The musician St Vincent, a 34-year-old Texan whose real name is Annie Clark, is talking about body piercings. Though her outfit today includes such exotic items as a leopardskin onesie and a pink blazer made of some sort of wetsuit fabric, Clark doesn’t have any outlandish piercings herself; she just has droll and strong opinions about them, as she has droll and strong opinions about a lot of things.

“Didn’t it always make you laugh,” Clark says, already laughing, softly, in the museum in London where we meet one summer afternoon, “how people in the 90s who had, like, tongue rings? How they’d always make some sort of comment, intimating that it made them, like, better at oral sex? That was the whole wink-wink thing, right? That a tongue ring meant they were kinda kinky? But then, I guess the challenge – because they were constantly fidgeting with this gross thing in their mouth! I guess the challenge became: no one wanted to get head from them.” She hoots with amusement, just loud enough to turn heads in the hushed museum.

Conversation with Clark is like this: a bit unexpected, a bit arch, a bit sexy. She sometimes speaks so slowly and carefully it’s as if she’s reviewing individual words before committing to them. But, as with the lyrics of the songs she writes as St Vincent – always inventive, always making disarming leaps between ideas – you can never predict where her thinking will travel next. Quickly the chat about oral sex gives way to the matter of her own death, and her expectations of a brisk cremation. Before I know quite how, she’s got me talking about an irrational fear of being buried alive. “Get cremated!” she urges.

I ask Clark – who will soon release her fifth solo album, a follow-up to 2014’s self-titled St Vincent – why she suggested we meet in London’s Wellcome Collection, to combine our interview with a tour around the museum’s collection of antique medical equipment. Clark peers with interest at a display of old enema syringes and explains that in every unfamiliar city, “you should try to see something real and strange”. It was something the Talking Heads frontman David Byrne once advised her about touring the world, and she’s stuck to it ever since.

So far I’ve enjoyed the kind of success where I might get a free appetiser sent to my table. But it’s never a main

That phrase – “real and strange” – describes Clark’s appeal as a musician. She is a generational talent on guitar, one of those poised, unperspiring types who can do the manually ludicrous while hardly appearing to try. Seen live, Clark’s fingers flit over the strings of her instrument with utmost precision – that’s the real in her. The strange comes via the writing and the composition, which on her four St Vincent albums since 2007 have tended towards the experimental and jagged-edged. Lyrically, she might choose a thing (prostitution, CCTV surveillance, prescription drugs) and then chew it over in repetitive, often anguished ways, before elevating the mood with a sudden joke. “Oh, what an ordinary day!” she sang on a track from her last album. “Take out the garbage… Masturbate.”

Genre labels won’t stick to her. Song to song, Clark might channel Björk then Iron Maiden, then belt out a disco number before pretending to be a fey, shoe-gazing whisper-singer. In the manner of FKA twigs or Héloïse “Christine and the Queens” Letissier, she is a performance artist as much as she is a performer; last year Clark played a gig dressed as a toilet, complete with cistern, protruding bowl and flush. And like twigs, who for many years has been in a relationship with the Twilight actor Robert Pattinson, Clark has managed to cultivate a shadowy, unknowable persona while at the same time dating a wildly high-profile superstar. For 18 months or so, until a break-up made public last summer, Clark was going out with Cara Delevingne, arguably the best-known model in the world.

Facebook Twitter Pinterest St Vincent and Glass Animals play in London, February 2014. Photograph: London News Pictures/Rex

In the museum, while leaning over a glass display of clay death masks and shrunken human heads, we discuss Clark’s scaling achievements as St Vincent. From album to album, over a decade, her sales as well as her reviews have improved in happy tandem. The most recent album, 2014’s St Vincent, was her best to date, a wild, raucous thing, written in part during Ambien-soaked nights on tour, that eventually won her a Grammy. “It sounds like a very Pollyanna-ish thing to say,” Clark says, “but my ethos has always been to just make the music that I hear in my head. And I’ve been incredibly lucky, so far, that that’s seemed to correspond to external progress.”

Where does she place herself right now in the music industry? “So far I’ve enjoyed the kind of success where I might get, like, a free appetiser sent to my table,” Clark says. “And that’s awesome, I’m thrilled by that.” She fixes a level gaze before adding: “But it’s never a main.”

A word about her hair. Three years ago, while touring and promoting that self-titled record, Clark had a fantastic and unforgettable do – a triangular mountain of silver-bleached curls that made her look, in her own words, “like a scary cult leader”. I half-expected her to show up that way today, under the same teetering pile of silver, but Clark says the bleach killed off that haircut years back. She had to shear off her frazzled curls, “and then my look was less cult leader, more ‘Why do you have a rodent on your head?’”

She has a flair for naming her own haircuts, having cycled through such past constructions as “the Audrey Hepburn with anger issues” and “the Nick Cave minus the receding hairline”, and when I ask about the straightened black parting she has today, Clark decides: “I want to call this one... the Lara-Flynn-Boyle-in-the-90s.”

She isn’t quite such a speedy creator of names for her albums. The new LP still doesn’t have a title. I’ve heard about two-thirds of it and it’s superb – the same appealing, enigmatic, genre-spliced collision of ideas and influences that St Vincent fans cherish, only this time with a sleeker, more accessible through-line that ought to further expand her listenership. Some of the tracks, such as the scratchy, stirring Hang On Me, would work as well over the titles of a grand HBO drama as played through fizzing speakers in a dive bar. There are moments of peculiar, wonderful poetry. “Sometimes I feel like an inland ocean,” Clark sings, on a track called Smoking Section. “Too big to be a lake, too small to be an attraction.”

A number of the songs certainly sound as though they pick over the end of a serious relationship, in particular an astonishing meta-epic she has written called LA, which seems to be about a break-up (“How can anybody have you and lose you and not lose their mind, too?”), while at the same time being about a fiercely avant garde musician’s reluctance to do anything as obvious as write about a break-up. “I guess that’s just me, honey, I guess that’s how I’m built,” Clark sings, “I try to write you a love song but it comes out in a melt.”

Art suffers when people get into that too-big-to-fail mindset. Things get really boring when people get too risk-averse

Delevingne would be the most likely identity of “honey” here. But Clark is far too cool in person – and too determinedly non-specific as a lyricist – to admit to anything like that. “I don’t love it when musicians speak about their records being ‘diaries’ or ‘therapy’,” she says. “It removes that level of deep instinct and imagination that is necessary in order to make something that transcends.” She adds that such ways of talking too often become “erroneously gendered, in the sense that the assumption from the culture at large is that women only know how to write things autobiographically, or diaristically, which is a sexist way of implying that they lack imagination.”

This being said, Clark concedes, “my whole life is in this record. And this is one of the first interviews I’ve done about it. And I guess I haven’t 100% figured out how to talk about it. I mean…” She laughs suddenly, a brilliant, solemnity-shattering hoot. Clark is aware there will be an assumption that a lot of her new songs are about her ex. “I’ve really got to figure this out, right? If I’m going to ever be able to talk about the record?”

As is her custom whenever she’s finalising an album, Clark has currently placed herself in what she calls “deep nun mode”. Single. Work-focused. “Completely monastic. Sober, celibate – full nun.” I’m pretty sure she’s joking when she adds, in her slow, funny, unpredictable way, “I mean there are always sex plans. But none for, like, a month.”

Facebook Twitter Pinterest Photograph: Arcin Sagdic/The Guardian

Clark was born in 1982, briefly an Oklahoman before her parents separated and Clark relocated with her mother and two older sisters to a suburb of Dallas, Texas. “My mom was a social worker. She dedicated her life to doing very admirable things. One of my sisters more or less followed on that path, making the world a better place. But I did not.” Though Clark would see her father during school holidays, she describes her teenage years as “matri-focal”. She was surrounded mostly by women. “And Mom’s mantra was: ‘We girls can do anything.’ She didn’t explicitly call it feminism, but it was baked into our DNA.”

Her mother had a quirky, creative streak. Once, after she’d accidentally crashed the family car, she was so intrigued by the aesthetics of the wreck, she climbed out to take photographs of it. “There was probably a picture taken of me and my sisters every day of our childhood. Have I seen any of those pictures? No. Has she gotten them developed? Mostly not. It was just her way of feeling safe, I guess, as if things would last for ever because she had documentation of it.”

Is Clark the same in her songwriting? Documenting and so holding on to vanishing events and feelings? “I’m trying to get rid of things,” Clark laughs. “I’m trying to expel them.”

We walk to Regent’s Park, where the warm weather and an outdoor art show have drawn a milling crowd. A sculpture installed by the park entrance resembles a tall pile of replica footballs. Fitting, as Clark was quite a player when she was young, soccer one of an eclectic assembly of high-school interests. “I was probably insufferable. I was the president of the theatre club, the kid who put Bertrand Russell quotes on their wall.” When I ask who her friends were at the time, she does not hesitate: “Oh, the sluts and the weirdos.”

Music was her main obsession. “I was a 10-year-old fan of Pearl Jam and Nirvana, and I would’ve got into a fistfight defending them. Art mattered.” Her maternal uncle, Tuck Andress, was a touring musician, half of a jazz duo called Tuck & Patti, and during the summer Clark graduated from high school he gave her a job assisting his band on tour. Clark enrolled at a music college in Boston after that and lasted a couple of years before dropping out and heading back out on the road, this time as a musician in her own right. She toured successfully as part of the expansive, experimental band the Polyphonic Spree and later as a guitarist for Sufjan Stevens.

Facebook Twitter Pinterest Clothes from a selection, garethpughstudio.com. Styling: Priscilla Kwateng. Stylist’s assistant: Stanislava Sihelska. Hair: Stephen Beaver at Artists & Company. Makeup: Dele Olo. Photograph: Arcin Sagdic/The Guardian

She’s always been a political liberal – these days, one in mourning over last November’s election (“I feel like we watched America vote on their daddy issues”) as well as the reign of President Trump, a man she refers to as “a cartoon yeast infection”. As early as her teenage years, Clark had to get accustomed to the fact that a great many political and social norms, predominant in the suburbs where she grew up, were not her norms.

She believes in the essential fluidity of sexuality and of gender. (“Boys!” she sings on a new track called Sugarboy, “I am a lot like you. Girls! I am a lot like you.”) “The mutability of gender and sexuality, as you can probably imagine – that was not a prevalent subject in the suburbs of Dallas when I was growing up. Not even a little bit! And no shade on it now. I love Texas, I’m there all the time seeing family. But I was always gonna get out of there. It felt imperative that I get out of there.”

In her 20s she moved to New York, borrowing the name St Vincent from one of the city’s hospitals, by way of its mention in a Nick Cave song. (St Vincent’s hospital was where “Dylan Thomas died drunk”, as Cave sang in There She Goes, My Beautiful World.) She released a debut record called Marry Me in 2007 and toured it through Europe to dispiritingly inattentive audiences, carrying away from London a special memory of “playing in a pub where you definitely couldn’t hear me over the crowd”. Between her next couple of records, Actor (2009) and Strange Mercy (2011), her career really started to take off. She performed on US chatshows; wrote and wrote; founded an influential creative relationship with Byrne, after he approached her at one of her gigs. “I was kind of stunned,” Byrne later said, of seeing Clark play guitar for the first time. The pair would collaborate on a celebrated 2012 album, Love This Giant.

I can only write about my life, and dating Cara was a big part of my life

By the time her 2014 album won the Grammy for best alternative album, Clark was entitled to ask, as she did ask: “Alternative to what?” Prince came to one of her shows, and she was invited to guest-guitar for the surviving members of Nirvana, later for Taylor Swift. As an award nominee at the Brits in spring 2015, Clark came and went on the arm of Delevingne – and pretty much overnight her public persona became a curious, split thing. As St Vincent, she was a fiercely respected musician, patiently fattening a fanbase in the most honourable way, by writing and recording and touring hard. As the “secret girlfriend” (Metro) who was “secretly dating” (Mirror) Delevingne, she was tabloid feed. Clark saw first-hand what it was like for somebody she cared about to be “hounded, hassled, hacked – all of that stuff”.

“Having seen certain levels of fame,” Clark tells me, “having been, y’know, fame adjacent... That in and of itself seems very hectic to me. If it’s a natural byproduct of doing what it is you love? Then great. But there are certain levels of fame that I’ve seen, just by proxy, that are unenviable.”

If the upward trend of her music continues, she might find herself in a similar place, whether willed or not. Clark shrugs. “I can’t control any of that stuff. So what am I gonna do? I’m just gonna keep making music. I know this is another Pollyanna answer, but it’s about the music. Did I write better songs than on the last album? Did I sing them better? Did I play better guitar? Did I connect?”

Facebook Twitter Pinterest ‘Certain levels of fame are unenviable’: with Talking Heads’ David Byrne.

Maybe it was that I heard a low-quality version of the track, but on a new-album song called Pills there was a minor failure to connect. I misheard the song as having a lyric about somebody being “defamed by fame”, something I took to refer to Clark’s 18-month stretch in a celebrity relationship and all the demeaning wrangling with paparazzi and gossip bloggers that must have entailed. Clark looks panicked and says, no, the lyric was about someone being “de-fanged by fame... What I was referring to was that people’s art sometimes suffers when they get into that too-big-to-fail mindset. How things get really boring when people get too risk-averse, or too comfortable, or when they have overheads that are too high.” She can’t seem to get my mishearing of the lyric out of her head, though. “Oh!” she says eventually. “Maybe ‘defamed by fame’ is better?”

For a moment she seems to be wondering how quickly she can sprint to Heathrow from here, and fly back to America to rerecord it. In the end she decides she’ll let listeners hear what they want to hear. “There is no way to control how people perceive a song. And if you try to, my God, are you in for a sisyphean task.”

In the park we walk up a promenade between neatly manicured flowerbeds. When we settle on a bench, Clark seems overawed. “This is so beautiful,” she says. “I love this. Do you know how hard we’d have to work, in the States, to keep something this beautiful this beautiful?”

Facebook Twitter Pinterest With former partner Cara Delevingne in September 2015. Photograph: Dave Benett/Getty Images for Burberry

She’s now ready to address the Delevingne quandary. When the new record is out, reference to her ex will be exhaustively scoured for – it’s already started to happen, as when Clark released a single called New York in June, and Vice responded with a think-piece: “Is St Vincent’s new track a love song for Cara Delevingne?” Nobody trawled through her past writing about CCTV surveillance, or masturbation, in quite that way. “Nuh uh,” Clark says.

She takes a breath. “Right! Um. I’ve always kept my writing close to the vest. And by that I mean I’m always gonna write about my life. Sometimes, in the past, I did that way more obliquely than now. But it’s almost like an involuntary reflex. I can’t help but be living and also taking notes on what’s going on, always trying to figure out how to put that into a song. And that does not mean there’s literal truth in every lyric on the way. Of course not. But I can only write about my life, and that – dating Cara – was a big part of my life. I wouldn’t take it off-limits, just because my songs might get extra scrutiny. People would read into them what they would, and you know what? Whatever they thought they found there would be absolutely right. And at the same time it would be absolutely wrong.”

Clark looks out across the park. “A song that means something very specific to me, a song in which I might be obliquely or otherwise exploring some really dark things, is a song that another person might hear and go: ‘Wow, this one really puts a smile on my face.’ I’m thrilled by that. I’m thrilled that people might take my songs into their life and make whatever suits them out of it.”

Clark nods: done. She lets her gaze travel over the park, over the sculptures in the distance, a couple of which look like giant ice-cream cones.

Earlier, she said that she’d got to a point in her career where strangers would send over free starters. If this new album does as well it should, I start to say… “I know, right?” Clark interrupts. “If I play my cards right? With this album? I might – get dessert.” She hoots.

• St Vincent’s new single, New York, is out now through Loma Vista/Caroline International.

• Opening photograph by Arcin Sagdic for The Guardian

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