There's a line in the 1968 Incredible String Band song, The Circle is Unbroken, which sings of "brothers from all time, gathering here".

It could have been written for this year's Celtic Connections, which sees the Incredible String Band's psych-folk sage Mike Heron join forces with his latter-day spiritual kinsmen Trembling Bells for a collaborative folk-rock performance. They'll rekindle songs from the first four Incredible String Band studio albums, and Trembling Bells' debut LP Carbeth, under the loose title The Circle Is Unbroken.

As with so much of the British folk-rock narrative, the collaboration was sparked by American producer, writer and catalyst Joe Boyd. Boyd invited Trembling Bells to perform at an Incredible String Band retrospective at London's Barbican in 2009. (Incredible String Band co-founder Robin Williamson declined to participate saying he "didn't want to look back"). The Bells and Heron struck a chord, and they've since toured together and issued a split seven-inch with Bells' ally Bonnie Prince Billy.

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"I guess Joe identified some kind of commonalities between the Incredible String Band and our song-writing, and that was incredibly flattering," says Trembling Bells' Glasgow-based frontman Alex Neilson. "Everyone in Trembling Bells is a massive ISB fan – they went a long way to forming our individual and collective musical aesthetic."

They are not alone: Paul McCartney called Incredible String Band's 1968 opus The Hangman's Beautiful Daughter one of his favourite albums; The Rolling Stones wanted to sign the band; Robert Plant is a devotee; even The Archbishop of Canterbury is an avid fan.

Neilson has long spoken of the revelatory impact Incredible String Band had upon him.

"Yeah, I think the first album I picked up, when I was at school, was [1967's] 5000 Spirits or the Layers of the Onion. It's genuinely psychedelic – it feeds the eye and feeds the mind. It kind of relocated esoteric philosophy and spirituality to Great Britain through these melodies that turned out to be Scottish or Irish, but just through your own kind of genetic memory, it felt like you recognised them without having ever heard them before. That, combined with degrees of improvisation, and experimentation with recording techniques, and their playful aspect, was really appealing."

When Trembling Bells released their outstanding debut, Carbeth, in 2009, some fans perceived echoes of Heron's warm, wavering tones in Neilson's voice. "On the one hand I can see there is a similarity," Neilson nods. "It's like when our band gets compared to that generation of folk-revivalists. But rather than trying to emulate ISB, or Mike Heron, it's much more to do with, dare I say, coming to similar conclusions – being really interested in field singers and traditional singing and experimental music and rock and jazz, and then arriving at what sounds like a similar point."

Trembling Bells and Mike Heron's psychic and sonic explorations reanimate bygone landscapes, yarns and connections, while spinning new ones. In addition to reinventing each others' songs, Trembling Bells guitarist Mike Hastings is now a full-time member of Mike Heron's band – as is Heron's daughter, Georgia. "Yeah, I guess that's part of the organic folk tradition, that feeding back into itself," offers Neilson. "Georgia's a real intimate part of that resonance – she's a really masterful interpreter of the Incredible String Band stuff, and it's incredibly moving seeing them work together; having that continuum."

For Heron, too, working with his daughter has cast new light, and life, on his work. "She's a very good piano player, and she has some interesting input – she comes up with things I wouldn't think of," he says. "The most integral thing is that now we do [1968 agrarian epic] A Very Cellular Song, and she conducts it from the keyboard. We couldn't really do the song without her."

Heron credits Trembling Bells with enabling him to revisit songs he otherwise could not perform. "I really like Douglas Traherne Harding, and you need people who can play in quite a subtle way to do that.

"It's also amazing to realise that there are so many different approaches to our songs that can work really well," he says.

Did Heron discern a musical kinship with Trembling Bells when he first heard them? "I did, yeah, but of course when we first heard their music when they were doing Incredible String Band songs [at The Barbican] – their interpretations were fantastic – and that was our entry into their music. But after that we got all of their albums, and we really liked them."

The Celtic Connections event coincides with the release of a live Incredible String Band's album, Live at Fillmore East 1968, (Hux). Heron recalls it fondly. "It was the last time we played before the girls joined the band. We'd been touring in the States for six months, and Robin's at the very at the top of his game – playing hundreds of instruments and being very imaginative. I'm not too bad either, but I'm eclipsed by him a bit," he laughs. (He is too modest). "I'm really proud of it; how it captures a moment in time."

How did that gig come about? "It was a fundraiser for the New York radio station WBAI, who'd always been really supportive of us. Actually, I think it was Joe Boyd who introduced us."

And so we return to Joe Boyd in this cyclical, cellular, musical tale of nature and history and relationships. The circle rings out louder than ever; breaking new ground, and still unbroken.

Trembling Bells and Mike Heron play The Mitchell Library on January 24 as part of Celtic Connections