Unannounced, in walk a blond boy and a blonde girl. "Hello, I am Olof," says the bespectacled boy, shyly. There's no beak or mask of any kind. "Karin," says Karin, one beady eye staring with possibly more intent than the other.

Nervously, we begin with a chat about that spectacular live show. In it, projectors are used to create the effect of placing the band inside a live action film, with screens in front and behind, while a series of disturbingly half-formed characters morph into life and disappear as quickly, mournfully mouthing lyrics while the masked duo play with steel drums and vocoders, backing tracks completing the accurately titled "audio-visual experience". How did Nilsson became involved, and how much of the show is his?

Olof, now seated, begins haltingly to answer. "It started with..." and then Karin, poised beside him, interrupts. "I met him a very long time before we began to work together," she declares. "We're from the same town, Gothenburg, on the west coast of Sweden. He played in a band called Silver Bullet, who were quite big in Gothenburg in the mid-'90s. That's when I met him the first time. We started to work together when he was involved in our first video in 2001, the New York Hotel video."

"I was really moved by that video," resumes Olof. "And since then he has continued working with us, doing the videos for Heartbeats and Silent Shout." "He understands really well what we are doing," says Karin. "It's very relaxed to work with him. We discuss a lot of references and ideas but it's not like we ever have anything against his ideas."

Without Nilsson's involvement it's just possible The Knife might never have performed live. Prior to that Scala show and the five-date tour it formed part of, they didn't play live, despite releasing two albums before Silent Shout. "It's because of him we do it," says Karin. "(In total) we'd made a three-track concert at the ICA last year before we started this year. So we'd never really done anything before we started this." Olof agrees. "It (our music) can't be done live. And we have never played anything by hand when we are recording either; we program everything." He pauses. "And this is not a really live show either. It's a video show, with surround sound music and... vocals that can be a bit improvised."

They decide what to do on stage based on the visual effect that activity has, rather than which musical parts need to be played. "I play very simple melodies; playing live doesn't add anything to the show so it's more about simple things for your eyes to put together," says Olof.

Another aspect of the live show is the projected figures who 'sing' the songs. "They don't have any names," says Karin. "They are very loose characters. They can be quite different from day to day, I would say. We took time to make something that we thought our music looked like." The macabre creations blinking sadly at the audience are compulsive viewing.

The Knife's most popular track prior to Silent Shout was Heartbeats, a cover of which by countryman Jose Gonzalez featured on a Sony TV advert, and Karin believes the increased exposure it generated was a mixed blessing. "When people in the UK heard us doing Heartbeats they thought we had done the cover. It's a very nice cover, but it wasn't a conscious decision to get our ideas out there. It was to be kind to Jose because we know him, and we got a lot of money to do our live show."

The show, says Karin, is expensive. "We don't really break even, but we can finance it with the song money." They've never licensed any of their own recorded tracks and Karin says she wouldn't. "I'm not happy about it; it was good to have the money, but I don't think it's good to sell your music to commercials."

Three years on from the Swedish Grammy nominated Deep Cuts, the album that featured Heartbeats, Silent Shout was released. It's a record with a singular, enigmatic and decidedly dark vision running through it from beginning to end. "Silent Shout is much more like our first album, much more direct in that sense," says Karin. "Deep Cuts was more of a project."

How did they set about creating it? "We start with the music, then Karin writes lyrics, then..." Olof tails off. Karin: "Then we often go back and start the music again." Olof: "Then we change the music to suit the lyrical content." Karin: "It's quite a long programme. We worked on Silent Shout for one and a half years, I think."

The heavily treated vocals, as well as the lyrics, are all the work of Karin. I ask why she morphs her vocals. "It was for fun," she says, unexpectedly. Olof explains their context within the fantastical, parallel world the music creates; having untreated vocals would be too 'real', and the music is about something beyond real. Fantastical, essentially, and certainly fantastic.

"I like the theatrical part of music; I think it has to do with us having influences from everywhere else but electronic music," says Olof. "Both of us have been very in to pictures and images and films," adds Karin, explaining that their influences are more cinematic than musical. "David Lynch, and Aki Kaurismäki, the Finnish director. If you see something you really like you get a strong feeling of something. And that's what gets you started with making music."

In terms of music, their influences are as disparate as anybody's of their age. "We were brought up with Bob Marley and Jean-Michel Jarre, Afropop," says Karin. "But then I've always been into bands who are more theatric; Cyndi Lauper, Eurythmics, Fleetwood Mac." She pauses. "But then later on, more minimalistic, I would say."

We get on to minimalism, and it doesn't take long for the name Steve Reich to crop up. "I have been listening to his stuff and I really like it." says Olof. "But if I will do something influenced by him I will totally do something as a reaction towards it. It's so stuck in that era, and it feels segregated. We often use this monotone way that Steve Reich is using. (It) is very hypnotic. I'm really inspired by that hypnotic thing, and the feeling you can achieve. But our music is not so monotone or experimental, it's easier."

Karin's definition of minimalism is maybe a little different. "When I think of minimalistic I've been listening much more to Shellac, that kind of drum machine sound. I like this minimalistic way," she says. "But I think we are both a bit too romantic to stop doing melodies. I like good hooks. But it's very important that it comes in something different, to create a dynamic around it. I have nothing against pop in that sense." "It comes out of our work together," says Olof. "We could do more experimental stuff on our own, but the compromise is what comes out of our work together."

Is English language lyrics a compromise? Why do Swedish acts, themselves included, not use Swedish lyrics? "I've never listened to any music in Swedish," says Karin. "I have no connection to it." Olof's explanation is a little more geeky. "Compressors are made for recording in English. It's very hard to get a good sound when compressing Swedish. I noticed that when I did a Swedish record... It sounds so odd."

But why English? Why not, say, Danish? "I don't understand Danish," says Karin. "I was interviewed by Danish TV last week and I don't know if we got each other. They wanted to speak Danish but I spoke Swedish and we didn't understand each other." And, ultimately, as Karin points out, the number of Swedish speakers is relatively small. "Sweden is a very small country."

For his part, Olof has moved from Stockholm to Berlin. As a techno DJ, he needs clubs. In Stockholm, he says, "There are some clubs, but they are very commercial and they don't have any good sound. People who have the clubs say to the people, 'This is like Berlin', and then people go there because people are not independent in Sweden. If some cool person says something in Sweden everyone trusts them; that journalist or that club person or whatever. It's terrible; we haven't got any good clubs." He thinks. "There is a small bar club that plays good stuff. And there is good club music being done (made) in Stockholm, but not played."

They also have a label to run. "I worked a lot with the Rabid label, administrative work," Karin explains. "The label is Olof's and mine and we run it. Then we license the music (to countries beyond Sweden)." Mailshots from the label come from a lady known only as Frau Rabid who, like the characters in the Silent Shout show, "is also a creation, I would say," she confirms. "It's hard to write newsletters and 'Come to this concert!' from Olof or Karin," explains Olof. "It's better to have a 'label boss'." "Everyone can write in her name; that's good," Karin adds.

But with the siblings now living in different countries, what of the future? Will they make another record together? "We don't really have any plans for the future, and I think both of us are quite keen to work on our own," says Karin. "We have been working now for seven years together."

Whether they work together again or not, Karin Dreijer Andersson and Olof Dreijer have, with Silent Shout and its accompanying show, raised the bar for anyone who dares to follow their lead.

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Mercury Prize 2009 nominees