What a difference a "V" makes.

Last year, a covert Glasgow trio called Churches released a thrilling synth-dirge, Lies. It sounded like Robyn, Tubeway Army and Erasure's Circus, cast in neon, and it caused a global cyber-frenzy.

If the online fervour shocked our heroes Lauren Mayberry, Iain Cook and Martin Doherty, then it also suggested their cerebral, celestial electro-pop had promise; that their name should be internet search engine-friendly. And lo, Chvrches was born.

Since then, Chvrches have appeared on television show Later … With Jools Holland and David Letterman, and their brilliant debut album, The Bones Of What You Believe, has reached the UK Top 10 and No 12 on the US Billboard Chart. They will see off a spectacular year live at Edinburgh's Hogmanay, and this weekend they play the Christmas bash for TYCI, Glasgow's ace DIY feminista collective, which was co-founded by Mayberry.

Chvrches are pop stars from Japan to Australia, and their music straddles continents (variously conjuring Sweden's The Knife and Canada's Purity Ring). But the group emerges from (and feed into) a great Scottish tradition of electronic music - from Eurythmics through rave to Errors and Rustie - and you can trace the roots of their gleaming synth-pop to their disparate bygone Glasgow bands: the barbed lyricism of Mayberry's indie melodists Blue Sky Archives; the gilded post-rock revelations of Cook's Unwinding Hours; the dramatic industrial-pop of Doherty's tenure in The Twilight Sad.

Chvrches famously claim they were born on the internet, but is Glasgow's subcultural ecosystem responsible for shaping them and helping them on their way to fame?

"Well, it is a community up here, and that is useful in every way," says Doherty. He is sitting with his band-mates backstage at Glasgow's O2 ABC. "The history of a local studio like Chem19, or a label like Chemikal Underground, or being 15 and going into West End records in Clydebank to order (The Delgados') Peloton - that's all part of Glasgow. It would be foolish to say that had not somehow shaped us musically."

"It's an interesting question," says Cook, ere of alt-rock deities Aereogramme (with whom Doherty also toured). "Chvrches probably could have survived outside of that system, because we didn't do the whole playing loads of shows and supporting other bands around town thing.

Somehow we managed to sidestep that." Perhaps because they had done the grassroots graft, and established their credibility, in other local cult bands first? "That is true," he says.

Mayberry nods. "I met these guys through the local community. I met Iain when he recorded an EP for Blue Sky Archives, and we wanted to go into Chem19 because of the legacy that studio has," she says. "And I think in terms of learning your craft, getting gigs, Glasgow's great for that."

You can hear Glasgow's counter-culture in Chvrches: their euphoric melodies, elevating verses and progressive sonic narratives evoke the city's burgeoning club scene (as do remixes from Optimo's JD Twitch, Miaoux Miaoux and Auntie Flo); and Mayberry's gorgeous, day-glo vocals are equal parts Cyndi Lauper and Adele Bethel of Sons And Daughters.

Doherty, too, sings lead on occasion. This highlights Chvrches' androgynous lyrics, which favour anatomy (lungs, skin) over emotion: talk of the heart is actively avoided ("did you wear it on your sleeve?"). The Bones Of What You Believe has a vivid lyrical idiom, galvanised by threats and weapons ("I will be a gun and it's you I'll come for"; "I'll be a thorn in your side" - are you listening, Annie Lennox?)

Did they set out with a specific lexicon, or concept? "We were not going for a particular theme," says Mayberry, "but all the lyrics were written over an 18-month period. It is probably just informed by things that were happening at that time."

There are exhilarating synchronicities in the album's words and music - By The Throat's shimmering keys ("all that's golden"); the burbling synths on We Sink - and it makes for a fascinating, unified body of work. This sense of cohesion extends to Chvrches' iconic visual aesthetic, thanks to their angular logo (hence the Roman "V") and related covers, designed by Amy Burrows. "The idea was that the artwork on every single would lead up to the album," says Doherty.

Everything about Chvrches is meticulous. You wonder how the trio ever managed to finish an album they recorded and produced in Cook's studio basement.

"Yeah, when do you stop tweaking it, if there is not someone telling you that your time's up?" asks Mayberry. "That's a skill we've had to learn - some of us more effectively than others," she says with a laugh. "Martin fiddles and fiddles."

Doherty shrugs. "It's not perfectionism. It's just I'm always like, 'Could this be better?'" he says. "I remember the first time I went into a studio, it was Red Eye in Clydebank, and I had my guitar and I was rocking out. A guy said to me afterwards, 'That could be better.' And that's stuck in my head, for the rest of my life. Every time I'm in a studio now, all I think is: 'That could be better.'"

Cook strokes his chin. "Martin, have you got that guy's number? I'm going to have a word with him," he says. "That's really interesting. It explains a lot. I can't believe you've never mentioned this before."

Doherty pulls himself up on the couch. "It's all pouring out here, this is like therapy."

The Bones Of What You Believe will uplift your mind and heart and soul. The cosmic hosannas are enlightening, and the choral electro anthems are heavenly, and if Faithless were right, and God is a DJ, then we can all find hope in Chvrches.

Chvrches play the TYCI Christmas Party at Glasgow SWG3 on December 21 (www.tyci.org.uk) and the Waverley Stage at Edinburgh's Hogmanay.