In the three-and-a-half years since their fourth album, GLA, a quiet revolution has occurred behind the scenes for Glasgow's Twin Atlantic. They've switched label, adjusted personnel, adapted their sound, returned to their home city to write their first album there, and yet, if anything hasn't changed, it's the choruses.

'When we write music together we just can't help ourselves,' laughs the band's singer Sam McTrusty, when it's pointed out that the hooks of key songs like 'Novocaine' and 'Barcelona', from the new record, Power, are still so large that an ice-pick would be required to scale them. 'There's just something particularly satisfying about knowing you can write a song like that. A lot of people pick up on that about our band; "the choruses are massive, how do you do it?" We wish we could be a bit more chill about it, but we get satisfaction out of crafting them, because it's a tricky thing to get right.

'On this record there's a lot more range than any of our previous ones, though,' he continues. 'Before, maybe we relied on an angsty, chopping style to tell a story. This time it's about instrumental textures, or the sound of electronics butting head with acoustics – it's a new way of working that we've embraced, which gives us a bit more of a canvas to write on in future. People seem to be embracing it, which is encouraging for us.'

The creation of this record has brought a moment of truth for Twin Atlantic. Following GLA they departed their previous label, Red Bull ('out of necessity and not design, if I'm honest … we managed to negotiate ourselves out of our previous deal,' says McTrusty), and the group set about life as an independent band, which they hadn't been in more than a decade. They were also now a trio composed of McTrusty, bassist Ross McNae and drummer Craig Kneale, with guitarist Barry McKenna officially leaving the group in 2019, but remaining as a live member.

'He's still a big part of all our lives,' says McTrusty of McKenna. 'Creatively we'd just reached a point where, similar to the record label, how we were creating songs maybe got a bit formulaic, too comfortable, and we all needed to up our game in some ways. It was the way we felt was best for the band to progress, and for Barry … it's been the best situation for all of us, for different reasons. We took the more modern, adult approach, rather than the old school rock 'n' roll approach of all falling out!'

The trio turned their rehearsal space in the East End of Glasgow into a writing and recording room, initially with the intention of just working up some demos. 'All of a sudden we were working independently, which is how the band kicked off,' says McTrusty. 'Working on music because we wanted to, with no advice or guidance from anyone – we basically ran with that and became addicted to it, the sense of being in control. All of the limitations we now had (compared to past recording sessions in well-equipped LA studios with big-name producers), we just channelled into the music, into our work ethic. This made it a much more personally satisfying record.'

He and McNae, in particular, worked as producers, and they opened up to a new range of influences. Where their past albums rocked, taking in aspects of emo and arena artists like Biffy Clyro, now they were looking to unlikely personal influences including Depeche Mode and LCD Soundsystem. 'Recording on our own, I suppose we were just looking for some short cuts,' says McTrusty.

'We found that by embracing the technology of recording software and lopping drum machines and things like that, we were able to work a lot faster. Initially it was a lazy answer to throwing a song together quickly, but then we didn't really want to replace these sounds with guitars. We liked the palette of sound choices we had, everything just suddenly went widescreen.'

Within time, they found the autonomy they had over sound choices wasn't just bringing together the beginnings of an album. 'We were making demos to shop to people, for them to maybe finance us to go and record another album,' says McTrusty. 'But we were doing something a bit more exciting and, I don't know, genre-stretching. Not just sticking to one lane. What we recorded encouraged us to keep going on our own, and it snowballed over a two-and-a-half-year period. At the end of it we found ourselves with a fully finished album, which Virgin EMI jumped on.'

McTrusty says that he'd also set out to write songs which were less personal on this record, which gave less of himself away; he has, after all, been in the public eye and writing lyrics since his late teens. 'I might have focused on that a bit too much in the past, where the songs might have been me trying to unpack things that had happened in my childhood or adolescence,' he says. 'But I suppose that's what everyone does in their twenties, try and process that and figure out what type of person you are.

'For this album, I went into the studio with nothing written. Again, it's what I was saying about embracing limitations; the idea was that, because I was writing with Ross in the room, the lyrics would match the tone of the music we were making. But I just couldn't help myself, the music took me to a more introspective place where a lyric would creep out and by the time we got to the big chorus, I was a victim of the emotion of the song myself.

'A lot of the personal stuff I'd written before was more cryptic, more shrouded in metaphor, whereas, for example, 'Novocaine' is me telling of how I met my wife and the sort of high she gives me. It was a different perspective to give, the excitement of a new kind of love as opposed to one that's broken down, which most guys with guitars write about.'

It's also possible to hear an amount of religious symbolism in his lyrics, I tell him. 'Religious iconography has always interested me, because I grew up in Glasgow and I went to a religious school, I was forced to go to church on a Sunday and all that,' he says. 'I've always had my eye on various different religions, and so many different cultures are crossing over right now, with the world getting smaller and so much information out there, and there's always something that's bringing people together or causing massive upset and divide.

'It's a particular hotspot moment for politics, and I couldn't help but go to that confused part of my mind where religion stirs the pot. Maybe that's because I was raised in Glasgow, I don't know … there's an underbelly that's been bubbling up a bit more in the last few years, I don't know if that's because of politics or football or what, but I've always tried to write honestly about what's going on around me.'

Ask him, though, and he's proud to be in a band from Glasgow, from his home city; and one which deserves more recognition as one of the city's serious success stories of late – not just a pop group for the youth, but artists who have moved with the years and brought their experience to their records. 'We do feel a bit … maybe triumphant is a bit much, but vindicated,' he says of the process of bringing Power to life. 'To be signed off your own merit, rather than the hope that you might do something good, was a huge confidence boost for us.'

Power is out now. Twin Atlantic tour the UK throughout March.