and toured a solo album, Go (2010), and he has lived with his American boyfriend (and Valtari producer) Alex Somers for seven years. But Sigur Ros's unique bond was proven on the new album's "Fjogur Piano [Four Pianos]", where the band members separately played along to a loop. Almost psychically coherent music resulted

"It was like that 18 years ago," says Holm. "We're inseparable. I would find it very, very difficult to make music with anyone else. Jonsi told me he felt a sense of relief when he came back to us." Some earlier songs spoke a language even more private than Icelandic. "It was basically babble," Holm says. "You can't understand it without understanding us."

'Valtari' is released by EMI on 28 May