Emma Pollock has long written songs for wonders that we cannot touch.

She serenaded chemical reactions – light and heat; smoke and sound – on her 2007 solo debut, Watch The Fireworks. She sang torch-songs stoked by probability theory for 2010's The Law of Large Numbers. And now Pollock – former member of Mercury-nominees The Delgados, co-founder of Scotland's revolutionary indie label Chemikal Underground, and one of our most vital, poetic and singular voices – has just released a career-high, thanks to In Search Of Harperfield.

It's a record that explores and excavates secrets and identity; life and loss; memories, ghosts and shadows that we cannot quite define. And cannot hold.

It is a remarkable, beautiful album that conjures jazz, pop, punk, rock, chanson and Laurel Canyon: an inventive, physical force of nature that builds a world from stories and characters – real and imagined – then swoops and soars around it. It sings of wolves and vacant stares, of monsters in the park and betrayal, of dark skies and clemency and alabaster. Its roots are in Pollock's family landscape – the titular Harperfield is a house that her parents inhabited before she was born; that looms large in her mind, despite having never lived there herself – and throughout you can discern the echoes of a parent lost (her mother died last year) and the hard-won life of another (her father has been seriously ill). Its secrets, too, are ground(ed) in ancestry. “They destroyed my mum,” says Pollock.

You might notice that her surname is turned upside down on the album cover. And little wonder, given the record's eddying sense of reflection, and its upending of roles and identities. Lives and bonds are frayed, untethered, uprooted. Buried. The sun comes up.

Emma Pollock grew up in Castle Douglas, played the violin, loved music, but never played in bands at school. Nonetheless, her teacher, Mr Davidson, chalked up her vocal talent. “He told my mum and dad one parents' night that I could be a folk singer – and I was like, folk? How?” she recalls with a laugh. Folk was about the only thing she didn't listen to at home. “My mum and dad were huge trad jazz fans, my mum loved Ry Cooder – that was my first concert – and Bonnie Raitt. Along with Nick Drake and Joni Mitchell, I listened to Frankie Goes To Hollywood, Erasure, Kate Bush, Depeche Mode. I have a pop heart.

“One of the things that really switched me on was New Order,” she continues, and lists their charms, which bear a distinct kinship to her own. “Their melodic sensibility. The coolness of their presentation and production, but the warmth of the pop. And the voice – there's a subversion going on with New Order,” she says. “You take pop music, and then you sing with that almost deadpan delivery.

[Bernard Sumner's] been slagged off for not being able to sing, but that's what's interesting about a vocal performance: it doesn't have to be technically good. It's never really been about that. That's why I think the X Factor is so, so reprehensible. Because they miss the very thing that gives a vocal its essential nature. And that is character.”

Pollock's own voice calls to mind Dusty Springfield and Chrissie Hynde, but sounds like no-one else. It's effortless, languorous even, yet thrilling. “I try to stick with that understated thing,” she says, and it is hard to overstate how very good she is at that. Yet it was a city, not her voice, that compelled her to make music.

“Glasgow was the force,” she says over soup and loud tunes in the CCA. “There was just so much going on. I came to study physics, then I met Paul [Savage, her husband, producer and former Delgado] at university, and realised there was loads of music around here. I started engaging with other bands. I started writing too. And I gave Paul some songs.”

They went on to form alt-rock heartbreakers The Delgados with friends Stewart Henderson and Alun Woodward, and soon thereafter, in 1995, the band launched Chemikal Underground – a label that released early records by Mogwai, Arab Strap and Bis, as well as their own, and which thrives to this day with acts like FOUND, Miaoux Miaoux, RM Hubbert, Bill Wells and Aidan Moffat. The label's Chem19 Studios, run by Savage, also bears noting: it's been responsible for records from King Creosote, Franz Ferdinand, Deacon Blue and Calvin Harris. Our musical landscape, it's fair to say, would be considerably more barren without The Delgados, who split amicably in 2005. There's a resonant line on chamber-pop aria, Dark Skies, where Pollock sings, “They gave us a stage, to write our own page of history”. And so they did.

There are myriad histories on In Search Of Harperfield, which also ruminates on the people our parents might have been before we were born. Pollock's father played clarinet, and loved to work the land (that's him on the album cover). Her mother could clock a pop hit at fifty paces.

“She told me the Bangles' Eternal Flame was going to be a Number One the first time she heard it,” Pollock smiles. “She was amazing.” Her mother died in February last year, on the same day as Pollock's maternal grandmother, and one often seeks – or offers – solace in such uncanny patterns when life, and death, throws them at us. But as the album's blind-siding opener, Cannot Keep A Secret, intimates, there's a great deal more to the story than that.

“My mum was born out of wedlock to an Irish girl in 1937,” Pollock offers. “My gran lived in Donegal, and when she got pregnant, she was dispatched to Glasgow. She had the baby, and there was a fairly forced adoption policy, so my mum was taken home by a cleaner of the hospital – kind of unofficially – and raised in Stobhill.

“My gran moved to London, she was a bit of a wild child – she knew Kenny Everett, she ran flats and a hotel,” she continues. “My mum and gran never really had a great relationship, so I didn't see my family in Donegal much.” There are three sisters referenced in Cannot Keep A Secret, who knew nothing of Pollock's mother, and vice versa, until two years before she died. “I've got three aunties in their sixties I didn't know about – and all because of 'The family shame'”, she says.

“It destroyed my mum, that whole thing. Destroyed her. And it's very common. That destruction of families. Horrendously common.”

Despite such devastation, In Search of Harperfield is not an angry album. And nor is it all about Pollock and kindred secrets and ties.

“Not at all – a lot of it's just daydreaming and exploration of character,” she says. “Quite a few songs seem to be concerned with very old testament ideas – betrayal, retribution, punishment. Maybe I'd been watching too much Game of Thrones,” she laughs.

Pollock's lyrics are cerebral, ambiguous and articulate, yet never heavy-handed. “I've never had any doubt that I want to write lyrics that are slightly too difficult to understand, so that nobody really knows what I'm talking about, but they're evocative enough for people to get their teeth into,” she says. “They're to be understood and interpreted in any way the listener chooses. And that's brilliant.

That's when art permeates people's lives.”

Was there a particular title, or image, or manifesto, that gave Pollock a feel for the album she wanted to make? “I began to realise that song was the enduring principle,” she reflects. “It didn't matter what vision we had going into the studio – what we had was the that holy trinity of music: rhythm, melody and harmony. And if ever there's been a lesson in the simplicity – or complexity – that offers, then this album has been that. It's got all these disparate elements; all these different ideas and tempos and genres. But at the end of the day, it's still me, it's still Paul, it's still our sensibility as musicians. You have to have faith that there's a thread. You've just got to try and find it.”

Our grabbing hands grab all they can. We grapple in the dark for roots, connections, recollections and humans to wind around ourselves.

We get wrapped up in secrets, lives, and loves, and myriad real and imaginary yarns. Sometimes we find magical, abstract things – like beats and words and melodies – that can unravel the world around us.

If we're lucky, those records are liberating and uplifting, and waste nothing. And, on very rare occasions, they light up the sky, they serenade science, they embrace family, landscape, home, pop music and the jurisprudence of large (and small) numbers. This is one of them.

Everything counts.

In Search of Harperfield is out via Chemikal Underground on January 29. Emma Pollock plays Oran Mor, Glasgow, as part of Celtic Connections, on January 29. www.chemikal.co.uk