The Last Shadow Puppets, Guildhall, Portsmouth

"Thanks for 'avin' us, Portsmouth," says Alex Turner. "It's our first time." The string and brass sections glimpsed behind him like ballroom ghosts are enough to tell you the Arctic Monkeys' prosaic urban dreams have been briefly left behind. His new band with The Rascals' Miles Kane, The Last Shadow Puppets, instead attempts urbane sophistication on record. David Axelrod and Love's Arthur Lee are among its challenging models. But tonight's full debut unexpectedly harnesses this sound to driven rock'n'roll. The shrieking strings aren't prissy adornments, but aggressive implements in the service of the old-fashioned, four-piece beat group Turner and Kane lead at the front. The daring of their experiment is clarified thrillingly.

The Last Shadow Puppets' inevitable classification as a Turner side-project is deliberately challenged. Kane takes most of the lead vocals and electric guitar, his partner literally keeping his head down in acoustic, anonymous support. They wrote the album with the give and take of early Lennon and McCartney, so it's impossible to separate their contributions.

While other groups have settled for plain street tales in the Monkeys' wake, the trend's instigator has left them in the dirt. Yet on "The Meeting Place", there's a girl who, "the colder the night, the deeper she shaves". And even as "My Mistakes Were Made for You" lashes the John Barry and Beatles of 1964 together, another girl is "as subtle as an earthquake, with the filthiest of minds". These could be the same people from the same Sheffield streets as in any Monkeys song; played now, though, as femme fatales, by Forties movie stars.

Kane tries Ethiopian jazz guitar on "Hang the Cyst", and long psychedelic blues notes on "I Don't Like You Any More". Turner dominates just once, crooning "Time Has Come Again". When he announces, "We're the Last Shadow Puppets" halfway through, he seems only half-convinced, as if they're not quite a real band; certainly not his, as the Monkeys are. But their album's pastiche feel and noir misogyny has been replaced by celebratory, innovative swagger tonight. You can feel Turner and Kane stretching into new shapes. Compared to their plodding indie peers, what they will do next is thrillingly unguessable.