In 2003, Scott Hutchison started bribing record buyers with biscuits.

He'd post them out with CD-Rs, dispatching tunes and crumbs to distant quarters, and he did so under the name Frightened Rabbit – a moniker inspired by Badly Drawn Boy, and bequeathed by his mum on account of his shyness. His brother Grant soon wanted in on the action ("he threatened his way in," jokes Scott) and since then, the Selkirk-raised singer/guitarist and drummer have grown into a Glasgow five-piece with three highly acclaimed indie albums to their name (not least 2008's exceptional Midnight Organ Fight), while a terrific major-label debut, Pedestrian Verse, is set for release via Atlantic next month.

After a celebrated stint on Brighton indie Fat Cat records, Hutchison acknowledges that there's a sense of trepidation in moving to a global conglomerate. "It's a fairly standard, well-trodden tale, isn't it? 'Band gets ruined by major label'," he muses, stirring his tea in an Edinburgh pub. "And of course I totally shared that concern. At one point I was paranoid that they were stringing us along, that they'd never actually put our record out – you hear these stories. But it was all in my head. And there was no meddling whatsoever; there was lots of discussion, but the final say was ours."

Hutchison had reason to be wary. Legend has it that the resolutely indie Frightened Rabbit turned down a major-label deal with Fiction in 2007, preferring to sign to Fat Cat, but the truth is rather more dispiriting. "It was a really horrid time," he recalls. "I'd put all my eggs in the Fiction basket, I'd even quit my job, and they withdrew their offer at the last minute. I'd actually thank them for it now, because we weren't ready, and it made us more resolved. We really thought, 'if this doesn't kill us off, nothing will'; but at the time it was like, 'Oh right – nothing.'"

This time the band are undoubtedly ready – eyes open, riffs blaring, TV and radio appearances escalating – and they're grateful for the breathing space Atlantic gave them to make Pedestrian Verse.

"A lot of the guts of the record came from us in a room playing live, which is the first time we've done that," Scott says of brother Grant (drums), Gordon Skene (guitar/keys), Billy Kennedy (bass) and Andy Monaghan (guitar/keys). "So we needed time to bring the songs to a boiling point. It also taught us to be a bit more brutal about what we put in the bin. [Producer] Leo Abrahams was really important for that. He introduced us to his attitude which was like, 'if it's not doing anything, if it's not contributing, it has to go'. We cut the songs down from 20 to 11. And in that sense, while it's not a sparse album, it's certainly more concise and decisive than our previous records."

True to this, Pedestrian Verse is a lean yet raucous record – from the God-lambasting drive-rock of Holy to the undulating hymn of December's Traditions – and it looks set to follow the indie-to-major stellar trajectory cast by alt-rock bands like Biffy Clyro and US label-mates (and recent touring allies) Death Cab For Cutie.

There are clear advancements on the record – a more live, band-focused approach; subtle yet surprising, forceful arrangements – but so too are there echoes of Frightened Rabbit's earliest works.

Pedestrian Verse's thrilling centrepiece, Late March, Death March is a beat-led power-pop anthem that traces Frightened Rabbit's career back to Scott and Grant's nascent days as a guitar-and-drums duo who recorded in a shed.

Grant nods. "I had a discussion with someone about that. They said that their problem with [2010's third album] The Winter Of Mixed Drinks was that our two-piece thrashing drums and guitars thing had gone, and that was the sound that they thought was our band. I kept that in mind this time round – I didn't want to replicate [2006 debut] Sing The Greys, but I thought it was important to keep our identity."

The band's most recent recruit, Gordon Skene, agrees. "Late March, Death March was one of my favourite songs to record, because we were all stood around in a circle, playing the drums," he smiles. Skene joined the band's ranks in 2010, but retains a fan's ear for their appeal. "Having been a massive fan of those early records, I knew what I really liked about them, so if something cropped up in the writing of the new one – like the way Housing (In) returns later on in Housing (Out) – I'd be like, 'right, I'm getting that feeling again, that needs to be in here.'"

Another immediate album standout is new single The Woodpile, a swaggering alt-rock anthem that's finding great favour with Radio 1. "We've never recorded a song as many times as The Woodpile," Grant laughs, which is testament to Atlantic's constructive input, and to the band's ambition.

"I think we did it six times. But people at the label knew that something like this [mainstream support] could happen with this song, so it was a case of trusting them and the radio plugger," he says. "They know what they're doing, they've worked on loads of big hit records – that's why we did so many takes. We wanted to get it totally right."

Despite The Woodpile's colossal charms and potential for amassing new audiences, the band were eager not to alienate or wrong-foot existing fans – hence the release of last year's State Hospital EP, whose tracks included a glorious duet with cult-pop versifier Aidan Moffat. "I think that if we'd opened with The Woodpile, without State Hospital coming before, it might have sent the wrong message," offers Scott. "I know what kind of song The Woodpile is, and I kind of knew that when I wrote it. It's the most commercial thing we've probably ever done, so I think that State Hospital maybe reassured people before it."

It's interesting how State Hospital is assimilated and re-contextualised within the album, and it illustrates the versatility in Frightened Rabbit's work. The song evolves from a convincing lead single to a long-player linchpin that offers literal, abstract and musical respite – chiming guitars, atmospheric arrangements, drums like heartbeats, and a promise that "all is not lost" – and it also gives the album its title. Given that Hutchison's canon has long been consumed by disease (The Modern Leper), disembodiment (Head Rolls Off) and (lack of) faith (Holy), does State Hospital suggest that, maybe, things are getting better?

"Well, I think there's a wee bit less disease on this one," he brightens. "State Hospital and Acts Of Man set the tone for that in a way – they were the first two songs that I wrote for the record. I kind of wrote them as a pair, and they set off a slightly new set of metaphors and language that seeped into the rest of my writing."

Pedestrian Verse's lyrical idiom remains vivid, corporeal and distinct, from bass-chug Dead Now's "devilled kidneys" to Late March, Death March's "funeral in your eyes". Why the continued obsession with anatomy, theology and mor(t)ality? "The reason I use a lot of religious and bodily imagery is because it's a language everyone knows, so it hits you," Hutchison offers.

"It's not exclusive, there's an immediate fast-track to its meaning, and whether or not you're religious, it still means something to everyone – it's very powerful, it has great weight behind it. And it immediately adds a certain tone and reverence, I suppose."

State Hospital's kindred song, Acts Of Man, is an arresting, piano-led album opener that sees Hutchison make a rare and show-stopping foray into falsetto. "I like using it for some of the most brutal lines, but I also thought that emasculating voice was quite important for the theme of that song," he says of a tender yet furious psalm that touches on misogyny, domestic violence and male braggadocio ("one man tears into another, hides a coward's heart in a lion's chest").

There is something else in Acts Of Man. It happens at three minutes, 40 seconds into the track. It's a familiar chord, a warm cadence, that says: "We are here, we are still the same." Just at that moment, the vocalist sings: "I am just like all the rest of them", but don't be misled: Hutchison and his outstanding band are anything but that.

The Woodpile is released on January 28; Pedestrian Verse is released on February 4. Frightened Rabbit play the Picture House, Edinburgh on February 26; Music Hall, Aberdeen on February 27; and Barrowland, Glasgow on February 28