You could easily get the wrong idea about Kathryn Joseph.

You could see her poised at her vintage piano and envisage a fragile balladeer. You could pore over her earthy song titles – The Good, The Mouth, The Bird – and expect a romantic singer-songwriter. You could read about her beating the likes of Paolo Nutini, Belle and Sebastian and Young Fathers to scoop this year's Scottish Album of the Year (SAY) Award, and imagine the win was a bit of a shock. But the only one truly surprised was Joseph. Some of us weren't surprised at all.

At the start of this year, Glasgow label Hits The Fan quietly issued Joseph's debut album, Bones You Have Thrown Me And Blood I've Spilled. The imprint, run by Claire and Marcus Mackay, released Frightened Rabbit's debut album, Sing The Greys, back in 2006, and then went into hibernation – until they heard Kathryn Joseph, an Aberdeen musician who had, by chance, moved in next door.

Her album arrived without fuss or fanfare: a record wrapped in brown paper, which looked, and felt, and sounded, timeless – from its sepia imagery and organic idiom, to Joseph's crackling voice and down-home piano. Its titles scanned like gothic literature chapters – The Blood, The Bone, The Crow – and its bruised, biting lyrics followed suit. And as for the songs? They were exquisite.

Joseph herself appeared, at that point, to be nigh-on hermitic: no photos of her were in existence, no interviews had been conducted. Little was known about the woman behind these visceral, striking, resilient songs. And so we supposed that she might be shy and retiring. A quiet soul. But we were wrong.

Which is why, on a Friday night in Glasgow, what begins as an interview over wine ends up as one of the most expletive-ridden, cackling exchanges I've ever had the pleasure of transcribing. Joseph is immensely good company – self-deprecating, honest, barbed, and clearly absolutely thrilled by the widespread loved-up response to her album.

She's been performing for the best part of two decades, but never thought she'd make this record.

“People always came to my gigs,” Joseph says of her early days playing live in Aberdeen. “But I never thought I could deal with the stuff that comes with putting out an album – the interviews, the thought of speaking on-stage, let alone having my photograph taken. That all just filled me with absolute dread.”

Joseph doesn't speak of this lightly. Early press photos depicted a woman with her face scored out in biro. “I've always hated what I look like,” she offers. “For me, the point of playing live was because that's the only time I don't think about it.'” For a time, Joseph even believed that the awestruck silence she commands when performing was invoked by her appearance. “I always wondered if it was because I gave everyone the creeps,” she recalls, rolling her eyes at herself.

This telling sense (misplaced or otherwise) of not living up to the archetype – or expectation – of a female artist was also a contributing factor in Joseph's rejection of a record deal with Sanctuary 17 years ago.

“They offered the same amount as I was making waitressing, and they were like, 'You don't need a manager – here's your manager!', and I recorded some sessions and they were like, 'Here's your album!', and there was this total awareness of me being a little girl with no-one around me who knew anything about it. It was all very weird,” she recalls. She turned them down.

She continued to work and perform in Aberdeen until around five years ago, when she moved to Glasgow and met Claire and Marcus Mackay. Marcus, a musician and producer who runs Glasgow recording studio The Diving Bell Lounge, heard Joseph support John Knox Sex Club and fell for her songs. He persuaded her to record with him on production duties and stealth percussion.

His wife, meanwhile, was instrumental in convincing Joseph that she should release – and, more pertinently, promote – the album. “Claire goaded me into it,” says Joseph with a laugh. “I told her I didn't want to do interviews and photos, and she said, 'Well, you'll just have to get on with it.' That was me told.” (It bears noting that Joseph's entire team – her label boss / manager, her PR, her pluggers, her photographer – are female.)

Since then, her face has been all over the papers, all over the telly. Has it been liberating to learn to let it go, to stop hiding away?

“It totally has,” she nods. “And the weird thing is now, when I look at the SAY Award photos, I don't actually mind what I look like. All I can see is how f***ing happy I was. I don't care any more. Liberating really is the word. You get perspective as you get older. And having kids makes you realise it doesn't matter. Plus, it makes you realise how little time you've got.”

Joseph has a four-year-old daughter, Eve. Five years ago, she had a son, Joseph, who was born three months prematurely. He lived for a week, and his life is at the heart of the album. “He was completely fine for the first week, but then he had a ruptured bowel,” she recalls. “We got phoned by the hospital that night telling us it was bad news, and on our way I said to my partner, 'If he doesn't make it, if he doesn't live, I have to do music.'

“I know it was a weird rationale,” she says of her coping mechanism. “But that's how I felt. And the luckiest thing was, two months later I was pregnant with Eve. She's f***king amazing. She said to me the other day, 'Mummy, you're complicated.' And I was like – 'Oh! What do you mean?' And she said, 'Because you're beautiful and lovely,'” she laughs. (Eve is spot-on.) “To be honest, I think she got that line from My Little Pony, but I loved it.”

Joseph is at pains to point out that this album is not about the loss of a child, save for its devastating swansong, The Weary.

“The songs are all over the place,” she offers. “They were written over the last ten years, and I think they show how much we think we change, and how little we really do. I know that in a lot of interviews people think the songs are all to do with my baby or whatever, but to be honest, most of them are about boys. They're about boys that f***ed me over.”

A glint in her eye. “And now I want to destroy them.” She throws her head back laughing.

This time last week, after toying with the idea for years, she officially changed her name from Kathryn Sawers to Kathryn Joseph by deed poll. Her daughter's middle name is Joseph and her boy, of course, was Joseph too.

What's the symbolism of the name? Is it a biblical reference? A Haydn homage? A nod to Conrad's Heart of Darkness? “I've just always liked the name Joseph,” shrugs the woman who won the SAY Award then danced until the sun came up. “I remember it was written on a lamp in my house,” she says smiling. “I don't know why”. Where there is darkness, there is light.

Kathryn Joseph’s new single The Bird / The Worm is out on 27 July.

Live at Wickerman Festival this weekend, Glasgow Hug and Pint August 1, Belladrum Festival August 6-8.