I laughed the first time I heard Tranquility Base Hotel & Casino, the new album by Arctic Monkeys. Imagine those arena shows later this year, when the sizable pints aloft section of their crowd mosh to, say, the record's first track, "Star Treatment". It's jazz, basically, with frontman Alex Turner doing stream of consciousness on The Strokes and Blade Runner. Half a song, half the end of a very long session, "Star Treatment" is so far from the sound that made the band's name that it barely seems to that band at all.

What's more, the opening number is indicative of what's to come. No shock, I thought, that they put tickets on sale for their tour before the release of this, their sixth album. No wonder they decided against putting any singles out, since there aren't any singles on it. On first listen, this isn't Arctic Monkeys, but rather a stoned Turner experiment, recorded on a piano in his home, set to alienate fans, and only featuring his bandmates because, five years since their last album - the hit-laden AM - they had nothing better to do.

Anyway, that was my first listen. A baffling hour of frustration and occasional recognition of what I knew this band for. Come second listen, those nods of acknowledgment became more frequent. "She Looks Like Fun" has a crunching chant of its title that wouldn't sound out of place on Humbug, plus a funny line about martial arts. "One Point Perspective" carries a riff not unlike the Dr Dre inspired, hip hop sort found on AM ("Why Do You Always Call Me When You're High", for instance); "Four Out Of Five" is a rousing and wry take on gentrification, I think, and the daft desperation for increasingly exciting bars and restaurants. (It is much catchier than that sounds.) Those three songs are terrific, nearly immediate and, if it's what you want, verging on what might be classed "full band".

Which brings me to "The Ultracheese" - the closest Turner's come to solo since the much-loved soundtrack for Submarine. It's the finest thing on Tranquility Base Hotel & Casino, arguably his most beautiful creation yet. A little bit like Jarvis Cocker fronting an Amy Winehouse song. "No1 Party Anthem" from AM is the only reference point from the band's back catalogue, with a serving of Turner's Last Shadow Puppets side project too, but the song is its own creature. Romantic ("I haven't stopped loving you once"); funny ("What a death I died writing that song"); sad ("Suppose we aren't really friends anymore") - "The Ultracheese" also touches on politics, which is new to a writer who's always been a keen observer of social politics, but ignored the bigger picture. It's hugely accomplished and confident.

So, yes, this is what happens. You listen once and feel detached, a little disappointed even, not dissimilar to the feeling people felt when they watched The Matrix Reloaded. Second time, however, despite not really having any hooks or choruses, what sounds like a mess becomes anything but. It is a deeply strange album - there is no point pretending this is commercial - but given production that glues everything together, it unveils itself as arguably the band's most cohesive to date; certainly their most fascinating.

Because this is, make no doubt, as bold a leap as Blur on 13 or Radiohead on Kid A. Those albums carried elements of what made their bands famous, while also rejigging the formula to the extent that they were never able to find the original mix again. But this is fine. It should be celebrated. Excellent albums should be awful on first listen.

It's what talented musicians do to challenge their listeners, and in this quiet album, with its observations made from within Turner's head, or at a stretch, the other side of the room, Arctic Monkeys deliberately and determinedly leave behind everything that was on their first album. That was 12 years ago, which leaves you with the feeling the monkeys have grown up, evolved, become more complex and - in the process - become more human.

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