There is a sea current that runs around the island of Foula to the far west of Shetland.

It's called the Moder-dy - an old Norn name that means 'mother wave' - and it occurs regardless of wind or weather in the place where two tidal streams collide. Local sailors use it as a navigational tool when travelling between Foula and the mainland; for the untrained eye it's barely visible from the surface.

The collision of two strong tidal forces, one constant underwater current - it's a neat image for the latest collaboration between fiddler Chris Stout and harpist Catriona McKay. These two musicians have been playing together for practically their whole careers. They met 20-odd years ago as undergraduate students at the (then) Royal Scottish Academy of Music and Drama, and have since worked together on projects ranging from Shetland's supergroup Fiddlers Bid to their haunting 2010 duo album White Nights. Their playing is fearless, dexterous and instantly recognisable: they're two of Scotland's classiest folk musicians.

Two years ago the composer Sally Beamish wrote them a piece, a kind of double concerto, called Seavaigers to perform with the Scottish Ensemble. Now they have recorded that concerto, and have also written a 20-minute piece of their own for the same line-up (fiddle, Scottish harp and string ensemble). Originally they called their piece Sunstone, but recently they've settled on another name that somehow fits better: Moder-dy.

We've arranged to meet in a bar in Finnieston. Though neither of them is originally from Glasgow - McKay grew up in Dundee, Stout in Shetland - both have long been based in this part of the city. They're an unlikely duo at first glance. He is slick-shirted, suit-jacketed, garrulous, while she's willowy and raven-haired, a splash of multicoloured tights and dangly earrings.

I ask about the process of writing music together. "Loads and loads of back and forths," says McKay. "In this instance we began by just improvising together then each went off on our own to pursue our ideas. Chris started with a really strong melodic concept and I started with a really strong rhythmic concept. Then we basically sat at our computers emailing files to each other." Wouldn't it have been easier to just share a computer? "Na, Chris always hogs the screen," she laughs. Side-by-side laptops, then? "No way!" they answer, simultaneously.

The main difference between working on Moder-dy and their other collaborations has been their approach to the ensemble writing. Usually they would arrange string parts to pad out their central material but, as Stout explains, that often turns the strings into a sort-of backup band. "And you can't have the Scottish Ensemble as a backup band." They have nothing but positives to say about the Ensemble - most intriguingly, they comment that the group's members "aren't really like classical players". I wonder out loud what they mean by that. "Not rigid, not locked to their scores," says Stout. "Somehow they swing in the same way as us. Folk music is about forward momentum, about being spontaneous and alive with the material. They get it."

And it was precisely the Scottish Ensemble's ability to 'get it' that made Sally Beamish think of bringing them together with McKay and Stout for Seavaigers in the first place. Her piece was co-commissioned by the Edinburgh International Harp Festival and Celtic Connections and was first performed in 2012. Its inspiration was the idea of a sea journey between Dundee and Shetland - a journey that would pass by whales, seals and dolphins, that could be stormy or calm, menacing or beautiful.

When I reviewed Seavaigers at Celtic Connections I admired much about it - the performance, the colours - but quieried the nature of its authorship. I wrote: "the piece is so utterly tailor-made it could never be played by anyone else. Beamish takes up the trademark Stout/McKay sound world - fierce muscularity, spare and sweet lyricism - and leaves plenty of room for improvisation, too. The Scottish Ensemble, luxury backing band if ever there was one, mostly adds textural support and the odd passage of doubling on unison violins. It's lovely stuff and superbly delivered, but Beamish only gently pushes the scope at her end. Maybe she was reluctant to impose 'classical' confines on two soloists who are both masterful composers in their own right."

McKay and Stout refute my suggestion that Beamish in any way relinquished her voice in this score, and defend Seavaigers as a genuine collaboration. "We always wanted to be able to say 'this works for us' - that we weren't just playing Sally's music," says Stout. "We had to have our sound in it. But that's what so incredible about Sally. I mean, how many composers could you find who would be so open to giving up that control?" It's true; the answer is very few.

He goes on: "if you're going to write a piece that is about folk music then you have to take on the philosophy of folk music." In that philosophy, in his opinion, amounts to the following: "as a musician you're given the bones of the music and you're expected to embody those bones for however long you happen to have it. The traditional musician thinks of music coming to them. You're given it by some higher power; you inhabit if for a while and then you pass it on. Your role is as a kind of keeper of the music. This classical idea that the composer is the main man isn't how it works for us. The composer is often forgotten before they've even left this world. The music is bigger than them."

And yet both he and McKay agree that Seavaigers is still very much Beamish's music. "There's no question that she owns her work," says McKay. "It's just that she has absorbed what these two worlds - the folk world and the classical world - are each about." Stout nods his agreement. "That's exactly it," he says. "Two opposing philosophies. It's great that Sally has been able to inhabit both worlds. For hundreds of years classical composers pillaged folk music and didn't credit their sources. It's a good place that we've got to now, where both forms of music can sit respectfully side by side."

Catriona McKay and Chris Stout play Seavaigers and Moder-dy with the Scottish Ensemble in at Perth Concert Hall on April 29, The Arches, Glasgow, on April 30 and The Assembly Rooms, Edinburgh, on May 1