Backstage at lovely old "workers’ theatre" Idno by a lake in the middle of Reykjavik, as swans glide by in the sharp night, in a cramped room down some rickety stairs, the atmosphere is rich, spicy and decidedly Glaswegian.

Sweat hangs foggily in what passes for the air. Young violinists from the Glasgow Academy Of Music mingle with a cellist and Gruff Rhys and Cian Ciaran from modern Welsh psychedelicists Super Furry Animals. Beer is being chugged with alacrity, lest it go fousty in the drinker’s paw. Desperately seeking to unwind, assorted musicians are reeking like jazz lums. Stuart Braithwaite is sunk into a sofa, shaven head glistening, patter tumbling from his wired brain and out through his tired mouth.

Mogwai have just come offstage after the second of their two shows in Iceland. They had played a hastily arranged last-minute warm-up the previous night, reasoning that they ought to sharpen up before the first proper public airing of the songs from their new album, Rock Action.

But this being Mogwai - hardest living band in the west - and this being Iceland, where booze is blood, their professionalism inevitably only went so far.

"We were nervous that we were just gonna have a momentary realisation that it was all shite," gushes Braithwaite. "But it was fine. We were really nervous because we’ve got a lot more equipment now. Tonight we were just fucked because we got trashed last night so we were a bit tired. It was quite debauched ..." he tails off.

He needn’t have worried. The next day Iceland’s daily paper Morgunbladid may headline their review "Big Noise In An Empty Barrel", but the gig was great. Sine Wave, the opening track on Rock Action and first track tonight, is as stately as the ornately panelled room we are in. Gentle guitar curlicues mix with staccato samples of white noise. Keyboards plink out a quiet refrain as the guitars gradually climb a tower of thumping drums. It is quite, quite lovely. (And not nearly as complicated as the aforesaid description made it sound.) On Helicon 1, Braithwaite picks along to a snicking drum click track. Then bass guitar and strobes flare, and Braithwaite’s shoulder leans into the effort of conjuring mighty riffs from his guitar. It sounds like God shifting his furniture. The violinists come onstage for Take Me Somewhere Nice, and Braithwaite hymns some quiet vocals. It’s no Bittersweet Symphony. It’s more laid back, less grandiose, more dextrous than that.

What signs there were of the band being unprepared - Gruff and Cian sitting on the stage by a giant piece of paper to read their lyrics to Dial: Revenge - only add to the intimate, barrier-breaking air.

Mogwai are among friends here. Icelanders love heroically ambitious "alternative" music. Out of a flood of bands from the island (the most recent noteworthy examples being Quarahshi, Mum and Kanada), Sigur Rós are the most internationally acclaimed. Their singer has his own language, Hopelandish, and uses a bow on his guitar. It’s as if Cocteau Twins’ Liz Fraser was fronting the Penguin Café Orchestra. But much better than that.

Such vaunting ambition would, these days, be ridiculed in poptabulous Britain. But to the art-loving, multi-disciplinary culture buffs that most young Icelanders seem to be, music is more than a soundtrack. It’s a way of life, a passion.

Thus, there is a sweaty little corner of Iceland that is forever Scotland. It is populated by people like Hiurih Svavarsson, 22, and Kristjan Blöndal, 21. Hiurih works - "it is a nothing little job" - on the Reykjavik harbourfront. His friend works in the capital’s pre-eminent independent music store, Hlojomalind. Their real occupations, however, are as Iceland’s biggest Mogwai fans.

Hiurih has been a follower since the release of the compilation of the band’s early singles, Ten Rapid. He had first heard them in session on an Icelandic radio show called Sour Cream. He first saw them at the Roskilde festival in Denmark in 1998. Tonight he saw them for the first time in his own country. "It’s brilliant. It was just missing Mogwai Fear Satan, the best song, of course," gibbers Hiurih, a string-bean-jean in faded denim, too-tight T-shirt and dirty bleached blonde hair. He is such a fan that he doesn’t speak English; he speaks Scottish. He swears often, and well. "They’re fucking good."

Why does he like them so much?

"I think it’s the emotion, and they just fucking rock - when they want to."

Is it difficult to have emotion if no your songs have no words?

"Fuck the words, fuck the words! You can get much more emotion out of guitar. A band like Godspeed (heroically enigmatic Canadian troupe Godspeed! You Black Emperor), they’re the most emotional band in the world and they don’t use words."

Or, in the words of the promoter of tonight’s show, Kari Sturluson, Mogwai’s music "just glows".

Mogwai were built for Iceland and it was built for them. Rock Action is their economically focused, 38-minute, third and best album - previously, the band’s double-album-sized girth made it difficult to see the woodwind instruments for the tree-tall guitar epics. Sample this new, improved, more rigorous Mogwai, or visit the elemental island and this hyperbole, plus Hiurih’s evangelically purist stance, will make some kind of sense.

Gruff Furry Animal has come over for the show with his bandmate to sing a song and play, as it turns out, three records of a "DJ set" for the band. How does he rate Rock Action?

"It’s just getting more refined as it goes along."

Are they kindred spirits?

"Yeah. Because they’re into their art and what they do and there’s no pretension there either. It’s just straight-up creativity."

Mogwai sound like Iceland. Really. The music of Scotland’s cultest band - no, not cutest - is full of big landscapes and unique perspectives, fire and ice and clashing contradictions.

It is classical music, yet seen as the work of archetypally weejie-indie beer-monsters (top Mogwai song title #1: Secret Pint).

It is rock music, but uses fantastic keyboard whizzkiddery, a cellist and, tonight, three violinists (top Mogwai song title #2: Oh! How The Dogs Stack Up). It is angry and confrontational, but sublime and soothing (top Mogwai song titles #3 and #4: Punk Rock/Puff Daddy/ANTICHRIST and May Nothing But Happiness Come Through Your Door).

It is attention to detail - they’ve set up their own label, Southpaw, the better to be taking care of business; those crosses-for-T’s in ANTICHRIST should be upside down; Mogwai’s now-famous T In The Park T-shirts read, precisely, "Blur: Are Shite". The colon, Braithwaite pointed out, is meant to convey that this was a dictionary definition.

This wasn’t any old handbags-at-dawn, headline-seeking muso tiff. This was punk-rock attitude with clever bells on. This was meant.

Hatred, Braithwaite has previously said, is what motivates Mogwai. So how come, particularly with Rock Action, they’re making such sublime music? "Hatred was never a musical energy," he says. "We’re just folk from Glasgow and when we sit in the pub, we sit and slag folk off. I’m sure you’ve done it yourself. It’s not actually a motivation to pick up a guitar, it’s just skills for comedy abuse rather than an actual musical energy. The music we do is totally about beauty and grace, or it’s totally about violence."

Is the world catching up with your innovative take on rock music? Or, who are the bands making Mogwai records now?

"When did I say that?" In your record company biography. "I was outta of the country," he grins. "I didn’t say that."

Are Radiohead making Mogwai records now?

"I don’t know what you’re talking about! No, they’re not, actually, I think they’re more into Boards Of Canada. They probably owe Boards Of Canada and Autechre a few royalty cheques. Is that what you think?"

A little, occasionally.

"But if we’re getting a band that go to number one in the charts into music that’s better than what they did before, ’cause they sounded like U2 f***ing before - not that I actually agree with you ... Falkirk?" He looks up. Someone has entered the dressing room with a scores update. "Falkirk, aye. They got humped the other day. Anyway," he resumes, "if we’re getting the band that goes to number one into better music, that can only be a good thing. You could slag off David Bowie for bumming up Kraftwerk but you wouldn’t want to take your copy of Low back."

Mogwai are like Iceland: they drink like fish, party like fishermen on permanent shore leave, play as if this was their last night before heading off to sea, play as if the ground beneath their feet is charged by molten, deep-core energy. And better to cause your own volcanic eruption than be swallowed by one.

Their last song tonight is a graceful, exquisite version of Jewish hymn My Father, My King, which will appear on producer Arthur Baker’s upcoming album. This is Mogwai, and this is the kind of rare, special thing they do.

Tomorrow, they’re off to the US. They’re playing ten shows, all of around 1,800 capacity. In June, they go back for 20 more dates. In October, they go back for 30 more.

"One of the reasons why we do really well in different countries is that there’s very few words in our music," opines Braithwaite. "We’re not superstars anywhere but we’re gonna play to people wherever we go. In places like here and Japan that have a real tranquil psyche, we go across really well. And people here are really unpretentious."

So tonight Matthew, we’re going to be five west-coast Buck-wild poets, toting street hassle and art rock and bringing love to the worldwide indie Diaspora ... Yeah. Hiurih would approve.