In a Glasgow basement the two men and one woman who make up Scotland's possible – probable?

– next big thing are discussing beards in pop. It may or may not be significant that two of the three of them are sporting facial hair.

"Unfortunately, I've been waiting for it to come in for a decade now-" Lauren Mayberry, lead singer and the youngest member of Chvrches, the band who are putting the electronic into indie, laments.

"Let's talk about Grandaddy, one of my favourite bands of all time," adds Martin Doherty. "They were beard rock! Are we beard pop?"

"I like beard pop," announces Mayberry.

"If the Human League were all style and Soft Cell were imaged up and that's the equivalent of clean shaven, then I guess our music is somewhat bearded because we deliberately keep things rough," continues Doherty. "We don't quantise things. We don't really go hard in the way that dance music is really hard and really clean."

"We talk a lot about this whole genre thing," Iain Cook chips in. "I know Martin in particular feels uncomfortable with the term 'synthpop' as it applies to us. I think we think of ourselves as more of an indie band because it's where we all come from. And our approach to what we do with the instruments is very much like an indie band; distorting things, making things edgier."

"Those Soft Cell records are all totally out of time actually," adds Doherty.

"But that's symptomatic of the technology," says Cook. "They wanted them to be in time. We're going the other way, trying to f*** things up and make things a bit edgier - and beardier."

Chvrches (yes, the v is deliberate) came from nowhere at the end of last year to be named on the BBC's Sound of 2013 list and namechecked by countless music journos, as well as being booked to support Depeche Mode on selected dates of their upcoming tour.

"Nowhere" in this case is Glasgow and a history of previous bands. Cook was part of Aerogramme and The Unwinding Hours, Doherty has played with The Twilight Sad, and Mayberry played keyboards and sang with Blue Sky Archives.

Cook and Doherty have been friends for years. They met Mayberry in the studio when Blue Sky Archives were recording an EP, invited her to sing on a demo for this "electro thing". She did. "I remember when Lauren left the studio we were both like 'what the f***-'" says Doherty. "There was lightning in the studio."

"There was a moment specifically when we were trying to fix Lauren's backing vocals on one of the tracks," adds Cook.

"We muted Martin's vocals to equalise the track, and I think we both just turned and looked at each other and went: 'This is the lead vocal'. It was one of those brilliant moments."

They became a trio, and wrote some songs. One of them was called Lies, a stomping electronic monster sweetened by Mayberry's girlish vocals. They gave it to an American music blog and things went, well, a bit mental.

Now they've got an album in the offing and a sense that they might be at the start of something. "We're sitting on the edge of the cliff, as it were," admits Mayberry. How high does the drop look? "Depends on what time of day it is. If it's after several gins in the evening, it would be high."

"I think I can speak for all of us," Doherty says later, "we've never come this far. But we're well aware it could all be over tomorrow."

Before we worry about premature failure, let's rewind a little. Chvrches is made up of three Prince-loving music obsessives with an unlikely relish for Toto (Doherty plays Africa when he DJs, Mayberry says it's the record she dances to late at night). This is their back story. Cue the flashback.

"Glasgow is the place of my birth," begins Doherty, "and a city that I'm really proud of and a city that holds a lot of great history, especially in music over the years. Someone like The Blue Nile, in my opinion, are the sonic equivalent of Glasgow's beating heart."

He was born in the Queen Mother's Hospital in the city. When he was 14 he started to come into the city centre every Saturday afternoon to go to Tower Records and Missing and stand at the galleries with the Goths. "But me and my pal were never really accepted by the Goths. We'd just hang on the periphery pretending we were never cooler than them. But it was just because they didn't accept us. I didn't look Marilyn Manson enough."

When he saw a bunch of people in a school talent competition playing guitars – "those guys were the kings of the school" – he learned guitar over the summer, started writing as many songs as he could and eventually ended up in a band with the guys he saw in the talent contest. He grew up a Radiohead obsessive, played in lots of bands, fell out of love with music in his late twenties, stopped writing music and started playing it with The Twilight Sad which reminded him why he liked it in the first place.

He says he's now obsessed with music again. Ask him about ambition, and he'll tell you "I just want to be king of the school, still."

Travel 30 odd miles north and a few years into the future, and you'll find a 16-year-old Lauren Mayberry playing in small-town bands in Stirlingshire, when "gigs put on in Thornhill village hall are the biggest thing that's going to happen to you all year". At high school a "very lovely and very religious" woman stopped her in the car park to give her a pamphlet explaining how playing rock'n'roll opens you up to the devil. She decided to take her chances anyway.

Rewind a few years and head south-east to Whitburn where Iain Cook is growing up in the church.

"My parents are both members of a church that is a spin-off from one of those American charismatic, speaking-in-tongues, falling-about-on-the-floor type places. In many ways it has really negatively affected my life and my personal development, but in other ways it has been really positive.

"Being a musician is one of them because you are thrust into this world where people are communally singing and playing together two or three times a week, and from a very young age I was learning to play bass guitar and figuring out chord changes and harmonies, singing and playing at the same time."

When he was in his early teens he'd go down to his grandparents' house because they had a video player (banned in his own house). "My gran would make me a big pile of bacon rolls and I'd watch Prince videos, Madonna videos, everything that was illicit in my house. And I think that was part of the appeal for me; that it was dangerous, it was dirty, androgynous and my dad would freak out if he saw it - My grandfather wasn't so keen on it either."

Cook and Doherty met at university, played in bands together and always talked about doing something together. "We had talked loads of times every time we got drunk," recalls Doherty. "It was actually our friend Campbell, who's now our manager, who forced us into the situation. He really pushed for it and pushed for it. Because I wanted to quit. I was bored. I was 28 years old at the time and ready to get a real job and stop being a fool -"

They met Mayberry, came up with a name ("I felt it was big and bold and it was one word," says Doherty), then stylised it with a V just to make it more Google-friendly, posted a song on the internet with little or no accompanying information, and suddenly became a phenomenon.

"No amount of fancy viral marketing is going to make people excited about songs," says Mayberry. "We were really lucky to have that amount of natural enthusiasm directed towards us at that stage. It was super-encouraging."

Now they've arrived at somewhere. It's probable that they won't be playing to 15 people in The 13th Note any more. They have different issues. Doherty is worried about how they are described. "While our music has pop sensibilities, I don't feel we're a pop band." The three of them are coming to terms with contracts and record deals. "Ideally I wouldn't have any decisions to make other than: 'Is that synth loud enough?'" admits Cook mournfully. And Mayberry is negotiating the pressures put on women in the music industry, the notion that"if you're a girl in a pop band you should dress in certain ways, you should be in certain magazines. I'd have to wear short skirts and crop tops and you guys would have to lose the beards."

Don't expect that any time soon. Chvrches are too razor-sharp and razor-averse for that. Now if Mayberry could only find out where Peaches got her facial hair-

Chvrches headline The Garage, Aberdeen on Wednesday and play Edinburgh's Corn Exchange on Thursday (supporting Two Door Cinema Club)