“If you think this is over, then you’re wrong.” When that statement echoed across the final minutes of Radiohead’s previous album, 2011’s The King Of Limbs, it seemed to be loaded with meaning. It was a curious choice of words for the last song on an album, one that fanned the flames of unsubstantiated fan theories that a companion LP was on the way. After all, this was the same band that released Amnesiac a mere eight months after Kid A, and The King Of Limbs was short by Radiohead’s standards, and surely after four years they had more than eight relatively lackluster songs to show for themselves?

Soon enough it became clear that no surprise King Of Limbs sequel was coming — four rad non-album tracks did materialize, for what it’s worth — so those of us who insisted upon finding deeper meaning in “Separator” were forced to instead read Thom Yorke’s lyrics as a pledge of perseverance. By 2011, Radiohead appeared to be winding down. Side projects were proliferating. Four-year breaks between albums had become the norm. Arguably the greatest rock band of the past 20 years (inarguably, when I’m in my feelings) seemed to have written themselves into a gray, glitchy corner. So it was heartening to hear Yorke affirm that this was not goodbye — or at least imagine him affirming it.

Still, when more than four years passed without word that a new album was in the works, it became easier and easier to believe The King Of Limbs might be Radiohead’s farewell after all. And even when we finally got official confirmation that the band was working on LP9, the prospect of another full-length was as terrifying as it was exciting. For a minute there, it seemed like Radiohead had lost themselves. But no: Turns out they had at least one more masterpiece in them.

After years of waiting, A Moon Shaped Pool arrived Sunday afternoon. Like all the best Radiohead albums, it echoes moments from throughout the band’s history but has no clear precursor in their discography. In this case, first and foremost that means abundant flashbacks to Jonny Greenwood’s greatest hits as an orchestral arranger: the celestial swell of “Motion Picture Soundtrack,” the dystopian chaos of “The National Anthem” and “How To Disappear Completely,” the magnificent procession that closes out “Pyramid Song,” the high drama of “Bloom” and “Dollars And Cents,” the post-McCartney pocket symphony that is “Faust Arp.” As teased by non-album loosie “Spectre” and advance singles “Burn The Witch” and “Daydreaming,” this is the album on which Greenwood’s compositional prowess takes center stage. It is a glorious sound to behold.

Nineteen years on from OK Computer, we’ve reached the point where this band can conjure the sound of “classic Radiohead” without relying on a ripping lead guitar part from Greenwood. He used to enliven Yorke’s point of view with incendiary six-string melodies from bizarre angles, riffs that moved like elastic and stabbed like knives. On songs like “Just” and “Paranoid Android,” his fretwork lent Radiohead’s music a funhouse mirror quality, supplying a different kind of genius to counterbalance the frontman’s self-serious miserablism. (I’d call him the Joker to Yorke’s Bruce Wayne if they weren’t working together on the same side, so maybe he’s more like Alfred.)

But these days Greenwood is best known for his acclaimed film scores in partnership with Paul Thomas Anderson, the director whose career arc has closely mirrored Radiohead’s. From Kid A onward, Greenwood’s contributions to the band have tended in that direction, as if whatever was fighting to get out of his fingers found an outlet beyond the confines of rock ‘n’ roll. And on A Moon Shaped Pool, in partnership with Hugh Brunt’s London Contemporary Orchestra, Greenwood applies his talent for skewed cinematic beauty like never before. His arrangements are slathered on soft, organic songs written mostly on piano and acoustic guitar, tracks on which Yorke’s otherworldly tenor rarely rises from a quiver to a growl. The album consistently skews closer to Neil Young than Autechre. Notably, even as Yorke continues to explore leftfield electronic production in his outside endeavors, on Radiohead records he’s finding more and more room for natural tones and textures.

Not that A Moon Shaped Pool sounds anything like open-mic night. It’s full of stylistic excursions, from the paranoid krautrock head-trip “Ful Stop” to the gleaming, samba-infected “Present Tense.” The gracefully off-kilter “Tinker Tailor Soldier Sailor Rich Man Poor Man Beggar Man Thief” keeps soaring higher until it disappears into strings and static, whereas luminescent piano ballad “Daydreaming” plunges ever deeper into beauty below. “Burn The Witch” is a guitar-rock anthem without the guitars, while “Identikit,” the album’s one real lead guitar spotlight, brings the funk to “Reckoner”-style muted melancholy.

There’s more happening in the mix than I can begin to wrap my head around in a day, and not just because of Jonny Greenwood’s aforementioned skill set. Radiohead’s supporting players remain clearly involved in the sound of these songs in a way that elevates them far above Yorke’s solo work. As demonstrated when “Daydreaming” reaches the point of euphoric overflow, Colin Greenwood can still flip a song on its side with one or two well-placed bass notes. Phil Selway’s drums continue to hold everything together in such a way that the melodic elements seem to drift in midair — I mean, just listen to the way he shepherds “Decks Dark” through all its phases and moving parts. Ed O’Brien — well, I still don’t know exactly what he brings to the band besides dashing good looks, but that man sure is aging well.

It may seem redundant to describe a Radiohead album as “moody,” but this music has a drowsy, half-dreamlike quality that reminds me of Wilco’s descent into darkness A Ghost Is Born and especially Beck’s symphonic folk breakup opus Sea Change (which was, notably, produced by Nigel Godrich, who’s helmed every Radiohead album since OK Computer). Those bent on a return to the hard-hitting overdriven anthems of The Bends, or even the postmillennial fireworks of “2+2=5″ or “Bodysnatchers,” will probably be disappointed. Rather, Pool burrows deeper into the post-midnight headspace that characterized The King Of Limbs, pushing past that album’s bleary disconnect and into the smoldering wreckage of personal and global trauma. There are crescendos aplenty, moments that will have your vertebrae tingling and your fingers lifted skyward. Radiohead just find ever more inventive ways to get there, ways that subvert both their rock foundations and latter-day electronic evolutions.

Speaking of Sea Change: Given that Yorke made this album during the end of a 23-year relationship with the mother of his children, it’s hard not to read these songs in the context of disintegrated romance — especially longtime live staple “True Love Waits,” which appears here in radically different form than the acoustic guitar ballad that closed out I Might Be Wrong: Live Recordings 15 years ago. Radiohead being Radiohead, though, almost anything that could be a diss aimed at an ex-lover could just as easily be a reference to some kind of geopolitical corruption. (Climate change, the refugee crisis, religious mania, shady bankers and politicians — take your pick.) From “You really messed up everything” on “Ful Stop” to “As my world comes crashing down” on “Present Tense,” those either-or moments abound. Is he mourning the end of his family unit or the end of the world, or both?

And, to continue searching for meta-text that may not be there, perhaps there’s still another dimension to the letting go? Radiohead have not stated or even hinted that A Moon Shaped Pool will be their last album together, so this is purely speculation, but A Moon Shaped Pool has a whiff of finality to it. Whereas The King Of Limbs seemed like a dead end, this one feels like a natural conclusion. The band went back to finish up long-gestating tracks (“Burn The Witch,” “Identikit,” “True Love Waits”) as if to tie up old threads before closing the book on Radiohead forever. Although it didn’t make the final cut, they even dug up “Lift,” a song that dates all the way back to 1996. And then there’s this tweet from Colin Greenwood, which reads to me like the words of a man who isn’t sure his band will ever make an album again:

Very happy, very proud we did this xx — colingreenwood (@colingreenwood) May 8, 2016

I’m probably reaching with these breakup theories — and I hope I’m reaching because goddamn — but if A Moon Shaped Pool does turn out to be Radiohead’s final album, it’s as grand a finale as they and their fans could have hoped for.

That’s never truer than on “True Love Waits,” the album’s awe-inspiring final track. The version of this song that has been in the canon since 2001 features Yorke warmly emoting over acoustic strums, a rare moment of tender simplicity in the band’s bleak, heavily processed post-Y2K era. As performed on the live album I Might Be Wrong, it felt like a happy ending. The studio recording is nearly as spare, yet it’s a total reinvention, transposed to piano and littered with abstract glimmers of spectral light. The song feels drained of all warmth, especially knowing the turn Yorke’s life has taken; his crushing final words, “Just don’t leave/ Don’t leave,” have taken my breath away and moved me to tears more than once. It’s yet another instance of this band’s longstanding ability to cull unimaginable beauty from absolute desolation. These are the moments that made millions fall in love with Radiohead, and those of us who spent the past five years waiting and wondering have been richly rewarded for our patience.

A Moon Shaped Pool is out now on XL.