You wonder if Trembling Bells' Alex Neilson is enacting his music career in reverse.

Rock and pop artists tend to migrate from commercial success to experimentation – Blur's Damon Albarn turned his hand to Chinese opera, Paul Weller started dabbling with psychedelic instrumentals – but Neilson made his name as a brilliant free-improvisation drummer, and has since re-cast himself as such a vintage pop swashbuckler that his band's new album, The Marble Downs, includes a cover version of a song by a Bee Gee.

The Marble Downs is a rousing, instinctive union between Neilson's Glasgow-based mythic folk-rockers Trembling Bells (whose fans include Weller and their Honest Jons label boss Albarn) and Kentucky alt-folk firebrand Bonnie Prince Billy (aka Will Oldham). Its roots can be traced to 2004, when Neilson and Oldham first met in the Highlands while working on Alasdair Roberts's long-player, No Earthly Man. They have since toured together often (once with Harem Scarem) and recorded a split seven-inch with Mike Heron, and perhaps this is why the album feels alive and organic, despite Oldham having posted his vocals from across the Atlantic. Along with original songs and a swaggering rendition of Oldham's incest-serenade, Riding, the album sees them covering Robin Gibb's Lord Bless All, and paying homage to "crooner music".

"I remember touring with Bonnie Prince Billy years ago," recalls Leeds-born Neilson, idly stirring a coffee in his adopted city of Glasgow. "We'd stop off at petrol stations and he would buy these Bing Crosby CDs. At the time I was just like, 'What is this crap? He's gone too far this time,'" he laughs. "It was only when I started to write my own music that I developed a very profound respect for classic songwriting and the mechanisms of songwriting, and I got really immersed in the Great American Songbook."

The record plays out as a series of bruised-country, folk and alt-rock duets between Oldham (Neilson renounces his vocal duties on this record) and Trembling Bells' extraordinary co-vocalist Lavinia Blackwall. The musical fabric of the Marble Downs, says Neilson, is inspired by "many American crooners – Johnnie Ray, Johnny Ace, Julie London and Nat King Cole. Their invocation of an epic, soul-exposing melancholy was very inspiring".

Oldham was an influence on Neilson long before they met. "Will was like a portal to a lot of things," he says. "Even as a teenager he moulded my appreciation of music, and his music typified a lot of the things I really liked about folk and improvised music – it smacked of traditional folk, old sea shanties and old testament language. From the very earliest stage he informed the way I fundamentally think about music. And I learned those lessons well. I took it very seriously at the time." (Oldham was in turn inspired by Scotland – he has long had a love affair with the country, and Glen Lyon in particular.)

Was it daunting or liberating, writing duets for Blackwall to sing with Oldham, rather than himself? "It was a peculiar set of challenges to write for other people in a duet format and to make that dynamic interesting over the course of an album," he offers. "I kind of conceived the song, and sang it the way I imagined it to be, but obviously Will's an infinitely more talented and versatile singer and songwriter than me [Neilson does himself an injustice]. So he reinvented the parts in ways that were completely unexpected and better for it. I guess it was kind of like a relinquishing of control."

Was that difficult to do? "It was, yeah," Neilson laughs.

Oldham and Blackwall's voices variously spark off and curl up to each other, his wounded growl the perfect, ravaged foil for her translucent soprano. "I did a lot of English choral music at school, travelling round cathedrals, singing lots of music by Hubert Parry, John Taverner, all these lovely works," Blackwall says of her classical training. "I got really interested in baroque music and mediaeval music at university in Glasgow, and then I did a Masters in early music at the Guildhall. I wouldn't say I'm any kind of purist at all though – I just find it's interesting to look back and see how everything fits together."

Before Neilson formed Trembling Bells as a conduit for his nascent songwriting in 2008, he and Blackwall performed as an acclaimed free-improv duo, Directing Hand. "I guess the impulses that drew me towards improvised music were to do with freedom of expression and trying to engage with some kind of creative impulse that wasn't contaminated by procedure, or convention," Neilson reflects. "These things attracted me to improvisation from a deeply human point of view, but the more I investigated it, the less human it seemed. It was very alienating for people.

"In some ways Trembling Bells was a reaction against that sort of music, while drawing upon certain similar strands – mediaeval, early and traditional music," he continues. "Trembling Bells was a way of refining those ideas in a way that was a bit more – well, palatable," he laughs.

The remaining members of Trembling Bells – guitarist Mike Hastings and bassist Simon Shaw – are equally intrinsic to Trembling Bells' lineage. There's a heady acid-wash to the band's mythological folk-baroque tapestry, which is redolent of Blackwall and Hastings' mid-2000s wyrd-folk troupe The Pendulums – who were, as Blackwall puts it now, "A Gong and mushroom-influenced psychedelic fun band."

"Mike is really hilarious," says Neilson of Hastings. "He's boundlessly good natured and has a massive constitution for intoxicants. He's a great musician with a lot of flair – I always think he could be playing Twinkle, Twinkle Little Star and he'd sweat blood into the performance."

Shaw, meanwhile, previously commandeered much-loved psych-folkers Lucky Luke, with whom Neilson played (when he wasn't performing with Scatter, or Jandek, or Motor Ghost, the list goes on). "Simon's a fantastically endowed musician," muses Neilson. "His parts are always very inventive and his musical taste ranges from feral free-jazz to saccharine country music, so he understands the scope of the Trembling Bells aesthetic."

That same aesthetic, while easy to fall for, is also borne out of experimentation. When Neilson turned his hand to songwriting (the fruits of which were showcased on Trembling Bells' outstanding 2009 debut album, Carbeth), it was in a bid to break new boundaries. "I just wanted to try something new," he says. "It was definitely done in the spirit of experimentation."

We have that to thank, then, for Bonnie Prince Billy and Trembling Bells crooning a song by a Bee Gee. "It's all about expanding your conception of what is possible."

The Marble Downs (Honest Jons) is out on April 9. Trembling Bells and Bonnie Prince Billy play The Queen's Hall, Edinburgh, April 25. An exhibition of Lucy Stein's artwork for The Marble Downs will open on April 24 at 24 St Vincent Crescent, Glasgow, with an after-show party at The 78 on Kelvinhaugh Street.