NEW YORK • What comes after heartbreak? For Bjork, it is "a love letter to enthusiasm and optimism", she said.
Her darkly formidable 2015 album, Vulnicura, reflected the break-up of her decade-long relationship with artist Matthew Barney in songs of nearly paralysing pain and simmering anger, weighted with dissonant strings.
But her new album, Utopia, prizes airiness: the breath that powers voices and flutes; the atmosphere where birds fly; structures and tempos that change freely rather than being locked to a beat.
The album, due on Friday, is the latest iteration of Bjork's career-long fascination with how nature and technology can interact.
In an interview at her apartment in Brooklyn, New York, she said Utopia had long been her working title for the album.
While making it, she read extensively about utopias: in academic studies and in stories through the centuries, from ancient fables to the science fiction of American writer Octavia E. Butler.
"Utopia has gone from everything being monasteries to feminist islands to socialism to Peach Blossom Spring," she said, referring to a tale of an isolated, idyllic community that was written in the 5th century in China.
If optimism ever was like an emergency, it's now. Instead of moaning and becoming really angry, we need to actually come up with suggestions of what the world we want to live in, in the future, could be.
SINGER BJORK on why her new album, Utopia, suggests a post-Trump world
Last year's election of United States President Donald Trump only strengthened her determination to envision hope.
"If optimism ever was like an emergency, it's now," she said.
"Instead of moaning and becoming really angry, we need to actually come up with suggestions of what the world we want to live in, in the future, could be. This album is supposed to be like an idea, a suggestion, a proposal of the world we could live in."
Her proposal involves "that feeling, post-Trump, when everything's gone horribly wrong", she said. "And you escape to an island and there're a lot of women there with children and everybody's playing flutes and everybody's naked and there're all these plants you've never seen before and all these birds you've never heard before, and orchids, and it has that feeling of pioneering into a new world."
Bjork, 51, played a nearly finished version of the album during one of her brief stays in New York City this year, on a muggy day back in July.
After playing through the album on her stereo, she conversed volubly about the music across her kitchen table, over cups of strong coffee.
"I started thinking about this album as a city in the clouds," she said. "It doesn't have gravity. It's more like floating in the air."
The album concludes with Future Forever, with shimmering chords and her voice floating above silences; she invokes a benign matriarchy.
"Imagine a future and be in it/feel this incredible nurture, soak it in," she sings, then turns to tech advice. "Your past is a loop - turn it off."
But she has been ruminating on the past in the wake of the sexual misconduct allegations against movie producer Harvey Weinstein and others.
In a recent telephone call, she addressed an episode she had decided to air. In October, she posted on Facebook that she had faced unwanted touches and sexual advances from a "Danish director": clearly Lars von Trier, who directed her in the 2000 film Dancer In The Dark.
"I don't want to be self-important in this," she said on the telephone from Iceland. "There are women out there who got it way worse than me."
But when reading about Weinstein, she said, she was struck by "how he used the media against the ladies". Stories had circulated at the time of filming that Bjork was "difficult" on the set.
But she said: "I was very conscientious. I showed up for every shoot on time", until there was a dispute over control of her music.
"When I talked about this project with Lars, he always promised me I had full control of my music," she said.
"But I was turning up at dance rehearsals and somebody else had been editing my music in a way that was totally musically wrong. And they would keep telling me, 'Oh, it belongs to us now, it's not yours.'
"After two months of just turning up for every single thing and really just accepting all the harassment and just becoming part of the whole - just keeping on doing what I was told, basically - I had one weekend where I stood up.
"I could stand up as a musician and say, 'I'm not returning back to work on Monday unless I get full control of my music.' And that took one day. On Monday night, they said yes and then on Tuesday, I returned to work."
After her Facebook posts, The Guardian reported that von Trier had told a Danish newspaper that he had not sexually harassed her.
Attempts to reach him for comment for this article received no response.
Bjork described a far happier working environment during the making of Utopia. Like Vulnicura, the new album barely resembles music for pop radio playlists. The songs are akin to chamber music and to the electronic experimentation of Bjork's collaborator , electronic musician Arca (Alejandro Ghersi), who grew up on her music. "He knew my back catalogue better than I did," she said.
She has often based an album on a particular sonic palette: strings for Vulnicura, the human voice for Medulla. For Utopia, she turned to the flute, the instrument she played growing up.
To record the music she had composed on her computer, she gathered an ensemble of a dozen flautists, all women, for "Flute Fridays" in Reykjavik.
"I tried to get as many colours out of the flutes as possible," she said. "We went between the churches in Reykjavik, trying to get the right sound. Plus, I recorded a lot of the flutes in my cabin by the lake - trying to create this world where you have people hanging out in your living room, playing flutes and singing and making beats, but it's part of real life."
Her new songs take up the more immediate pleasures of music and burgeoning romance.
In Blissing Me, she sings about "two music nerds" falling in love by "sending each other MP3s". In Courtship, she looks into software-assisted dating.
"Vulnicura was the end of a chapter and this is the beginning of a new chapter," she said.