"Would Radiohead really title an album A Moon Shaped Pool?" a friend texted me on Sunday. It was an hour or so before the band's secrecy-shrouded ninth album was due to materialize online, and some crafty Reddit sleuth was claiming to have pried a clue out of Amazon's vaguely creepy in-home robotic assistant. We agreed that it was likely a fake: You're telling me someone asked the sad laptop from "Fitter Happier" if it had any inside Radiohead info and it said "Sure"? Yeah, right.

A Moon Shaped Pool is real, of course (and it's spectacular). But that flicker of doubt reflected a deeper truth about Radiohead, a hugely popular band whose biggest fans are prone to second-guess their every move. We're an obsessive bunch; we overthink things. In-too-deep devotees put 2011's The King of Limbs down as a dud and spun conspiracy theories about a nonexistent sequel. And those are the people who like Radiohead. At the other end of contemporary rock fandom are people who don't much care about Radiohead (fair enough, particularly if you're a high school senior born the same year as OK Computer) and lazy snark monsters lashing back at the band's critical hegemony. Beyond those particulars, modern audiences can be hostile to any rock lifer offering a big ambitious statement album — just ask U2 — which might have something to do with why nearly a decade has passed since Radiohead tried to usher one into the world.

That ends here. A Moon Shaped Pool charges headfirst at the question that's faced the Oxford quintet every time they've entered a studio this century: Why make a new Radiohead album at all? The 2007 instant classic In Rainbows looked backward for the answer, turning up the guitars and leaning into the melodies to create the last great alt-rock album of the 1990s. The King of Limbs tacked in the opposite direction, aiming for clever and weird instead of big, which yielded a handful of deliciously dank apples and oranges. The new album synthesizes those approaches with startling grace and clarity, making a passionate argument for Radiohead's future that's grounded in the band's rich history. At its best, it transcends those boundaries entirely.

There's a crackling current of unpredictability running through songs like "Decks Dark," a jazzy late-night chiller that suggests 2001's "Pyramid Song" if it loosened up and learned to dance. Thom Yorke sings about spaceships and aliens — briefly echoing "After the Gold Rush," one of his favorite Neil Young songs — and a parting of ways: "Have you had enough of me? Have you had enough of me?" Jonny Greenwood and Ed O'Brien's guitars spiral up toward the night sky, and fear mingles with excitement into an overwhelming feeling of infinite possibility. Two tracks later, on "Ful Stop," that mood has curdled into a dark resentment that's equally electric. "You really messed up everything," Yorke mutters over dissonant treble notes and a sinister low-end rumble from bassist Colin Greenwood that makes the song feel like a long-lost cousin to 2000's "The National Anthem" and 2001's "Dollars and Cents."

Neither "Ful Stop" nor "Decks Dark" could be mistaken for a retread, but both songs call on freaky sounds and nocturnal frequencies that some Radiohead fans wondered if we'd ever hear again. They put A Moon Shaped Pool in direct dialogue with Kid A and Amnesiac, the end-of-a-century dyad that crowned Radiohead's canonical genius and set the band scrambling into new directions — often fascinating ones, but never quite the same. It feels as though Yorke, the Greenwoods, O'Brien, and drummer Phil Selway are finally picking up a torch they put down 15 years ago because it burned too hot.

The album's tracklist is bookended by a pair of songs closely associated with that era: the formerly mysterious "Burn the Witch," recorded on and off for more than a decade but never revealed to fans beyond a teasing hint of a chord sequence, and "True Love Waits," a beloved ballad seemingly put to bed on a 2001 live EP. It seems obvious now that neither of those mythic grails could have belonged to any time but this. "Burn the Witch" turns out to be a sharp counterpunch against xenophobia and authoritarianism — far more necessary in the time of Trump than ever before — with an orchestral arrangement that uses violins like fists. The studio version of "True Love Waits," meanwhile, shows up 10 tracks later sounding stark and defeated. The steady surge of Yorke's acoustic strumming is gone, lost to distant piano notes that linger just out of sync with his heartbroken pleas: "Just don't leave / Don't leave." The effect is almost unbearably beautiful.

A Moon Shaped Pool's other devastating piano ballad, "Daydreaming," is a stunner, too: the sound of Yorke piloting a gondola slowly down a river of bittersweet regret in the underworld. "It's too late," he sings not long before strings, bass, and delicate studio effects pour over the edges of his boat. "The damage is done." You'd have to go back to 1995's "Bulletproof ... I Wish I Was" to find the right parallel for the song's numb beauty, but even that comparison fails. Two decades ago, Yorke could sing about wanting to feel no pain; now, it seems, he's learned to live with it, and the weight of that realization makes the song hit far harder.

The lead vocals are mixed high on "Daydreaming," making the hurt in Yorke's voice intimate and immediate. The creeping anxiety often associated with Radiohead's music has given way to a less acute but deeper ache, a mature sense of loss. Those hyper-inquisitive fans have already decided that the song's swirling psychedelic coda contains a hidden message: Reverse the file and Yorke sounds like he's singing the words "half of my life," an apparent reference to his amicable separation last year from his partner of "23 highly creative and happy years" — half of his life, as of 2015.

But you don't have to play anything backward to detect signs that A Moon Shaped Pool is a breakup album. "I feel this love turn cold," Yorke sings on the pretty, mournful vignette "Glass Eyes," the album's shortest and most plainspoken song. "Broken hearts make it rain," he repeats until it becomes a mantra of acceptance on "Identikit," a seductive spectral-funk groove laced with that same sadness. He finds some solace in the forward momentum of "Present Tense": "Keep it light and keep it moving," he sighs over a lightly loping acoustic guitar figure. "I'm doing no harm / As my world comes crashing down / I'll be dancing, freaking out." After so many albums teeming with charmingly cryptic poetry, it's a shock to hear Yorke speak so frankly about his inner life here — comparable at times to the radical shift his friend Björk made for last year's masterful Vulnicura. A Moon Shaped Pool is named after an ellipse, but it's Radiohead's least elliptical album in many, many years, and that emotional leap, in its way, represents as significant a step forward as any of the vaunted musical reinventions the band has pulled off before now.

Above all, A Moon Shaped Pool provides a thrilling answer to the existential concerns that confront any band that's made it this far. Why Radiohead? Because no one else could have made this album. After all this time, hearing these five old friends challenge themselves into a new phase of evolution can still blow even a jaded fan's mind. Whatever comes next, we're ready.