He's looking well, isn't he?

Looking better, perhaps, than he did in the days before he was an artist, in the days when he was in one of the biggest pop bands in the planet. You don't recognise him? Rewind the face 30 years and put a bouffant eighties haircut on him (not quite a mullet but certainly in the neighbourhood of mulletry) and maybe it will become more familiar. A-Ha, you exclaim and you would be right.

Once upon a time Magne Furuholmen was keyboardist for Norway's premier pop band A-Ha. You'd see him standing behind Morten Harket on stage and in videos picking out the synth lines for Take on Me and The Sun Always Shines on TV. In their imperial days A-Ha - Furuholmen, Harket and Paul Waaktaar-Savoy - were huge. Number one hits. Platinum albums. James Bond theme tunes. Some 60 million albums sold, eight MTV Music Awards. Playing to 198,000 at the Maracana in Brazil in 1991 as part of the Rock in Rio II festival.

And then they split up and went their separate ways and came back together again then split for good in 2010 after farewell gigs but are now coming together again later this year to celebrate the 30th anniversary of their debut album at Rock in Rio. (They remain big in Brazil).

But in the days in between Furuholmen did other things. He got married, raised a family, discovered that he had atrial fibrillation - a cardiac condition that revealed itself when he fainted while driving. Oh yes, and he became an artist.

It's the artist who's standing beside me today, here in Edinburgh's Dovecot Gallery. One of his grown-up kids is in the city too, checking out the university. Furuholmen and I, though, are looking at a tapestry entitled Glass Onion and discussing its potentially phallic qualities. I am telling him what I can see in front of me. There's a record in white vinyl on the right, I say, the needle arm of an old record player on top and an object that looks - let's soften its lack of softness with allusion - a bit like Norman Foster's Gherkin building with - shall we just call it stuff? - coming out the top.

"Some people have noticed a certain penchant for shapes in my work," Furuholmen admits in perfect, unaccented English. But then he adds, "for me it all starts with letters". He points at the thing that I think looks like a record. "An O," he says, just as I begin to think I can see something oniony in it. He points some more. An N, an I. "It's a mirror image," he continues in perfect artspeak, "of me writing 'glass onion' on wood and building up an image and losing the original readability."

Hmm. I point to the Gherkin. Come on, I say, are you telling me that isn't an erect male member at the point of climax. Or am I just projecting? "Well, you're not the only one. This one was rejected by the Dubai Art Fair because of the phallic shape." He looks again, points to the stuff coming out the top. "It could be a Vesuvius volcanic type eruption."

The tapestry made by the gallery's weavers in collaboration with Furuholmen and based on one of his original works is the centrepiece of an exhibition of Furuholmen's work. We are surrounded by woodcuts, screenprints and ceramics, all of them scrawled with letters and words. Here's one now. A self-portrait. One of a series, he says, "almost in the Cindy Sherman way of staging yourself as something else." It is basically a self-portrait of the artist, using a four-letter slang word for female genitalia. So how accurate is this particular self-portrait, Magne? "It's debateable," he laughs.

"I have a variant of this called 'Myself as Tracey Emin's vagina'... which I'm not, but feel I know a lot about through her practice."

Furuholmen grins a big Cheshire cat grin.

Don't be fooled though. He takes his art - the art he creates with chainsaws and words and ceramics and baseball bats (there are some misshapen ceramic pillars on display which have felt the force of Furuholmen's swing ("It's very therapeutic.").

Furuholmen is not a hobbyist artist. He's not Ronnie Wood. He's staged many exhibitions, had his work collected by galleries and is working on his biggest ever commission - "approximately 50 tonnes of clay," he says - for Scandinavia's largest ceramics park. And if his A-Ha money helped him find his feet as an artist these days it's his art that's helping finance some of his more recondite musical offerings; the solo album and the work of supergroup Apparatjik Furuholmen formed with Guy Berryman of Coldplay, Jonas Bjerre of Mew and producer Martin Terefe back in 2008; which is, as he admits, half music project, half art project.

The Dovecot show, entitled Peeling A Glass Onion, is both a retrospective and a chance for him to do new things. There's a work entitled Oh Scotia which is a response, he says, to the independence referendum which was in full swing when he came to the Dovecot in 2014. "These ones," he says pointing to screenprints on another wall "I just finished about a week ago." He starts reading the writing to be found on them. "Nonsensical cotton. Ocular Erotica Utensils. Surrealist Stationary."

There are a lot of words to be found in his work. All in English too. What's wrong with Norwegian, Magne? "I've worked in the English language since I was 16 as a musician. All our heroes - whether musicians or visual artists - were always working in the English language." He starts to talk about James Joyce's Finnigan's Wake as an inspiration.

"Ocular Erotica Utensils could be a lyric in a song by The Fall," I suggest. His eyes light up. "I love Mark E Smith. He was a huge inspiration when we came over to England in the eighties."

If that surprises you then you don't really know the story of A-Ha. Three boys who grew up loving The Beatles who make an animated video for a song called Take On Me and suddenly found themselves turned into something they didn't think they were. Pin ups. Teenage fantasies in flesh.

Some people would have loved that. Some people would have ran with it, sucked up all the juice that success offered. Some people but not the people who made up A-Ha. They always seemed reluctant pop stars and that still seems to be the reading Furuholmen prefers. "I think most people find that when your dreams are realised you find that wasn't the dream. And I think there was a lot of depression around in the band about not being able to get the music across without this idolisation and this image that was projected.

"You become very much caricatures and it's a very constricting feeling."

I get that, I guess. You think you're in the same team as Mark E Smith but you find yourself subbing for Kajagoogoo. Still, you'd think there must have been some fun in all that adulation. You must have enjoyed some of it, Magne. Success must be narcotic to some degree. "Yeah and there were a few years of addiction. That was part of it, I think. Luckily addictions can be broken. And the ones who can't break it end up with problems whether it's drug problems or general bitterness at the world for giving them this great privilege. That is a sad thing."

It was probably harder for Morten, he admits. "Morten is the one who's out there facing an audience asking him to play Take on Me every night. That's a pressure he has to deal with. We don't get that request. No one has ever asked me to sing Take on Me." He starts laughing at the idea. " I've had it from people who don't know what they're talking about and they wouldn't want it to happen if they did."

The price of success for A-Ha might have been friendship. Three friends became three people in the same band. "It can turn to animosity and we've had our share of issues. But I think that's part of going through things together."

Really? What was the worst fight A-Ha had with each other? "Uh, we weren't the fighting kind. It probably would have been good to whack each other with guitars every now and then." Sullen silences then? "Yeah. We're typically Scandinavian in that regard."

Rewind. When he was a boy, six years old or thereabouts, Magne Furuholmen lost his father. Father was a musician who went to catch a flight. But the plane went down. All that was left for the son was a trumpet case containing a squashed trumpet.

A few years later Furuholmen met Morten Hacket for the first time. They introduced themselves, talked about their background, their parents. Furuholmen talked about the loss of his father and how he died. Hacket told him he had seen his dad's plane come down, had been standing on a bridge watching as it went into the ground. "Very strange for us as 16, 17-year-old kids to try to relate to at the time".

The loss of his father has been a recurring loose thread in his life. You can find it wound through his music and art. His first museum exhibition was based on his dad's notepad found with the trumpet, a notepad full of the titles of old jazz standards. At the start of the century he started worrying that he was "building temples to a dead father". He thinks he is past that now.

Until his mid-teens he didn't know if he wanted to be an artist or a musician. At 15 he worked in a gallery in Oslo. He met passing artists. David Hockney. Yoko Ono. "And I was mesmerised. It was the first time I realised you can make a life out of this. It was unclear to me at 15 whether I would be a visual artist or a musician but being in a band from 12 and practicing seven days a week and having a dream of making that your life and my father was a musician anyway and it suddenly took over."

Push him and he'll find some upsides. He remembers a long car ride with Robbie Robertson and George Harrison "and realising the absurdity of being in that car with them, bringing yourself to the child of 12 years old, the fan of the Beatles and The Band. Those are the things that spring to mind."

But clearly success wasn't what the three of them wanted it to be. "This is the irony of a lot of people who achieve success. A lot of them turn out bitter and hollow as people because they felt like 'oh, this is so much more important. Why wasn't this a hit?' It's a very dangerous path to go down. I think at some point that clicked in me."

He stared growing large beards to hide away from the caricature, the guy in the pop pages. And at some point he returned to art. "It was a kind of saving grace," he says. "It was always part of who I was. But, of course, it came with a whole set of new dilemmas because whether I wanted to be or not I was all of a sudden a celebrity painter. My name and my image was already out there attached to this one particular history and that meant that whatever I did would be seen in that light. The doors that were open to me, there were a few I didn't want to walk through. And the ones I was interested in a dialogue with were not interested in having a dialogue with me. There was a time I even considering showing my work under a pseudonym but then I think, luckily, deciding against it and taking it on full front.

"At the end of the day it's the work that's left and it will be judged differently in ten, 20, 30 years time. And it is. We've been very fortunate because very few people expected much to come out of our musical legacy. And in fact years down the line you have bands who were influenced by us growing up purely on a musical level, people who weren't wearing the wrist bands and copying the more mainstream effects around it. And that's been very rewarding. Being given an Inspiration Award by Q, a magazine that probably wouldn't have touched us back in the day."

Magne Furuholmen is an artist now. Maybe people are beginning to realise he always was.

Peeling A Glass Onion continues at the Dovecot Gallery in Edinburgh until April 25.