The end of the world is nigh, maybe.

According to some interpretations of a 5125-year Mayan calendar, we have two days left until our time is up on the prophesied 21.12.12. After that? Unspecified. Fire or floods, possibly an inverse big bang, possibly a whopping meteor collision or a great spacey void. Or possibly we get up on Saturday morning and make breakfast to a new calendar.

For the folks at Red Note Ensemble, the point is not really the technicalities of whens or wherefors. "We've predicted it so many times," says composer Gareth Williams. "The millennium, the crazy cult leaders - there's always some kind of use-by date for human civilisation. We keep resetting the clock."

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Here's the big question, then: why are we the kind of people who keep predicting our own demise?

"On face value that felt like the starting point for a show, so I invited a few people to respond creatively." Those people included playwright Oliver Emanuel, Finnish-British vocalist Hanna Tuulikki, composers Colin Broom and Red Note chief John Harris, and the Tron's artistic director Andy Arnold.

The show – The End of the World (for one night only) – came together speedily; it had to. From the seeds of an idea to fruition in less than six months. "There's never enough time when you're talking about the end of the world," says Williams. "It's the ultimate deadline."

The results will be aired at Edinburgh's Summerhall on Friday, with Red Note's small crew bolstered by production input from the Traverse Theatre and about 30 drama students from Telford College. Still, it will be a cosy show. An audience of 100 will be divvied up into small groups and led by a narrator around the depths of the former Dick Vet School: around the basement nooks and cages, the dissection rooms and post-mortem spaces. "A displacing journey where people never double back on themselves," is how Arnold describes it.

Along the way the groups will stop in on little vignettes Emanuel has concocted for the event. "The whole thing starts with a playwright – that's me, I suppose – getting a call to say the world is going to end," explains Emanuel. "He goes around Edinburgh listening in on everyday people going about their everyday business. The scenarios are apocalyptic in the sense that there is impending doom, but poignant because the characters don't know.

"From my point of view the challenge was that most stories about the end of the world are theatrical epics set in New York. Whereas ours is intimate and Scottish."

Emanuel started from the assumption if the world was going to end, we likely wouldn't have any warning. "There would be no time to get ready. Even if the authorities knew a meteor was about to strike, they would keep it quiet to avoid mass panic."

So he wanted to tell stories about unfinished lives. Someone who hasn't told his first girlfriend he loved her all along. Someone who hasn't finished his cup of tea. "The thing about Hollywood apocalypse narratives is that they're always about people who survive the disaster. I was interested in creating a narrative where things do simply just stop." He describes a "diminuendo" rather than a "grand gesture" and quotes the last lines of TS Eliot's The Hollow Men: This is the way the world ends/This is the way the world ends/This is the way the world ends/not with a bang but a whimper. "I'm interested in that whimper," he says.

Once the audience has eavesdropped on several Edinburgh scenarios to the ambient backdrop of a John Harris soundscape, the small groups will congregate for the final musical segment of the event. Emanuel says he wants his vignettes to prod the imagination, to trigger contemplation about how we would each feel if the world really was to end later that night. "What's good about being human? What's good about the world that we'd miss if it all stopped? Hopefully I've illustrated different dimensions of what it is to be alive on this planet, and I want the stories to make the audience think about their own lives while they listen to the music. It's exciting, because I don't know whether each person will be thinking joyous or sad or profound or trivial thoughts. It'll be a particularly subjective theatrical impact in that sense."

As for the music? Without giving too much away, Williams hints at what's in store. There's a simple song; a quintet for musical saw and strings; a work based around audio interviews. When he commissioned the scores he gave the composers (including himself) one basic remit: to write the last piece of music they'd like to hear if the world was ending. "Most people don't remember the first piece of music they ever heard. Actually, I do: it was Prince Charming by Adam and the Ants. But what would you choose for your last piece?"

Personally, just the idea of having to make that choice is torturous. Would I go for something profound, reflective, transcendent? Emanuel listened to Arvo Pärt's Cantus in Memoriam Benjamin Britten – a mournful elegy of bells – to get him in the mood while writing the show. Or maybe the best strategy would be the exact opposite: frivolity and irreverence, more Monty Python's Always Look on the Bright Side of Life than Messiaen's Quartet for the End of Time. Either way, having to write your own apocalypse music sounds like an immense pressure.

"Actually the process was pretty liberating," says Williams. "Say we do all wake up on Saturday morning and it turns out the Mayans got it wrong, I'll have had the nifty catharsis of having already written my last piece. And that means I can wipe the slate clean and get cracking on my first piece again."

For his part, Arnold says he's not used to working along the now-or-never mentality of one-off shows: "I guess there can be no warm-up and no repeat performance for the end of the world. Hence the second half of the show's title." He has already planned his closing lines – his pre-calamity postscript, as it were.

"I'll stand up at the end of the show and say, 'ladies and gentlemen, we're not quite sure at what exact moment the world is going to end, but I hope you will join us in the bar where we can wait it out.' Although death might be an individual experience, when it comes to the end of the world we must all be in it together. And that's not bad for a bonding theatrical experience."

The End of the World (for one night only) is at Summerhall, Edinburgh, on Friday.