Maybe if St Vincent and I had got massages together, things would have been different. If we’d gone for a hike in the scorching midday sun of Burbank, California, or sat in a small pink box getting high off paint fumes, perhaps we’d have had a better time. She’s done those things with other journalists during this press cycle, in an effort to disrupt the stale dynamic of interviews – of which, she told BBC Music from inside that newly painted box, she’s done “a million”. As it is, we’re sitting in her room on the 12th floor of a London hotel, and things aren’t going well.

St Vincent, AKA Annie Clark, is in the early stages of a 37-date world tour in support of her new album, Masseduction. The shows – which she’s doing without a band, opting instead to accompany her own fearsome guitar with rearranged backing tracks – are fascinating, sometimes exhilarating affairs. She doesn’t throw herself around the stage in a self-flagellating fervour, as she did a few years ago on the Digital Witness tour, nor this time has she employed the shuffling, robotic choreography of Annie-B Parson.

Instead, Clark exposes herself in a different way – by carrying the show alone. As a blue curtain gradually pulls back to reveal nothing in particular, she places herself in various positions across the stage. Sometimes she faces the audience, sometimes she stands side-on as if utterly unaware of their presence. At one point she curls up in the foetal position on the floor. The idea, she says, is to plot the trajectory from fear to freedom.

“Some people loved it and were brought to tears and thought it was the best thing they’d ever seen, and then some people were incensed by it,” Clark explains. She was in Manchester last night, London the night before. Now, she’s draped over a black chaise-longue, demonstrably exhausted, her feet spilling on to the armchair beside her (when I ask if she’s tired, she says flatly, “I don’t care, my emotions are irrelevant.”)

Does she mind that the shows, particularly her decision to play without a live band, have received such a polarised response? “Whatever,” she says. “I think it’s cool that some people hate it.” She rolls her neck around to glance at me – the semi-horizontal position she’s taken has thus far meant minimal eye contact. “Did you hate the show?”

Not at all, I tell her. I really liked it. Then I add, in an effort to avoid bland effusiveness and because she’s still looking at me with a sceptical eyebrow raise, that perhaps I found it more intriguing than moving, and anyway it would have been hard to beat the experience I had seeing her at End Of The Road festival a few years ago. I realise too late that my words have landed with a leaden thud.

“Great,” Clark says. “It’s the third show. I mean, when I played End Of The Road, that was one of the last dates I did. Tours take a while to alchemise.” She pauses. “Also, if a rapper got up on stage and didn’t have a live band, which most of them don’t, no one would be bummed at all. Why is the assumption that I need to have a live band onstage for something to be authentic? It’s about the management of expectation, and I think it’s similar to people thinking that they have a glass of milk, and then they drink it and it’s Sprite. ‘I don’t like this.’ Actually you like Sprite too, you just weren’t expecting it.”

St. Vincent has made a career out of giving people something they weren’t quite expecting. Her music is bold and melodic – but only if you catch it at certain angles, like a magic eye book that only makes sense if you squint the right way. With each album since her chamber pop debut Marry Me a decade ago, she’s pushed her sound further towards a place between beauty and ugliness, aggression and vulnerability, adding scuzzy synth layers, distorted guitar riffs so heavy they drag half a second behind the beat, and lyrics both profoundly moving and a little grotesque – images of severed fingers, for example, that anchor a tale of drunken heartbreak.

Masseduction, her fifth LP (or sixth, if you count her David Byrne collaboration Love This Giant), is a poignant, kinky masterpiece. It’s a work of staggering frankness, with anthemic pop melodies that float atop crunchy riffs and gasping synths, as Clark’s fingers wring out every peculiarly arresting sound a guitar can make. She has a pithy tagline for each of her albums. 2011’s Strange Mercy was housewife on pills; her self-titled record was near-future cult leader; this one is dominatrix at the mental institution.

She sings of loss and depression, of BDSM and pill popping, vacuous cities and self-destructive urges. Her voice is pure and resplendent, but it also creaks, stretches into a sigh or plummets to a growl. On “Hang On Me”, as she pleads with someone, “Please, oh please don’t hang up yet,” a million unsaid things pour into the cracks in her voice.

“If you want to know about my life,” she told fans in a statement when the album was announced – aware both of her historic inscrutability and of the increased thirst for personal revelations her relationship with supermodel Cara Delevingne had prompted – “listen to this record”.

Clark performing this Summer. Photo: Getty

In the past, Clark has recoiled at the suggestion that her songs are diaristic, saying that such an idea “presupposes – in a kind of sexist way – this idea that women lack the imagination to write about anything other than their exact literal lives.” Still, this record is a little different to the others. “It’s very close to my heart. It’s not literal, because if it was literal it wouldn’t be art, but you know, it’s very heart on sleeve.”

Is there a particular way she hopes people interpret it? “No,” she says, exasperated. “There’s not. I’m happy to be misunderstood. It’s not even about being ‘misunderstood’, it’s just up for interpretation. Any interpretation is fine, as long as it’s not, ‘She’s a racist, sexist or homophobe’. I’d be bummed if someone thought that. I’m not the one writing the think pieces on it. That’s not my job. My job’s to make a thing, it’s not to do all the interpreting and explaining. That’s didactic, and shows a profound lack of respect for the audience’s intelligence.”

Hoping she might be open to at least a small amount of explaining, I put it to Clark that there’s a restless quality to the album. She’s quite often leaving, or being left, or wanting to leave. On “Slow Disco”, a plaintive orchestral waltz and one of the most beautiful songs she’s written, she asks, “Am I thinking what everybody’s thinking? I’m so glad I came, but I can’t wait to leave.” Did she notice that theme running through the album’s veins? “Yes.” I wait for more, but instead she pulls her phone out of her pocket and starts typing. “Keep asking away.”

I do as she says, but the air in the room is uncomfortable. I wonder if I should clarify what I said about the show, but I think the moment’s passed. I forge on instead. In a previous interview, Clark said that “Slow Disco” was about how “the life you’re living, and the life you should be living, are running parallel.” Is there a life she feels she should be living? “Yeah,” she says, phone still out. “I should be in Turks and Caicos with a fucking pina colada coming out of a coconut, just getting a sick tan.”

“I mean, I don’t even think I should be living,” she adds, before puffing air out of her lips. “Hilarious joke. No, I feel super lucky that I’m living the life I am. Everything I’ve ever done, every person I’ve ever met, every experience I’ve ever had, is because I got good enough at moving my fingers at micro-movements across a piece of wood and steel. That’s bonkers.”

That’s a fairly self-deprecating assessment of how St Vincent got to where she is. Her inimitable skill at moving her fingers at micro-movements across a piece of wood and steel – more commonly known as playing the guitar – is part of it, but there’s an intrigue and charisma to her music, and the persona she presents, that goes far beyond technica​l skill. It’s an intangible talent, one that has steadily drawn her into the limelight – though it was her self-titled fourth album that really thrust her into the big leagues, topping a handful of Albums of 2014 lists, and earning her a Grammy for Best Alternative Music Album.

Clark with ex-girlfriend Cara Delevingne. Photo: Getty.

Then she fell in love with someone unthinkably famous, and was thrust into a more insidious kind of limelight, the kind where paparazzi followed her around, where tabloid journalists tricked her relatives into revealing painful personal information, the kind that fuelled her anxiety and depression. Though being on the road for endless stretches of time didn’t help with that. In an appearance on the New Yorker’s podcast, she said that between her self-titled album and this one, she needed to do a “radical reorganising of my life in order to fulfil my destiny as a creative person”.

“Oh my god! Who am I, Jim Jones?” she says laughing, when I quote this back to her. “Wow. I said that? It’s like a Paulo Coelho meets Jim Jones inspirational talk. I think I meant that I was just in a monastic period, I just wasn’t drinking or having sex or really doing anything that you’d consider fun.” The only pleasure she allowed herself was getting Chinese massages in New York City. I’ve never had a massage, I tell her. Perhaps I have a lifetime of tension. She looks aghast. “You probably do. You carry it with you, you know?”

Did she find it helpful, this monastic period? “Oh it was so generative. I got so much done. Completely eschewing certain things that can otherwise take up a fair amount of time left so much time to be productive. I really loved that time. Being on tour is just a different kind of energy. It’s performance all the time. Obviously I’m not putting on my best performance for you today.” She laughs again. The icy atmosphere is starting to melt, but our time’s up.

I bid Clark goodbye. She would get up, she says, but she’s too tired. I’m glad we managed to drag the encounter towards conviviality, but – though I’m sure she won’t spend another second dwelling on it – I don’t think either of us had much fun.

The next morning, my phone buzzes. Clark’s messaged me on Twitter. “Dude!” she says, “I’m sorry I was a cock.” She explains that she was exhausted, “which is not an excuse”, but that she’d felt especially defensive because she’d been getting negative tweets about the show all day, and had thought my comments were an attempt to go for the jugular. “I really misread the interaction,” she says, “and have been feeling horribly guilty ever since. I thought you were just there to tell me my show sucked and I got real defensive and yeah, it went downhill from there.”

As it turns out then, her emotions aren’t irrelevant. She feels things deeply, all the time. You can hear it in her music, in every riff, every crack in her voice, every line about loss, or leaving, or wanting to leave. Those negative tweets were sprinkled amongst a litany of praise, but – though she wore an insouciant armour when we met – she clung to them anyway. “You carry it with you, you know?” I hope she carries the good things too. I hope she gets some sleep.