Nowadays, Alex Turner sounds like no one more than Seventies Lennon to me, only without the peace protests and the Yoko. Imagine how great Turner could be if he attached himself to a political cause, or had a spiritual conversion! Tranquility Base Hotel & Casino, the Arctic Monkeys’ sixth (and sci-fi inspired) album, is another considerable advancement for the indie urchin genius of 2006. It was written entirely on a Steinway that was given to him for his 30th birthday.

Space has long been the metaphor for self-exploration in rock – in Ziggy Stardust, or The ArchAndroid, the story of Janelle Monáe’s cyborg alter ego, who’s been retired now that she’s become a bit more human. Space is where a musician can let their solipsistic weirdness emerge – in 1976 Jon Anderson made a mad solo album, away from Yes, called Olias of Sunhillow. The flip side of self-exploration is alienation. And there’s a lot of that on Turner’s new album – because it is Turner’s album: the band said it sounded like a solo record, and he disagreed. They brought loads of other guest musicians in, but it is still the work of the Little Prince – now with beard – working away on his planet of one.

Turner’s intergalactic hotel is a recognisable earthly setting: he has been living in LA since 2013. There are all the usual comforts there: “It’s such an easy flight” (“Four Out of Five”). There’s cars and bars, and a baby grand. But there is also a profound sense of dislocation – from the tyranny of modern pop culture (“Everybody’s on a barge, floating down the endless stream of great TV”), and in the sense of being still young and potentially washed up in the USA (“Dancing in my underpants... I’m gonna form a covers band... I fantasise I call it quits”). Maybe dislocation is the only way to feel when you’re told, at 19, that you’re the new Shakespeare, and your band is the last hope for rock’n’roll.

The term “lounge music” has been applied to Tranquility Base Hotel & Casino, which made me expect the English lounge of Tony Christie, or Richard Hawley, which sits so comfortably within Turner’s wheelhouse – the red velvet curtain, the fag in the ashtray, the arch narrator looking back on a tough life from within a shiny suit. I’m not sure exactly what “lounge” people are hearing in this savoury, experimental record, with its irregular structures and piano-led meandering, unless it’s an airport lounge – in that strange mixture of airless comfort and constant flux. There’s a spindly, Keith-Emerson-meets-Italian-video-nasty-style synth on the title track. The album emerged after a period of writer’s block: Turner told the NME that he wrote it by recalling his memories of learning piano as a child.

More than one track reminds me of the slinky “Benny and the Jets”, Elton and Bernie’s satire on a fictional band set in the seedy Seventies. “Maybe I was a little too wild in the Seventies,” says Turner on “Star Treatment”; he’s always yearned to be old, and now he sounds like the oldest 32-year-old I know – the voice overwhelmingly rich, the Yorkshire singing accent all but gone, as happens when a rock star goes to America.

His new look has been a talking point – people staring with horror at his long hair, pointy beard and linen suit, shirt unbuttoned to the chest. It reminds me a bit of Dave Gahan in the early Nineties, leaving the rest of Depeche Mode for Los Angeles, growing just such a beard and hanging around with Jane’s Addiction. But while Gahan’s was a messy, real-life experiment in being a rock star, there is something in Turner’s curled expression – “Yeah? Like my trousers, then?” – which is messing with you. The Turner of the photo shoots is the same as the Turner of the interviews – where he is generally ineloquent, and often a bit rude. It’s a different one, introverted and intellectual, who writes the songs.

He has said that he’s given up writing about love, on the advice of a friend. His women often felt unreal, an assemblage of model parts and drunken, standing-up snogs. The press campaign on his last record – the second album from his side project the Last Shadow Puppets – derailed when his collaborator Miles Kane was sleazy to a female interviewer. On “Science Fiction” he sings: “I tried to write a song to make you blush but I have a feeling that it may end up way too clever for its own good, the way some science fiction does.” Self-assessment, or self-criticism, from behind a protective layer – a kind of songwriting in transition, perhaps.

Turner is no longer spitting bars, joke after joke. Thoughtful and full of twists, Tranquility Hotel Base & Casino could be the first album where his music outshines his words simply because that’s where the surprises are. His tunes are less pert; it’s weird that we still think of jazz breaks and experimentation as the sign of a musician losing their direction, rather than finding it. It’s more original than Arctic Monkeys’ last album, the desert rocker AM – though it may well make you want to go back and listen to AM instead. People said, years ago, that Turner was the spokesperson of his generation, and for now he lies completely outside of it. It’s another step on the journey.

Tranquility Base Hotel & Casino, Arctic Monkeys (Domino Records)

Tom Gatti and Kate Mossman discuss the Arctic Monkeys' sixth album Tranquility Base Hotel + Casino, the new play at the Old Vic Mood Music and celebrate the noniversary of Willow.

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