The point of an artwork – and it’s hardly controversial to say that Radiohead is in the business of art – is that it plays hard to “get”. It should be slippery, elusive, unknowable to a certain extent, and certainly not an object upon which one can casually bestow critical judgement in a matter of hours after a surprise release.

Nevertheless A Moon Shaped Pool gives a sense of itself relatively quickly, compared to the band’s 2011 predecessor King of Limbs. Generally understated in mood, it is utterly beguiling, profoundly moving and politically urgent, particularly in an environmental sense.

It will likely rehabilitate lapsed post-King of Limbs Radiohead fans, as that album’s glitchy and patchy style gives way to an enchantingly lush orchestral soundscape; pleasantly unexpected, yet somehow inevitable.

Not Let Down

Radiohead’s output is commonly characterised as a diversity of radically contrasting utterances, a trajectory with roots in grungy guitars, the subsequent embrace of technology and computer-based musical invention, and the ever-increasing influence of Jonny Greenwood’s forays into soundtrack and orchestral composition.

Yet the sense of a unifying through-line in Radiohead’s nine album output is equally important. Theirs is a many-layered approach to musical and emotional texture: from endlessly fascinating musical surfaces that spin just beyond rhythmic predictability to famously long-breathed, arch-like phrasing to exquisite combinations of tonal colour that shyly reveal their emotional meaning only over time.

Much of A Moon Shaped Pool continues this trajectory. The great big idea of Radiohead – whatever alchemy it is that generates their unmistakeable “voice” – permeates the 11 new tracks.

It opens with Burn the Witch, one of several songs on the album already familiar to fans for a number of years through various hints and teasers, especially at live concerts. The song introduces the album’s rich orchestral theme with an engine of nervously propulsive string playing. The insistent col legno (striking the string with the wood of the bow) forms a minimalist spine that runs from the beginning to the claustrophobically spiralling end. (The mesmerising influence of Steve Reich, Philip Glass and Terry Riley is never too far below a Radiohead surface.)

The staccato accompaniment contrasts in classic Radiohead style with Thom Yorke’s disembodied long lines in the chorus - the group’s signature vision of the ancient musical principle that contrast creates interest.

This obsession with rhythmic and textural complexity as a sonic cushion for soaringly emotive vocal lines is a defining aspect of the band’s sound. The chorus of Burn the Witch is a typical example of one of the ways Radiohead creates that complexity; larger melodic, harmonic and rhythmic units operate along seemingly independent timescales. Rather than lining up neatly, the musical threads overlap, like slow-moving waves, creating a kind of ambiguity and lack of groundedness that is inherently interesting to listen to.

Relentlessly bright major chords give the song a kind of glare that exacerbates the tension of its lyrical message (which may or may not be about any number of socio-political themes ranging from refugee crisis commentary to condemnations of various aspects of social media).

The tightly coiled album kick-off is a bait and switch. Daydreaming resets the album’s tone as one of beautiful desolation, at a luxuriant six and a half minutes.

The initial sense of stasis is deceptive. Like so many Radiohead songs, a larger shape evolves over time. Without even noticing the progression, the song slowly mushrooms, an expansive and sleepy climax that evaporates into weird exhalations (apparently a sample of Yorke’s voice repeating “half my life”, played backwards).

The unassuming Decks Dark is one of the least commented on tracks so far in reviews, perhaps because of its nothing-new classic Radiohead vibe (it seems to hark back to or even borrow from earlier songs) but I suspect it could prove a sleeper favourite.

Icy droplets of elegantly arpeggiated piano figuration reflect the weightless outer space lyrical theme. Elongated choral vowels briefly enhance the unearthly feeling, as does the use of a subtly unusual (Phrygian) modal inflection in the underlying harmonies. A nastier, slow funk bass line re-orients the song’s feel throughout the final 60 seconds.

The fundamentally acoustic nature of the album is made clear at the beginning of the hypnotic Desert Island Disk. It takes over two minutes for something major to happen in this song. Radiohead’s songs often dissolve pre-fabricated verse/chorus structures.

Whether a collage-like cut, as in Desert Island Disk or subtly evolving transitions (such as the ominously creeping and menacing opening of Ful Stop), Radiohead enjoys structures that unfold over time. A song that opens in an unassuming manner will suddenly turn a corner, greeting the ear with a new sonic vista.

The cumulative impact of this kind of soundworld is what gives it such power. The glissando string harmonics at the end of Ful Stop create their “ful” hair-raising effect only in the context of the existentially troubled music for which they provide a coda.

Radiohead appear to think of a song as a canvas, an open space for pouring sound in and through. Glass Eyes, the next track, is a perfect example of their frequent departure from the conventions of pre-existing song forms.

Eschewing percussion of any sort, Glass Eyes exists outside of pop-song time. The London Contemporary Orchestra’s blooming string sonorities create an unbearable tenderness on this track.

The song’s lyrics speak of love turned cold, an anxious protagonist loses his way. This is another common Radiohead affective device – somehow the typical desolation of a Radiohead lyric is inevitably healed, or made into something beautiful by the nature of the actual sounds those lyrics are conveyed through.

(Music as a kind of therapy for melancholy is of course a long-standing tradition. Another Englishman, John Dowland, was famous for it at the turn of the 16th century. He identified with sadness so much that he punned on his own name with a composition called Semper Dowland, semper dolens – that is, Always Dowland, always doleful.)

Identikit, the next track, seems to explore the consequences of aforementioned cold love. A glum groove lifts the tempo of the album momentarily, and “Broken hearts/make it rain” is probably the album’s catchiest hook. The Numbers pivots away from introspection, apparently a call to environmental arms.

In Radiohead albums, groups of songs sometimes emerge, often as trilogies. The Bends had the crescendo of Nice Dream, Just, and My Iron Lung. OK Computer was remarkable for the two opening trilogies: the delirious Airbag, Paranoid Android and Subterranean Homesick Alien, followed hot on the heels by the emotional rollercoaster of Exit Music for a Film, Let Down and Karma Police.

The final three tracks of A Moon Shaped Pool are probably those that will most firmly wedge this album deep in the hearts of fans. The gently shuffling bossa nova of Present Tense drips with regret. The threat of climate change probably animates the weird and haunting soundworld of Tinker Tailor Soldier Sailor Rich Man Poor Man Beggar Man Thief. Sliding intervals give this song its unique sense of movement.

Finally, True Love Waits propels the album’s conclusion into the realm of pure emotion. Thom Yorke’s aesthetic goals have never included clear diction – consonants and vowels functioning as mere vehicles for the raw emotions signified by the text. Yet it’s hard not to hear the line: “Just don’t leave, don’t leave” as especially wrenching in light of Yorke’s recent separation from Rachel Owen, his partner of 23 years.

A reading of True Love Waits as autobiographical would, however, be both misleading and confining. The song is, as many fans know, just over 20 years old. Always performed live, fans have patiently waited, for a studio version. And patience has clearly rewarded both band and audience.

As the planet’s throng of Radiohead fans dissect and devour the new offering, some complaints are inevitable. Gen Xers will bemoan another failure on the group’s part to return to its “rock and guitar-based roots” (i.e. the salad days of Pablo Honey (1993) and the dizzying impact of The Bends (1995)).

The Modernists will be disappointed that the group has, at first glance, again failed to replicate the earth-to-moon sized developmental leap and stylistic growth spurt that took OK Computer into the weightless and absorbing orbit of Kid A.

And the Sceptics will no doubt hear what they usually hear in Radiohead’s music – a morose morass of droning gloom-mongers.

But Radiohead’s music usually requires a bit of patience, a willingness to listen “slowly”, deeply, and with an open mind.

Radiohead isn’t the only commercially-based group of musicians whose output benefits from repeated and patient listening. But they might be the most prominent still working in the modern incarnation of progressive rock.