In a rehearsal room at the Icelandic Academy of Arts, something is stirring.

A posse of six Scottish musicians has arrived to join forces with a similar number of their Icelandic contemporaries to prepare for The Great Scottish Icelandic Concert, a Burns Night celebration taking place in the bar of the uber-hip Kex Hostel on the edge of Reykjavik. A couple of Canadians arrive to prepare for their performances the next night, part of a rich, if under-the-radar, international exchange that could only happen in Iceland.

These aren't just any musicians. From Scotland, maverick pianist and composer Bill Wells is here with his inaccurately named National Jazz Trio of Scotland, teaming his piano with vocalists Lorna Gilfedder, Kate Sugden and Aby Vulliamy, the latter doubling up on viola. Between them, the group have connections with many of Scotland's more exploratory left-field combos.

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Also in attendance is singer Alasdair Roberts, who has reinvented the Scots folk tradition to make it sound both ancient and thrillingly contemporary, in much the same way Nick Cave has done with the blues. His new album, A Wonder Working Stone, has been hailed as one of the first major recorded delights of the year.

Finally, and tirelessly, maverick piper Barnaby Brown lends a classically trained gravitas to proceedings.

As the band file in with their host, Icelandic singer-songwriter and composer Benni Hemm Hemm, they're greeted by an electric guitarist, a bassist, two keyboard players and a trumpeter. Under Hemm Hemm's direction and with Roberts on lead vocals, this newly formed big band thunder their way through Scots song, The Blantyre Explosion and make Burns's The Twa Corbies sound like Patti Smith's Because The Night.

Brown takes charge of The Fairy Flag, Circassian Cirle and the Canadian Barn Dance, adding pipes and his own mouth music to a vigorous stomp-along. The band then rehearses two of Hemm Hemm's songs, which sound even bigger. Canadian singers Clinton St John and Laura Leif join in on backing vocals, making the band a 14-piece.

Roberts played a solo set the night before in Kex's Gym and Tonic room, a kind of Viking banqueting hall decorated with punch bags, vaulting horses and Mexican wrestling posters. Wells and the NJToS will be there tonight. Gym and Tonic will also be the venue for a more traditional Burns Supper hosted by the Icelandic Edinburgh Society, when Roberts, Wells and Vuliamy become the ceilidh band, and Brown leads the dancing.

As the rehearsals hinted at, it is the massed Scottish Icelandic collaboration in the bar that proves to be an unmissable, once-in-a-lifetime spectacular.

The brains behind all this is Hemm Hemm, who was approached by Kex's unlikely managerial cartel of former international football stars after hearing how he had forged links with Scotland's musical community when he lived in Edinburgh. With a quiet January to look forward to in the newly opened establishment, a Scots member of Kex staff suggested a Burns night, and the Kex Scottish Festival Week was born in 2012, its first year featuring Edinburgh acts Withered Hand and Wounded Knee in what was a comparatively small affair.

This year Brown, Hemm Hemm and Roberts hooked up with Icelandic novelist Andri Snaer Magnason at Toppstodia (Top Station), a former power station now used as offices and studios by an arts collective. The interior of Toppstodia hasn't been touched, and the retro knobs and dials and racing green paint job resembles the sort of space-age sound-stage where the denouement of a James Bond movie might take place.

After comparing notes with Magnason on the common ground between ancient Scottish and Icelandic cultures, Brown plays the Sardinian triple pipe, then the bag-pipes, in the space, adapting to its acoustic as he marches around the iron floor. Later he visits Icelandic composer Hilmar Orn Hilmarsson, who recites an ancient Icelandic epic poem. Brown returns dressed in full Highland regalia just as the band have finished a gloriously bombastic Blantyre Explosion, sounding a little like Test Department scored by Ennio Morricone.

There are at least three musicians on Kex's tiny stage who weren't at rehearsals earlier. The two drummers and flugel horn player are part of Hemm Hemm's regular ensemble, and add a martial thunder to the other songs as well, despite never having heard them before. An analogue synthesiser adds apposite science-fiction textures to the roaring Scots outings, and by the closing performance of Hemm Hemm's song, Retaliate, it's clear something very special has just happened.

Not everyone got it. Given the wilfully misleading name Wells has given his band, more than one member of the audience was left wondering what happened to the jazz band, while a refreshed Danish sailor asked whether they were likely to play any Runrig numbers. If he stuck around for the Burns Supper the next night, the sound of Brown, Roberts, Vuliamy and Wells leading a mass sing-along of Loch Lomond might just have made his night.

Neil Cooper visited Reyjavik courtesy of Icelandair and Kex Hostel (