Caroline Polachek was writing about the danger of trying to change for somebody from her first hit with indie-pop group Chairlift. “I tried to do handstands for you,” she sang on 2008’s twee yet melancholy Bruises, which made the Boulder-to-Brooklyn transplants ubiquitous after it was used in an iPod advert. The charming track caught the trio in a similar bind with their audience. “Even when we released our second album, which was much grittier than the first, people pushed back and said: ‘We want more Bruises,’” Polachek recalls.

To their credit, Chairlift never caved in. Over three albums, the trio-turned-duo easily outstripped the fast-diminishing Brooklyn indie scene of the early 2010s. She and Patrick Wimberley were as fluent in 80s Japanese pop, esoteric English songwriter Virginia Astley and opera as they were contemporary R&B. They split, amicably, in 2017, proud of their distinctive sound, says Polachek, if disheartened by the limited perceptions of what an indie band could become.

Polachek had released a pop album as Ramona Lisa in between Chairlift’s second and third albums; Beyoncé ended up recording a Ramona Lisa castoff, No Angel, on her self-titled fifth album. An ambient record, billed to CEP, followed Chairlift’s split. The shifting names, she says, offered conceptual limitations that guided her work. Pang, her first album under her own name, arrives free from such scaffolding – so much so that it was never supposed to exist. Thankfully, it does: it’s among the year’s finest experimental pop albums, blending acoustic and synthetic textures into a surrealist yet affecting listen. Co-producers Polachek and PC Music alumnus Danny L Harle wield elegance and precision worthy of a sushi master, or peak-pop Peter Gabriel.

After Chairlift split, Polachek felt her life lacked structure. “I figured I would just try a bit of everything,” she says over lunch in Paris last month. She’s here for fashion week and her outfit suggests someone at home there: a leather vest over a blousy white shirt that makes Polachek, with her striking, almond-shaped face and wide eyes, look like a modish Joan of Arc, whereas I would look like an employee at a medieval-themed restaurant. In summer 2017, she was in LA to write songs with Harle, the idea being to pitch them to Katy Perry. A magic-mushroom trip made her second-guess her plans. “I remember thinking: what I do with my time right now is really going to determine what happens next,” she recalls in her cut-glass accent. “I shouldn’t be wasting my time on things that I don’t care passionately about.”

When she called Harle to cancel, he suggested they write for her instead. Polachek had been making a “warmer, auburn, folk-tinged, peaceful” album titled Calico that she didn’t see working with the hard, shiny, electronic sound Harle was known for. Still, she agreed. Perhaps inevitably, they came up with something that overshadowed Calico and kickstarted a fruitful collaboration. Their first song, Parachute, “is about a total loss of control,” says Polachek. “And it’s not giving that control up to another person, it’s giving it up to life – and that’s the scariest thing.”

Like a peak-pop Peter Gabriel ... Caroline Polachek. Photograph: Nedda Asfari

It turned out to be premonitory. Polachek had been experiencing inexplicable adrenal rushes that stopped her from sleeping and accelerated her metabolism. She called them “pangs” and sought to recreate the sensation in her sessions with Harle. “I couldn’t tell if my excitement about all these musical breakthroughs was triggering my body,” she says, “like I was manufacturing drugs internally.” Six months later, her marriage of two years ended. “All these structures that had seemed essential to my identity and my time fell away,” she says. “Everything happened very fast. I felt a giant shift within myself that caught me by surprise. As much as I fought against it, I had to learn that the body knows more than we do.”

Polachek had felt rooted in New York in her relationship. Then she experienced “what Joni Mitchell calls the hejira, this need to fly to another place,” she says. “A lot of the music comes out of that conflict of wanting this other thing and feeling guilty about wanting it, and then it guiding me somewhere despite my kicking and screaming.” She is opaque about the relationship “out of respect for privacy”, she says carefully, welling up a bit. Following those impulses entailed “a digestion of shame and self-questioning that, nonetheless, led to a resolution that things would be OK”. She felt she was running towards something rather than away from it, although she admits she felt burdened by “a crystallised idea of what the world was” in New York – even though the Brooklyn heyday was over, she still saw the same faces on the street every day. “I felt like it was a weight that was always on whatever I did.”

She is more cutting in her lyrics, which repeatedly touch on being asked to change her nature. “When I stop caring, you stop caring,” she sings on I Give Up, which crests on a frustrated heave of a chorus. (Polachek describes her music brilliantly: “The whole song is an expression of apathy, and I wanted it to feel like something was being chucked really hard.”) She had never written that plainly before, though it came easily. “Chairlift felt like a comfort blanket because Patrick and I were like brother and sister,” she explains. “But it subconsciously imposed a platonic neutrality over everything we did, which stopped me from approaching things with a certain emotional intensity. I wanted to make sure he felt like he could get behind everything.”

Polachek has found transitioning into a solo career easier than expected, it bringing new fans who hadn’t followed Chairlift. “I felt the perception of what I was doing as ‘indie’ was going to travel with me, but it hasn’t at all, which is really exciting,” she says. Aged 34 and with 12 years in a band behind her, she had worried about being a late starter, a notion she made herself reject. “I’m just beginning,” she says. “I think women are taught in the music industry that once you’re 35, you’ve expired, and I’m here to prove that factually incorrect.”

There’s just so much more public female intellect on display now than there ever has been Caroline Polachek

The week we meet, Polachek tweets that her new album had marked the first time that journalists asked about her vision, not her appearance. “There’s just so much more public female intellect on display now than there ever has been,” she says when I ask why that might be. “Young people have realised that an artist is in charge of what they’re doing – this crazy cynicism that artists were puppets has disappeared. They have [music production software] Ableton Live and know how hard it is to write a song.”

If Polachek clings to any vestiges of the late-00s Brooklyn scene, it’s that DIY mindset: she directs her videos and recently started her own imprint within Sony, Perpetual Novice. “I do way more of my own stuff than I should be at this point,” she says. “I’m so obsessed with doing it myself.” Although in person her thoughtful answers and clarity evince academic-level focus, she describes herself as “easily distractible”, always divided between four different endeavours; even this short stay in Paris has produced a possible new musical collaboration. Not only does Polachek not want to know what other people think she should be doing, she doesn’t want to preordain it herself. “I want to keep different options for different futures open all the time.”