John Grant and Edinburgh were made for each other. 'I'm so happy to be back in your incredible city,' said the bearded, oak-voiced singer from Colorado, who also told us he'd been pondering learning Scots Gaelic. 'It looks like whoever built this place thought, "this is gonna be the centre of the universe", there's nowhere else like it. Rome, Edinburgh, maybe St Petersburg …' At which point, on cue, someone shouted out 'Glasgow!' and the spell was broken.

They whole exchange echoed what we might expect from a set by Grant himself. For more than a decade the singer with mournful Denver alt.rock group The Czars, a personal meltdown caused by drug and alcohol abuse and his relationship with his own sexuality drummed him out of the music business for a time, before 2010's debut solo record kicked off a critical and commercial renaissance. His music, therefore, bears the mark of someone who is right at the top of their creative game, yet who can afford to be self-deprecating to an existential degree.

His stage is set like an empty nightclub, the band surrounded by dry ice and LCD lighting towers, and Grant sings like the last person locked in after the party has moved on; pondering grocery shopping and the tragedy of children who have cancer on the existential evocation of depression 'Grey Tickles, Black Pressure'; considering the state of humanity (including his own) in 'Global Warming'; and self-aggrandising to a very funny degree in 'GMF' ('I am the greatest motherfucker / that you're ever gonna meet,' he hollers).

The last few songs carry an almighty upturn in tempo, with the monolithic electro riff of 'Pale Green Ghosts' making neckhairs prickle across the room ('when I made that with Daniel from GusGus, I said I want it to hit them right in the testicles,' deadpans Grant, 'and the girls too') and the cataclysmic finale of 'Queen of Denmark' giving way to 'Black Belt's closing club groove. His new album is due later this year, and shows like this set the bar high for its arrival.

Reviewed at Playhouse, Edinburgh, Mon 20 Aug.