The first in this year's series of New Voices commissions is a little different from the norm – not that there's ever been a "norm" in musical terms, given the diverse panoply of artists' responses over the project's 15-year history – in that it reprises two compositions originally premièred in 2011 and 2012: accordionist Angus Lyon's 3G and bassist Duncan Lyall's Infinite Reflections.

Each piece earned glowing reviews first time around, so the main case for revisiting them rests on their musical merits, but the show also marks their release in album form, recorded in Lyon's South Lanarkshire studio over the past year. Both featured in each other's line-ups for those first performances, as well as sharing several other band members, and got talking after Lyall's show last year about ways to secure a more extended life span for their work.

"We'd both got so much out of doing the commission, creating a whole new extended piece of music, that it felt quite frustrating for it all to be finished after just one concert," the bassist says. "You put so much work into the writing and rehearsing, then the gig is over, so the first thing Angus and I agreed was that we'd encourage each other to make studio recordings – that way we'd have some kind of permanent record of the experience. Then a couple of months later we approached Celtic Connections about doing a gig as an album launch – a really wise move, as it gave us a deadline, otherwise the recording would almost certainly have been pushed on to the back burner by other projects."

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The show also highlights the legacy of the New Voices scheme, often cited by musicians as one of Celtic Connections' most distinctive and valuable strands. Several other participants have gone on to record, and many more have echoed Lyall and Lyon's sentiments about the impact of the experience.

"As a bass player, this was the first time I'd ever stepped to the front as a composer and band leader," Lyall says of his piece, structured as a musical version of a classic filmic narrative. "It opened up a lot of new possibilities, gave me confidence in new areas. I'm writing another piece for a concert this spring, and I've got much clearer ideas of what I want to achieve, and how to go about it. Plus I've now got an album out of it, under my own name – which is also rare for a bassist."

"I'd written plenty of tunes, but New Voices enabled me to start thinking of myself as a composer," adds Lyon, whose three-part suite evokes the changing experiences of his family over three generations on the same rural farmstead where he has his studio. "It's not only the actual writing, but putting a band together, arranging and scoring the parts – the whole experience has been hugely beneficial for me, and I now feel I can go out looking for more of that kind of work."

Duncan Lyall and Angus Lyon play the Mitchell Theatre, January 20, 1pm. New Voices is supported by the Sunday Herald