Enigmatic French New Wave film Last Year At Marienbad has crept across decades of culture since its 1961 release.

Blur paid homage to its monochrome surrealism in their video for To The End; it had a formative bearing on Kubrick's The Shining; and a recent Karl Lagerfeld fashion collection was inspired by the movie and its Coco Chanel-designed costumery. Now, Californian sound-artist Julia Holter, a beacon in America's DIY pop underground, has cast new light, and life, on the picture, thanks her madrigal pop opus, Marienbad. The track opens Ekstasis – an album that quotes Virginia Woolf and Frank O'Hara, evokes Laurie Anderson and Brian Eno, and which engendered such praise on its low-key US release that it's now being reissued by indie powerhouse Domino.

"Marienbad started with this idea of a topiary garden," offers Holter down the line. The sometime Linda Perhacs and Nite Jewel collaborator is in LA shopping for Thanksgiving, and the market hubbub in the background recalls her urban field recordings. "My mum told me that Last Year At Marienbad featured a topiary garden, and that it might inspire me. After I saw the movie, I wrote more lyrics and added more to the song – my writing process is never clear or linear," she reflects. "It's not like it all comes to me at one point. I get different parts at different times, then I move them all around." This approach underscores Marienbad's (and Holter's) charm: vivid ideas and surprising narratives are imbued with choral vocals, astral electronica and harpsichord swells, to create an abstract pop of ages.

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"When I'm inspired by something, whether that's an essay or a film, I draw from it and build something else – well, not usually an essay, it's not like I read millions of those," she laughs. One treatise that did rouse her muse was Decreation: How Women Like Sappho, Marguerite Porete, And Simone Weil Tell God, by Holter's former University of Michigan tutor, the poet and classicist Anne Carson. "Yeah, that essay uses the term ekstasis, but it's also a common word that's used a lot in philosophy," the musician says of the Greek label for being "outside of oneself", which also imparts the linguistic roots of ecstasy.

The title Ekstasis is at odds with Holter's previous (and equally remarkable) album Tragedy (2011), a conceptual electronic suite that inhabited and enlivened Euripides's ancient Greek tragedy, Hippolytus.

Does Holter feel an affinity or fascination toward Greek history and art? "I understand why people think I must be into Greek culture, but it was a coincidence," she says. "I don't know that much about it – I was just trying things out." This collusion of academia and down-home experimentation is echoed in Holter's earlier work, which has fused classical theory and toy-box pop, or interpreted John Cage's Circus On piece via the medium of a 1920s cookbook.

Ekstasis and Tragedy were written simultaneously, and while they're distinct propositions – "Tragedy is more unified, while Ekstasis is a collection of independent songs," says Holter – they resonate with, and embrace, each other. One track, Goddess Eyes, appears on both albums, in varied forms. Its disembodied, vocodered line, "I can see you but my eyes are not allowed to cry", reads as a lament from Artemus in Tragedy, then its words gain new meaning – and force – across aeons, as they re-emerge on forthcoming single (and an Ekstasis highlight) Goddess Eyes II. Therein, it plays out as what could be a lovelorn downtime party aria.

The concept of ekstasis – its sense of "entrancement, astonishment and displacement" – feels apt when describing, and enjoying, Holter's empyrean art-pop. "When I wrote Ekstasis, it was a time in my life where I was trying all these different things so it was like being outside of yourself, in way – you're pushing yourself, you're going beyond your normal place," she says. "I also think that when I perform – or anyone performs, probably – you have to be a little bit unconscious; you have to be a bit, like, beyond. Normally I'm kind of boring," she concludes with a quiet laugh – which just goes to show that although she is wonderful, Julia Holter is not always right.

Ekstasis is out via Domino today; Goddess Eyes II is released on December 10.