Round midnight in a provincial disco on the northernmost edge of Europe, someone is grinding their bottom into mine. In front of me there is a dancefloor teeming with burly, over-refreshed farming lads and over-enthusiastic lasses wearing three, maybe four outfits at once (leopardprint leggings plus puffball skirts plus bolero jackets plus baseball caps). Right behind me, bumping bums, his skinny-malink body bent double, his little pixie face beaming up at me, thumbs aloft, is Jón 'Jónsi' Birgisson: poet, artist, songwriter, inventor of his own language ('Hopelandish'), and possessor of a beautiful, mystical, keening singing voice that has helped lend the band he fronts an air of mystique and wonder unsurpassed on the world stage.
'Wooh!' yells Birgisson before goose-stepping his way onto the dancefloor. Just over there, his normally furrow-browed bandmate Kjartan Sveinsson is pole-dancing - that is, dancing with a pole, on his own - to the Spice Girls' 'Wannabe'.
Sigur Rós's reputation, it's fair to say, is as artsy, aloof, distant and awkward. The four-piece make celestial music that routinely solicits purple prose wondering if this is the very sound of God moving his furniture and crying as he squashes his thumb and blah blah. They're infamous for being monosyllabically unforthcoming in interviews. One album was titled ( ), aka Brackets; its eight songs were nameless. Nothing as straightforward as strumming for Birgisson: he plays guitar with a cello bow. The closest to the mainstream they've ever got was when 'Hoppípolla', from their half-a-million-selling last album Takk ... , was used as the theme music to David Attenborough's Planet Earth series. Sigur Rós had signed to EMI prior to the release of Takk ... in 2005. The major label was, among other factors, wowed by the cult acclaim their three independent albums, and by the enthusiasm of Hollywood tastemakers such as Cameron Crowe, Tom Cruise, Gillian Anderson (perfect for yoga, said the X-Files lady) and Gwyneth Paltrow (Apple Martin was born to their hymnal strains). But Sigur Rós's actual first release for EMI was 2004's 'Ba Ba Ti Ki Di Do': a 20-minute score for a ballet by New York's Merce Cunningham Dance Company. Radiohead, who 'discovered' Sigur Rós and had the Icelandic band support them on 2000's Big Top tour, composed one half of the score. Sigur Rós's half was entirely instrumental and was recorded, recalls Birgisson, using ballet shoes: 'My father, who is a blacksmith, welded us a special stand, and we hung eight ballet shoes on it, and put contact microphones in each one, so we could hit them and use them as percussion.'
So far, so bjönkers. But then came our Saturday night in Iceland's second biggest city, Akureryri, and seeing the tanked-up members of Sigur Rós, sensible woollen jumpers and all, letting their hair down is some sight. But it all, weirdly, fits. I had come to Akureyri, 45 minutes' flying time north of Reykjavik, to witness something else that brilliantly tips Sigur Rós's somewhat precious air flat on its arse: the debut screening of Heima (At Home), the band's first DVD. It's a documentary chronicling a two-week series of concerts they undertook around Iceland last summer. The idea was that the band, supported by female Icelandic string quartet Amiina, would round off the 14-month Takk ... world tour with a bunch of gigs in a variety of unusual locations scattered around the periphery of this huge, sparsely peopled island. Almost 10 per cent of the island's population of 300,000, from babies to grandparents, must have turned out for the shows. As Amiina violinist María Huld Markan - the wife of Sigur Rós's Sveinsson - puts it in the film, the tour had the effect of 'joining the soul of the Icelandic public'.
Heima wasn't cheap to make: after the band discovered that the tour footage lacked narrative and coherence, they hired Hollywood film-maker Dean DeBlois, a Pixar employee who had written and directed (wait for it) Lilo and Stitch. He studied the 120 hours of existing footage and worked out what was needed: he had the band undertake some more, smaller performances, and persuaded the limelight-wary members to be interviewed on camera. And in order to pay for all this, EMI insisted the band deliver an album too: hence Hvarf (Disappeared) and Heim (Home), two discs that compile, respectively, five studio versions of previously unrecorded songs (fan messageboards are seriously aflutter about that) and six old songs rendered acoustically on the tour.
Last summer I saw two of the shows documented in Heima, one in remote Öxnadalur, where 500 or so mountain folk, sitting on the grass round a blazing bonfire, watched Sigur Rós perform in a meadow. As the clock reached midnight and daylight lingered stlll, the crowd were hushed by the band's prog-orchestral magic. Even the droning of the ever-present flies sounded like a rude intrusion.
In Reykjavik, some 20,000 turned up including the President, Ólafur Ragnar Grímsson, and the Minister of the Environment - a mark of the band's exalted status in an island with a small population but a disproportionately huge landmass (four-fifths the size of England).
In the film Sigur Rós also play in a country tea room, cheek by jowl with families eating cakes and drinking tea from flasks; in a silo in the metallic bowels of an abandoned herring factory; in the national park at Ásbyrgi, two hours east of Akureyri, during Iceland's only annual bank holiday, when people traditionally go camping. Norse mythology has it that Odin's horse - a giant, flying, eight-legged beast called Sleipnir - stepped down in Ásbyrgi. 'It's a mark in the ground like a hoof, and it's humungous,' says bass player Georg 'Goggi' Hólm. 'Extraordinarily beautiful.'
'Before we started the tour, we had meetings where we were asked what we wanted and we only had answers to what we didn't want: not a typical rrrrockumentary,' the genial bass player continues, the brilliant burr in his accent making the word sound even more ridiculous than when it was first used, in Spinal Tap. ' Because Iceland is a different place, and Iceland people are different. We want to capture something unique.'
Oh, and it has massive cliffs and windswept valleys and lunar desert and hot mud and humungous - Odin on a bike! - everything. Snow in summertime. Daylight till midnight. Iceland invented geysers. (Well, it's an Icelandic word.) The landscape is like remote northern Scotland as reimagined by Tolkien, multiplied by the Moon. And yes, that is the cellist's real name.
It's the perfect setting to hear a music - epic, sweeping, intense, intimate, mystical (it is sung in Icelandic after all) - that is, on CD or in normal rock venue, almost too much to bear. It's become a cliche that the music made by these four clever blokes on the cusp of their thirties echoes the majestic, natural drama of their fantasy-epic homeland. But that doesn't make it any less true. It's a place that knows the meaning of hardship, Hólm says with a philosophical grin. 'In that sense it definitely has influenced our music. We do create music from our hearts as much as we possibly can.'
Wintry isolation and - until relatively recently - an insulation from western TV and radio have helped make Icelanders this way. 'It'll be interesting to see the generation to come, see if they're just as creative as it has been,' muses Hólm. 'Today it's all open, but when I was young there was no TV on Thursdays, and none in July.'
Sigur Rós formed in Reykjavik in 1994. 4 January 1994, to be precise, as the dreamy but exact Birgisson tells me. 'We always go out on the band's birthday,' he says. They were named after his little sister Sigurrós - it means Victory Rose - who was also born that week. She's 13 now and yes, says her big brother, she likes the band, although she prefers Justin Timberlake.
Did this bunch of schoolkids have a vision then, of making music that would be defiantly ... other?
'I don't think we did,' says Sveinsson, who's considerably less stern than first impressions suggest. He started playing with Birgisson, Hólm and their original drummer in August '94; it would take him three years to officially join the band. 'It was never talked about. It was just developing something interesting. But at this time we were listening to [Spiritualized's] Lazer Guided Melodies, and Ride, and the first two Verve albums. That kind of stuff. I'm sure there is kind of a similarity. And Loveless, My Bloody Valentine.'
'Maybe we had a vision in our head, without talking about it too much,' says Birgisson. 'The first song we did was called "Flying",' he grin-grimaces, 'really cheesy. It was our hippy era. Really spacey and ambient, floaty. Then for one year after that, we were trying to get back to that sound, but we were playing just like Smashing Pumpkins.' Then their old drummer gave Hólm a cello bow for Christmas. It didn't work on his bass so he passed it to Birgisson to play with his guitar. 'And when we got the cello bow in the guitar the atmosphere started to come a little bit then.'
Birgisson cuts a compelling figure on stage and in person. He's gawky and awkward, his hair tufted into a wonky Tintin-esque mohawk. Yet he has a compellingly strange grace about him, and his soaring falsetto is properly spine-tingling. For all that, in keeping with the warmth and humanity that spills out of the screen in the lovingly filmed and meticulously constructed Heima, today in Akureyri he's relaxed and genial.
'It's kinda cool,' he says, smiling, of the fact that the film thaws all notions of the band's supposedly icy demeanour. 'It takes the hood off of just four nerds. There's no mystery with the band.'
Birgisson talks readily about his American boyfriend, Alex Somers, a fine art student studying in Reykjavik. It's Somers's stencils, and hands, we see under the opening titles of Heima; the elegant postcards he painted of each of the Icelandic show venueslast summer were typically gorgeous, typically Sigur Rós tour merchandise. They met in 2002, after Somers's brother came backstage at a show in Boston, toting a CD of his ambient music. 'And I was like, "What the hell? I've never seen such a beautiful person in my life." He was kind of glowing!' gushes Birgisson. 'And I was like, "Woah, he's definitely straight" - like every cute boy I meet! There's something about straight guys ...' Birgisson sighs.
Drinking champagne and burping like a naughty kid , he babbles enthusiastically about his teenage obsession with Duran Duran ('I had a big poster of Andy Taylor on my wall!'), how he'd love to meet Antony Hegarty of ' ...and the Johnsons' fame, and of how he and Björk, Iceland's other great cultural export, have been thwarted every time they've tried to work together. He would call her, but 'I'm just too shy and quiet.'
Politics, unsurprisingly, is not something that Birgisson wants to get too involved with. Yet Heima does function as a movie with a message. Last year Iceland was ranked the most competitive economy in Europe by IMD, a world-leading business centre based in Switzerland. The country's entrepreneurs now own some of the UK's most famous brands, including House of Fraser, Karen Millen and West Ham football club. The problems inherent in economic 'progress' are captured in Heima when the band play in Kárahnjúkar, site of a protest against a proposed dam. I might have got carried away with the majesty and power of Heima but I fancy that here, and elsewhere in the film, we see a battle for Iceland's soul.'The question is,' says Hólm, 'how does Iceland want to portray itself, now and in the future? We are trying to sell ourselves to tourists as the purest country in the world. We have the best water, the best fish, the best lamb, the best air. It's all a matter of taste, of course!' he adds hastily, wary of bumptiousness entering the unassuming world of Sigur Rós. 'But do we want to just ruin that by polluting everything with aluminium? 'Cause the factories pollute a lot. We don't have nuclear plants or coal. Why do we want to bring the aluminium pollution? To me, it's ridiculous.'
The images from Kárahnjúkar - before and after it was flooded (the protest was futile) - are counterpointed with scenes where Sigur Rós celebrate Iceland's folk tradition. They take the stage with a man called Steindor Andersen, president of the rímur society, an age-old voice-only form of singing. They perform with a stone marimba comprising individual rocks found by a quasi-hermit called Páll Gudmundson - he also uses 100-year-old rhubarb as percussion. They sing with local choirs and play with a local brass band, whose name translates as the Horny Brasstards. They attend an annual feast called thorablot, at which the remnants of the winter's stored up - and rotten - food is eaten.
'I think we don't like to be a political band,' says Birgisson, 'we don't like to make statements - we usually don't like bands who make crazy statements. If you're going to do it you have to be educated about it, know what you're talking about. But it's nice how it turns out in the movie - it's mild, more pictures talking.'
Several hours later, on the floor of the club in Akureryri, as the DJ whips the crowd into a brennivin (evil Icelandic vodka) frenzy, Jón 'Jónsi' Birgisson lets his dancing do the talking. Now he's strutting his stuff to 'YMCA'. Sigur Rós played this happening nightspot three times back in the day. Indeed, they began writing the song that would become 'Untitled #8' on ( ) here.
See Heima and see the rock film brilliantly reimagined. Hear Hvarf and Heim and discover a band reaching for the stars yet snuggling up close. And spend a weekend with Sigur Rós on home turf, larging it big style, and you'll discover a band who, contrary to popular belief, are not the messiah. They're just very clever - and funny - boys.
'We've invented a new kind of CD sleeve,' a still burping Birgisson had told me as he drained his glass of champagne. It's called the Z sleeve, and is specially designed to hold two discs.
'So when Arctic Monkeys make a double album, we'll get a percentage of that, baby! And we'll do ringtones - yeah baby!' said this hilariously surprising booze-pixie, snapping his fingers and shooting out his forefingers.
· Heima's UK premiere is at Cecil Sharp House, London, on 24 October as part of the BBC's Electric Proms. The band will also play an acoustic show. The DVD is issued on 5 November, along with the Hvarf/Heim double album (EMI)
