Tahliah Barnett was a dancer before she was a singer, and that matters. Dancers learn ways to inhabit music differently, to physically respond to it, to internalize it and make it a part of their body chemistry. And Barnett was a serious dancer, one who went to school for it and who used to make her living working in the background in various pop stars’ videos. (“Video Girl,” a song from her LP1, is about the experience of being recognized as “the girl from the video” and denying that it’s her.) As FKA twigs, Barnett sings like a dancer. That’s not a knock on her pure vocal ability, which is no joke. Twigs isn’t a belter, but she knows what to do with the thinness of her voice, turning her sighs into coos and her coos into wails. But when I say that she sings like a dancer, I mean she doesn’t just sing over the top of her tracks. She wraps herself in them, disappearing into them. She comes up with subtle counter-rhythms, interrupts herself, hold exhalations until they become notes. Her music takes elements of dance music — drums, synths, open space — but it arranges them in counterintutive ways, unfurling into thickets of sound rather just thumping. Those backing tracks aren’t beats. They’re something else. It takes a special kind of dancer to know what to do with tracks like that, and it takes a special kind of singer to bring them to life. Twigs is both of those things.

On LP1, her first full-length, twigs does things with her voice that sound like physical movements: short leaps, slow pirouettes, stuttering kicks. And she’s singing about physical things, her words evoking intertwining bodies in some evocatively concrete ways: “My thighs are apart for when you’re ready to breathe in.” But this is interior music, music about living inside your own head. Most of the songs are about longing, about the point where the desire for intimacy stops being a craving and starts being a physical need. Even “Two Weeks,” the one where she’s straightforwardly asking someone to leave a lover behind — “I can fuck you better than her,” “I know a thousand ways to help you forget about her” — she’s imagining the conversation, not actually having it, as the great Jessica Hopper points out in her Wondering Sound review. The whole song seems like the result of a weeded-out daydream: “Higher than a motherfucker, dreaming of you as my lover.” It’s not clear whether she’d actually talk to another person like this. And most of the time, she’s not even dreaming about those connections; she’s lamenting them when they’re gone (“Was I just a number to you”) or lamenting the idea that she’ll never find them (“So lonely trying to be yours”). And so the album is a knowing conundrum, an intimate and instinctive and sexy piece of music about how impossible it can be for two people to find any real connection.

Musically, it’s hard to even describe what’s happening on LP1, let alone explain it. The songs have a central pulse to them that feels as natural as breathing, but you don’t hear the rhythm in the drums; you hear it in the bass, or they synths, or the way twigs breathes. The drums echo in from every direction, sounding more like dub-reggae sound effects than like mechanisms for keeping time. Meanwhile, keyboards and voices layer all over each other, creating disorienting fogs. You can get totally lost in your own thoughts listening to these tracks. They seem to fold in on themselves, to make linear thinking difficult. At times, the album feels like some lost artifact from a lost alternate-universe 1996, one where Portishead’s Beth Gibbons made a whole album with Richard D. James Album-era Aphex Twin. A song like “Pendulum” works as a sad and beautiful and lonely ballad in a lot of ways, but these clusters of electronic percussion keep erupting and rippling and bursting in out of nowhere, fighting against the flow of the song rather than aiding it; in a lot of ways, it reminds me of Aphex’s “Bucephalus Bouncing Ball,” if some mad scientist had turned it into a torch song. In this case, though, there’s no single producer playing Aphex to twigs’ Gibbons. The album has a lot of producers working on it — internet-cool synthesists like Arca and Clams Casino, big-pop ones like Adele collaborator Paul Epworth or Lana Del Rey collaborator Emile Haynie. But listening to the album, you don’t really hear any of those producers’ sonic signatures; all the tracks fold seamlessly into twigs’ soundworld. She seems to be the one with all the agency, and everyone else comes off like a hired hand, just there to help her actualize her vision.

There are two singers, Aaliyah and Björk, whose names come up in every LP1 review, and both are helpful, to an extent. Like Aaliah, twigs conveys sex and longing through poise and restraint and timing rather than through loud exhortations or showy technical displays. And like Björk, she’s created her entire universe, one that moves her outside any outmoded body/mind or thought/feeling binaries. But twigs also has a precise, distinctly British locution that reminds me of ’80s art-pop types like Kate Bush or Talk Talk’s Mark Hollis. And the ease with which she negotiates these tricky, futuristic, altogether alien tracks recalls early Missy Elliott, casually talking shit over otherworldly Timbaland beats as if that were the most natural thing in the world. All of those comparisons get at little things she does, shades of her style, but none of them is quite right. That because twigs really sounds like nobody else and belongs to no genre. With LP1, she’s put together a glittering, emotionally cathartic, musically weird-as-fuck gem, an album that lingers, in part, because it does things we’ve never quite heard.

LP1 is out now on Young Turks. Stream it at iTunes.

Other albums of note out this week:

• Mirel Wagner’s beautiful Luomo-produced folk seance When The Cellar Children See The Light Of Day.
• The Gaslight Anthem’s waterfall-chasing Get Hurt.
• The Underachievers’ hazy, psychedelic rap debut The Cellar Door: Terminus Ut Exordium.
• Porter Robinson’s dubstep-pop move Worlds.
• FaltyDL’s horny electronic album In The Wild.
• Dama/Libra’s ghostly, droning Claw.
• The Silver State’s soft psychedelic reverie Outside.
• Childhood’s jangly, nostalgic Lacuna.
• Porches. side project Rivergazer’s evocatively jammy Random Nostalgia.
• Sinéad O’Connor’s reliably tough I’m Not Bossy, I’m The Boss.
• The dance-heavy soundtrack to the Hohokum video game.
• Operators’ EP1 EP.
• Coral Cross’s 001 EP.
• The Partysquad’s Wake ‘M Up EP.