So what to do? Sadly that traditional Swedish headline-grabber, an affair with Ulrika Jonsson, is out — they are all happily married men. Ditto their British PR woman’s brainwave, after some especially virile group photos, of trying to court the gay press. The staid world of jazz is not immune to pop-style promotion: currently Sting’s trumpeter, Chris Botti, is wowing American audiences as “the sexiest man in jazz”.

But this, you suspect, is not the sensible Swedes’ way. Svensson is bemused at the gay idea. “Well, I don’t know,” he laughs, “I have a lot of friends who are.” He smiles, too, at the reported ambition of his manager, after the success of albums such as Seven Days of Falling and Strange Place for Snow, of turning the group into “the Pink Floyd of jazz”.

A jazz trio as stadium monsters? “Well maybe; he has a lot of ideas. But it’s true that when we started I told him that I wanted to play only small venues and not concert halls. Then we played a few and we found that we could make it work. Last year there were shows to 4,000 people in Spain and France. In Vienne we played to 8,000. If you have good sound and can use lighting in a good way and can keep the music together, it works. So who knows where we can take it?”

Svensson, a genial 40-year-old, is holding court in an East London café. He is in the midst of scooting round Europe to plug the band’s new album Viaticum. But for all the good humour, he says he’s tired and getting over a cold. The price of being an in-demand jazz outfit that has built its name over ten years is continual travel (at a time of life when a successful rock band would be easing off to see more of the kids).

“It’s been really tough, the past few months. First we recorded the album, then we travelled to the States. We went back home and mixed the album. Then we went touring and it was work, work, work for 40 or 50 days, playing every night or being in the studio.

“My life is two worlds. We do 100 gigs a year and the touring is very organised. At home I’m on the floor with the kids playing with the Lego.”

Viaticum is a more understated album than recent predecessors — no funk grooves, instead a slow-burning intensity and a classical feel to several tracks. What has Svensson been listening to? “In fact, not very much. I find I just don’t have time while touring. My own music is enough to think about, but the other guys (Magnus Öström, drums; Dan Berglund, bass) have been checking out the new U2.”

Viaticum is an album designed to be heard as a whole (please note, iPod rippers and burners). “We tried to create a complete work, a journey from beginning to end — like a book,” says Svensson.

As for the title: “It’s a Latin word meaning provisions for a journey, and it has a spiritual meaning, too. Life is a journey and it’s not always an easy one. We need some kind of viaticum now and then. This is our spiritual food for anyone who needs it.”

The record is a further advance on “the EST sound” in which Radiohead and Swedish folk can have as much influence as bebop. Of all the in vogue jazz pianists — Brad Mehldau, Lynne Arriale, Tord Gustavsen — it is Svensson who is ploughing the most individual course. Which is fine for European audiences, but has raised eyebrows in America. The trio has yet to conquer the “home” of jazz. “We have heard that people like Branford Marsalis have said that what we do is fine but we shouldn’t call it jazz.”

Svensson refuses to be drawn into a dreary debate about what the term means. “We talk about what we do as improvised music. Jazz is part of improvised music, but there are so many languages you can use — a classical language or a swing language or bebop. So yes, maybe mix them up.”

And will EST be back on MTV? Svensson isn’t sure. “I have got the computer with me and I’m seeing if I can cut a track down for promotional purposes. But I rather doubt it’s possible with this kind of album.” He shrugs. But does it matter? The Pink Floyd never needed MTV.

EST play the Sage Centre, Gateshead, on March 19 (0870 7034555) with a full tour in May; Viaticum is out on ACT

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