The first time the Yeah Yeah Yeahs played Baltimore, they played first on a four-band Ottobar bill, one headlined by skronk-punk out-of-towners Milemarker and Arab On Radar. The only locals on the bill were League of Death, the mutant hardcore band whose two-man core went onto become the two-man core of Double Dagger. A year or two later, I interviewed the incipient Double Dagger, and Nolen Strahls, Double Dagger’s singer, was still fuming about how much he hated the Yeah Yeah Yeahs: “Her whole thing, like, ‘Oh, look at me, I’m so crazy because I’m spilling beer on myself and I have a ripped Versace T-shirt!’ Who gives a fuck? That is so forced!” What Nolen hated about the band was, of course, what the rest of the world, me included, loved about them — this outsized and fully-formed star, proudly posing out front of a band cranking out a spare and bloodthirsty variant on turn-of-the-century DIY punk. The band didn’t take long to leave behind the Cramps-addled sound they had at those early shows; they went onto arena-campfire alt-rock on Show Your Bones and dizzy synthpop on It’s Blitz!. But all the while, they’ve maintained that dynamic, globe-trotting fashion-icon types who came of age in a time when even next-big-things — and they were very much next-big-things by the time they made it to Baltimore — were expected to do time in the trenches, opening for Milemarker and dropping EPs on Touch & Go. Mosquito is the band’s fourth album, and it’s the leap-into-maturity move expected of any band that lasts for albums. But even as the band slows down and stretches out, they’re still very much that band.

Mosquito doesn’t lurch in any particular single-genre direction the way the other YYYs albums have. Instead, it feels like a historical taking-stock moment, and the band makes sure to find room for bits and pieces of all their old songs. Take, for instance, the alien love song “Area 52,” the goofiest and most unhinged song on the whole album. On the face of it, its mutant-garage bluster is a throwback to the anarchic beer-spitting early years. But it’s got the expertly recorded big-room chaos that co-producer Dave Sitek likes to bring to things, and that self-conscious enormity feels very Show Your Bones. (That first EP, after all, was sparse and clean in a way that nothing here is.) And It’s Blitz! could show up, just slightly, in the form of a plinky-plonk synth melody. So even as the focus shifts, the whole album feels like the band reminding us, for really the first time, just who in the fuck they are.

We also get some new big-star studio decisions here, but even those serve to situate the band’s members in a sort of temporal context. The way the gospel choir shows up to stomp and hoot through the end of “Sacrilege,” for instance, is a total “Like A Prayer” move, or in any case it’s the move of a bunch of musicians who were kids when “Like A Prayer” blew their collective mind. And the band recruits Kool Keith (in his Dr. Octagon guise, no less!) for a guest-rap on “Buried Alive,” it’s a sure sign of a group whose rap tastes are permanently stuck in indie-nerd 1997, who haven’t even gotten around to checking out those Mos Def 12″ singles on Rawkus yet. No band with a single member under the age of 30 would attempt either of these moves, just like very few bands of the indie-narrowcasting era will ever fuck with production this bright or enormous or melodies this unabashedly cheap-seats celestial. That sense of grandeur might show the band members’ collective age and reveal their remove from the current musical climate, but it works. That Kool Keith guest verse? It’s great!

So Mosquito sounds big and bold and adventurous, and even when the YYYs are pulling ideas and sounds from their past selves’ fingers, they’re rehashing nothing. They rove around from song to song, pushing each one as far as its own aesthetic will go, before launching off into something totally different on the next one. “Buried Alive,” the one with the Kool Keith guest verse, is also the only one that James Murphy produced, and it’s a fierce and slashing piece of disco-punk, its guitars as chaotic as its beat is focused. “Under The Earth” has dub-echo drums and slow-burn Peter Gabriel digging-into-eternity synth-lines. “These Paths” has drums sounds that converge on you from everywhere, like the carnivorous bugs of the album’s title — the ones paid tribute on the album’s title track, which sounds how Lydia Lunch might’ve sounded if Tegan And Sara had sent themselves back in time to write choruses for her. These songs spread their tentacles in all different directions, but there’s nothing polite or restrained about any of them; they remain an indie band from an era when indie bands still had plenty of punk in their DNA. They still rip.

But as much ground as the band covers, as much as they’ve always covered, one thing has remained constant about the Yeah Yeah Yeahs from that first EP. It’s this: The faster, brighter, harder numbers that jump out in front of you and grab your attention straight away, but when the band slows down and opens up their collective heart, that’s when they really grab you. “Subway” is the second song here and the one that immediately follows the elemental whoop of “Sacrilege,” and it’s easy to overlook at first. But it’s a near-perfect song, building itself over a loop of train-clatter, its pillowy synths slowly and gradually covering everything. And then the album ends with a trio of ballads that work together to destroy every part of you. “Always” is a diffuse and synthetic thing, one where Karen O coos the title over and over, like a plea. “Despair” builds with an assured grace, pounding amazing hook after amazing hook into our brains as Karen offers up a genuinely powerful ode to friendship: “You’ve always been there, you’ve always been there, you’ve always been there.” And then “Wedding Song,” Karen’s song for her husband, is total devastation material: “You’re the breath that I breathe, the breath that I breathe” as keyboards pile up but never reach anything like that “Maps” guitar explosion. It’s a simple, quiet, comfortable song about absolute devotion, and it absolutely slays me dead. If and when this lady has kids, can you imagine how heartwrenching her songs will become? I seriously cannot wait. For now, though, this is the sweeping and overblown rock-star love hymn that we need in our lives.

Mosquito is out 4/16 on Interscope.