The musician Empress Of, real name Loreley Rodriguez, is trying to tell me about her new album, but there is a problem. A Los Angeles native, she’s in London for a week of press, with starry trappings: a show at the Jazz Cafe; an appearance on Radio 1; dinner with friend and fellow pop star Rina Sawayama at a Mayfair restaurant, where she was stunned to find the chicken priced at £140.

Now she’s in a corner on the third floor of the Barbican centre, finishing her coffee before we head into its exhibition on textiles. No trace of Mayfair glamour today: she’s looking low-key in a black bomber jacket and slick ponytail. After describing the photoshoot her team set up for this article – “Fashiony, very Mugler, Schiaparelli. The Guardian isn’t ready!” – she moves on to her album, but we keep getting interrupted by people wanting to know whether the Barbican’s conservatory is open today. With our dark coats and coffees, we could pass for gallery staff. But we don’t work here, we say. A woman shuffles away, affronted. The encounter feels polite and passive-aggressive at the same time, and therefore quintessentially English.

Back to the album. “The record is sexy,” she says, once we make our way into the exhibit. “It’s my single era.” She downloaded a dating app for the first time – Raya, an exclusive dating platform notable for its celebrity users. “It’s grim,” says Rodriguez. But everything is material, and this is a time of fun, frivolity, and “trying not to take myself too seriously” – the songs are “more pop-sounding than anything I’ve ever done”.

It’s a new turn for Rodriguez, who burst on to the electropop scene with her 2013 EP Systems, and 2015 debut album Me, its idiosyncratic, often experimental tracks confronting capitalism, sexism and heartbreak. By her own description, many of her earliest backers were Pitchfork readers, “culty” music fans – “usually a straight guy”. Later, 2018’s Us, and 2020’s I’m Your Empress Of saw the musician expand on themes of womanhood, relationships and her Honduran-American immigrant family. She’s also opened tours for Lizzo, Maggie Rogers and Sawayama and says her fanbase has since “grown in a way that feels really queer”. Maybe that is because of the draw of seeing “a woman in her own body create this alternate persona … ‘Empress Of’ is someone I’m using as a channel to make stuff happen. I can be very shy but if I’m on stage, I’m like a loose cannon.”

There are a few personas on new album For Your Consideration – named because you see the phrase “everywhere” in LA. “Everyone’s trying to win some award,” she says. The album begins with the title track, a song about a breakup that feels very LA (“Took me up a canyon / Just to say you needed space”). Featuring ASMR breathing from Rodriguez, alongside a sparse beat, it sounds purposely discomforting and achingly wistful.

“A lot of the album is centred around sounds I can make with my own voice,” she says. Rodriguez recalls that work on the record began after a director she was in love with, who had just launched his Oscars awards campaign, took her up a hill before telling her he was emotionally unavailable. Asked about the possibility of internet super-sleuths teasing out his identity, she is unbothered: “I don’t care, whatever.” After that opening shot comes a series of pulsating house and dance tracks, half in Spanish, all of which are odes to sex, flings, and chaotic nights. “I’ve written so many breakup songs,” Rodriguez says. This time, “I was like: ‘I don’t want to write about heartbreak.’”

Moving from room to room, we’re surrounded by installations of all colours and textures. Igshaan Adams’s golden Prayer Clouds glitter across the walls, looking fragile as glass; Rodriguez is mesmerised by a quilt from Loretta Pettway, swathed in shades of blue. Rodriguez tells me she did feel some fear about going more pop. “When I was in the studio, there were a lot of moments when I felt very vulnerable in an embarrassed way about how indulgent the songs were,” she says. She would panic that something was “the worst song I’ve ever written”, before deciding, “I’m going to be very direct about this being a pop song. A love pop song – I haven’t really done that.” She sometimes feels that people still regard her first album as her best. That seems like an inevitable fate for Pitchfork darlings who break out of the mould, I say. “And thank God!” she replies. “Thank God. I would hope to aspire to more.”

Making our way out of the exhibition and through the Barbican’s main lobby (“70s space age,” she says approvingly) we pick up our conversation on a corner sofa. Fresh distraction comes in the form of a toddler who pulls faces at us, then grows shy when Rodriguez waves hello. Rodriguez explains that she wanted to be a musician from a young age. When she was growing up in Los Angeles, her dad was a musician in a Honduran band, and her mother a nanny. “I was always curious about music,” she says. “We had a piano in the house. I would try to figure out how to play it.” At 12 she asked for vocal lessons, and wanted to be a jazz singer. An interest in pop grew as she discovered Björk and Imogen Heap. She studied at the prestigious Berklee College of Music, before moving to New York in 2011 and cutting her teeth in the local music scene. It was an “amazing time”, she recalls. “There were so many DIY venues, warehouse shows. I saw Grimes play to 250 people.”

Flourishing underground music scenes like New York’s have since come under threat. Artists face many economic challenges. “Maybe it’s the recession. Maybe we just don’t know how to make money because we’re not getting enough royalties from streaming.” Rodriguez says that, as with many musicians “it’s hard for me to tour. Everything costs a lot.” There’s also the other side of being a working musician. “So much of my career is social media. And being on my phone. And being an internet person.”

That can feel relentless. “There’s pressure to be like: ‘Here’s everything, here’s a behind-the-scenes, here’s a little dance, here’s a trending thing’” – she sometimes yearns to “just have something for myself”. Just yesterday, “I had to post a photo about me going on the BBC. And I was like: ‘OK, I’ll post a selfie, because they get more engagement.’ And I was standing on the street taking a million selfies to get the right one. That is also my job.” Live shows, however, “are incredible. They remind me that there is a whole world outside my phone.

“I would love to not be underrated,” she adds, when I ask about her future hopes. She may even be ready to be overrated, she jokes. For Your Consideration’s cover shows the musician atop a large star, painted gold like an awards trophy. Paired with the title, it feels like a playful nod to her starry aspirations. “I mean, For Your Consideration,” she says, making a sweeping hand gesture that suggests that the answer to what she’d like to achieve, is right there, staring me in the face. “If I got …” Then she pauses. “I’m not even going to say it!”