“I just wanted to be one of the Strokes,” sings Alex Turner at the outset of the Arctic Monkeys’ sixth album. “Now look at the mess you made me make.”

Certainly, he and his band seem to have traversed a far greater distance in the last 12 years than any of their peers, to the point where they seem almost unrecognisable. This is evident from the way they look – posing in snakeskin shoes and expensive overcoats they resemble characters from a film, something you could only have said of them in 2006 if it had been directed by Ken Loach – to the way they sound. There is almost nothing to connect the music on Tranquility Base Hotel & Casino with the muscled-up stadium indie rock of its 2013 predecessor AM, let alone the contents of their debut.

Facebook Twitter Pinterest ‘The songs can feel like less than the sum of their parts’ ... Arctic Monkeys. Photograph: Zackery Michael

Instead, Tranquility Base displays the same endearingly puppyish, have-you-heard-this? enthusiasm for Serge Gainsbourg’s Histoire de Melody Nelson and the Beach Boys’ Pet Sounds as the first album by Turner’s side project Last Shadow Puppets did for late 60s Scott Walker. Low-slung and agile, virtually every rhythm track and bassline here could have stepped straight off Gainsbourg’s 1970 masterpiece, while Pet Sounds is paid homage everywhere from the vocal harmonies to the forensic recreation of its sound on The World’s First Ever Monster Truck Front Flip. Their combined influence is heard not just in the sound, but in the songs, which are melodically far richer and less concerned with verses and choruses than anything Arctic Monkeys have previously produced. At their best, they’re fantastic – American Sports and Four Out of Five sound lavish and fresh, their tunes and chord sequences twisting and turning unexpectedly. At worst, uncoupling the songs from a standard structure makes them ramble, as on Batphone.

Along the way, Turner has had to deal with the problem that inevitably affects artists who become hugely successful by offering up sharp-eyed vignettes of everyday life: what happens when you become, as Philip Larkin alliteratively put it, the shit in the shuttered chateau, insulated by wealth and fame from the everyday life that initially inspired you? On Tranquility Base, Turner settles on an imagistic collage approach to writing, where snatches of overheard conversation are jumbled together with snappy observations and a dash of Father John Misty-esque fourth-wall-breaking (“I want to make a simple point about peace and love but in a sexy way where it’s not obvious”).

Turner is clearly a very smart guy: smart enough to treat rock-star ennui as a joke rather than a subject that’s supposed to elicit sympathy – “I’m gonna run for government,” burbles the jaded narrator of One Point Perspective, “I’m gonna form a covers band an’ all” – and smart enough to tackle the hackneyed topic of social media and its impact with real wit and originality. It’s hard to stifle a groan when it becomes clear the latter is one of Tranquility Base’s preoccupations, but Turner is both funny – “dance as if someone’s watching, because they are” – and bold enough to suggest that the face-to-face contact always promoted as the solution to social media’s remote unreality is a pretty fraught business, too: “I’m so full of shite, I need to spend less time stood in bars waffling on to strangers”.

The problem is that a smart guy is sometimes all Turner seems to be. The songs can feel like less than the sum of their parts: a selection of one-liners, wry observations and knowing winks to camera that leave you struggling to work out what he’s driving at – and wondering if he knows, or cares – and to locate any real emotional connection or impact. You find yourself occasionally wishing the kid who plaintively, incisively skewered the demonisation of chavs on their debut album closer A Certain Romance would show himself again.

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It’s an issue compounded by Turner’s voice, which has changed a lot. The Yorkshire dialect that was once his USP is now deployed sparingly, as a jolting effect: “He’s got him sen a theme tune.” Elsewhere, his voice carries traces of Gainsbourg’s sprechgesang, and Jake Thackray’s careful enunciation and chewy vowels; he regularly shifts into a mid-Atlantic easy-listening croon (“a lounge singer shimmer,” as Star Treatment has it) that seems deliberately mannered, another knowing wink to camera. It’s an odd mix that’s sometimes compelling and sometimes a bit pleased with itself, as if Turner is delivering every line through a supercilious smirk.

At turns thrilling, smug, clever and oddly cold, Tranquility Base Hotel & Casino is only a qualified success; there’s something quietly impressive about the fact that it exists at all, at least as an Arctic Monkeys album. The obvious, craven thing to do would have been to release it as a solo project, then make a crowd-pleasing album in AM’s vein. Instead, here it is, evidence – albeit flawed – of a certain musical restlessness: the very thing, one suspects, that’s caused the band to travel so much further than their contemporaries that they’re virtually the last indie band standing.