Announcing your return from a five-year recording hiatus by deleting your Facebook and Twitter accounts is a unique way to relaunch your recording career, but then again, Radiohead have always zigged when the world zagged. The band who popularized the then futuristic "pay what you want" model of music distribution with In Rainbows in 2007 have moved forward by pushing backwards, by mailing letters — remember letters? — to fans with a cryptic announcement a couple weeks ago. Days later, they dropped a new video on the world for lead single "Burn the Witch," and then the new album, A Moon Shaped Pool, followed on May 8.

Like the honest authenticity of deciding to inform the world about the new album via snail mail (which of course was immediately photographed and uploaded to the Internet), the band who helped bring alternative rock forward into the 21st century with Kid A's infusion of electronica have also been moving forwards musically by moving backwards. "Burn the Witch" kicks off the album with a sound that was the cutting edge of 1816 — a string quartet playing con legno — smacking the strings to create a percussive effect that floods our senses with a human urgency and beauty and makes it one of the most affecting songs of the year. It's also clattering, discordant, and full of both dread and decay, in no small supply when this compelling music is paired lyrics like "abandon all reason / avoid all eye contact / do not react / shoot the messengers / burn the witch." Is it Thom Yorke's commentary on the 2016 election season, a statement about the European hostage crisis, or perhaps a sobering look at the disintegration of Yorke's love life? It could be all those things, yet the song has actually been floating around Radiohead studio sessions since as early as 2000, according to producer Nigel Godrich, with the lyrics posted on the band's website back in 2007.

The completion of older songs is one of the interesting facets of A Moon Shaped Pool, with at least four of the new tunes dating back to the last decade, and one, "True Love Waits," having been released in a solo acoustic version on their 2001 live album. It's not the first time Radiohead have let songs simmer to the surface over years, but the time and distance of shaping the material has, in this case, enabled the band to create a work of full grandeur, with the arrangements on A Moon Shaped Pool showing a strong classical influence, no doubt reflecting the recent work of multi-instrumentalist Jonny Greenwood, who has mostly been composing soundtracks while the band were on hiatus.

Always among the most ambitious rock bands in history, Radiohead have long morphed elements of indie rock, punk, prog, Krautrock and electronica into their mix — and the strings and choral orchestrations are not new elements but their prominence is, flavoring the album along with the occasional Latin rhythm ("Present Tense"), funk bass ("The Numbers"), angular guitar ("Identikit") and sustaining piano ("True Love Waits").

On some songs, Yorke's lyrics seem to be informed by the recent breakup with his partner of 25 years — and though it's certainly not the first Radiohead album to be filled with a sense of forbidding technological unease (hello, OK Computer!) — so many of these songs pile on an aching sadness and regret, the analog human emotions join with the increased use of acoustic instrumentation to achieve a new depth for Radiohead. Instead of wallowing in navel-gazing pity, the album is alive; combined with the production dexterity allowing every song to unwrap in unexpected sonics, A Moon Shaped Pool surpasses Radiohead's last few records.

Critics are already falling over themselves with adjectives — calling it "brooding, symphonic and poignant," "a haunting, stunning triumph," and Radiohead's "most gorgeous and desolate album to date." Radiohead are one of the few bands in rock history to have pulled off the trick of being able to create music this stunningly original and with an emotional resonance 20-plus years into their career.

To paraphrase the OK Computer lyrics, "Fitter, Happier, more productive," A Moon Shaped Pool could be Radiohead's "deeper, warmer, more human(e)." It's an amazing album from one of rock's greatest bands.