The music made by Savages, the four-piece London band who released their debut album Silence Yourself today, is a direct and linear thing. It’s easy to get the sense that the band plots out its arrangements on graph paper, figuring out the intricacies of guitar/bass interplay with mathematical precision, or that its reduced every element of its music down to the skeletons, the way Spoon might do. But Savages’ music has a chaos to it, too — a messy straining to create a system of beliefs, to resonate as something more than music to soundtrack your internet browsing or whatever. As everyone on said internet seems eager to point out, their music has direct postpunk antecedents, Public Image Ltd. and especially Siouxsie And The Banshees chief among them. But when I listen to Silence Yourself, I flash back on other bands, bands that were determined to mean something in any way they could: Nation Of Ulysses, Refused, Born Against, At The Drive-In. Those bands were noisier and more given to entropy than Savages, but they were similarly drawn to jangled manifestos, to audio clips of old movies, to backwards sound experiments, to anything that could grant them a resonance that, to their minds, a simple guitar riff might not do. And with Savages, as with those other bands, the flailing doesn’t distract or detract from the art. The flailing becomes the art. And it’s been a long time since we’ve heard a band flail so exquisitely.

At SXSW this year, Savages were something like Odd Future were two years ago; they were the group who came to, in a strange way, rule the festival. People went down to Austin excited to see the band, and we walked out of the band’s shows blown away, even after elevated expectations. We muttered to each other, “No, but have you seen Savages yet?” We kept them out of our mental best-shit-we’ve-seen roundups, partly because it seemed as unfair to compare them to, say, Parquet Courts as it did to compare them to Justin Timberlake. They played a million shows during the festival, but they still stood out as their own thing, apart from the tumult and the guest lists and the long lines for free Tito’s Vodka. That’s because whenever they stepped onstage, they presented themselves as a complete thing, a closed system. They all wore black; they all wore their hair short. They didn’t smile. They didn’t say hi to any crowds. They didn’t thank any sponsors, or make fun of any sponsors, or acknowledge the existence of any sponsors. They glared. They jutted their elbows. They knocked out razorwire postpunk anthems, behaving less like musicians playing rock songs and more like artists unveiling particularly severe sculptures.

The music was nothing alike, but in terms of how they carried themselves, they had a lot in common with the xx, in that they had their shit utterly and completely figured out before we ever caught a glimpse of them. Savages and the xx both had the black clothes, the restrained stage-movements, the deep rhythms, the exact haircuts that you would hope they’d have. They both somehow figured out ways to keep their bullshit-extraction process away from the audience. The two bands actually share a producer, Rodaidh McDonald, and the guy deserves credit for making these two great bands spartanize their respective sounds, to radically different effects. And as with the xx, there was absolutely no doubt that Savages would pull it off when they got around to releasing an album.

Silence Yourself is a special album. It comes coated with its own manifesto, something about shielding your brain from digital noise and immersing yourself in something greater. But that manifesto would mean nothing attached to a lesser album; Silence Yourself does a much better job at making the argument than the band’s words could ever do. It’s an album that demands attention and determination. When it’s on, I clench my teeth a little tighter, tense my muscles a little tenser. Colors seem more vivid and sharply defined. Any task I’m working on — the blog post I’m writing, the dish I’m scrubbing, the diaper I’m changing — takes on a breathless new urgency.

“Husbands,” the band’s breakout song, is about waking up and realizing that you don’t know the person next to you, making that sound like the deeply apocalyptic prospect it should be. The Talking Heads sang about something similar on “Once In A Lifetime,” but that song had wonder and beauty in it; this one gets its point across in a terse, flinty surf riff like the one on the Dead Kennedys’ “Police Truck.” “Shut Up” launches headlong from an introductory Cassavetes dialog sample into a spidery wailer that never lets up. “City’s Full” is just as fast but thicker and beefier, and it makes plenty of use of the faint but icy accent that raised-in-France frontwoman Jehnny Beth blessedly never lost after she moved to the UK. “Hit Me” is a squealing, feedback-addled post-hardcore sprint, but even its peals of noise feel precisely manicured. The hard and triumphant “No Face” may be the strongest of the album’s bangers, and its hook (“You have no face! You have no face! You have! No face!”) has been rattling around in my skull since the first time I heard the album.

But the song’s greatest moments might be the two where the band slows down and gives its attack some room to breathe. “Waiting For A Sign” almost qualifies as doom-metal, but the song’s thunderous whomp comes undiminshed by effects-pedal pillowing, and there’s nothing nostalgic or comforting or bongwater-scented about its deliberate pound. “Marshall Dear,” meanwhile, has eerily placid pianos and a honking jazz saxophone that somehow never push it toward X-Ray Spex territory; the extra instrumentation give the song a measured calm that would’ve played great on early-’90s alt-rock radio. Those two songs, in particular, are the ones that convince me that Savages won’t be a one-album wonder, that their sound has more shadows to it than the wonderfully stressed knife-rock that the rest of the album offers. They’re the rare signs that the band is still learning new ways to channel its power. But that power, already entirely intact, is what makes Silence Yourself so special. Savages come to us as a fully-formed wrecking crew, and they’ve already made a debut album fierce and intense enough to shame bands that have been around for much, much longer.

Silence Yourself is out today on Pop Noire/Matador.

Other albums of note out this week:

• Deerhunter’s messily garage-rocky Monomania.
• Mikal Cronin’s generously sunny classic-rocker MCII.
• She & Him’s reliably bright and twee Volume 3.
• Van Dyke Parks’s lush, long-awaited Songs Cycled.
• Hokey Fright, the winsome but dark debut from the Uncluded, the unlikely team of Aesop Rock and Kimya Dawson.
• Talib Kweli’s hilariously titled Prisoner Of Conscious.
• Still Corners’ introverted, synthy Strange Pleasures.
• The Child Of Lov’s soulful but mysteriously glitchy self-titled debut.
• Co La’s wriggling electronic Moody Coup.
• Way Yes’s smooth midwestern indie-popper Tog Pebbles.
• The slick, star-rock Great Gatsby soundtrack.