St. Vincent @ Edinburgh Playhouse, 26 Aug

St. Vincent’s Annie Clark is standing left of centre on the Edinburgh Playhouse’s imposing stage. She's wearing a full nude bodysuit, thigh-high orange boots and an oversized matching belt. Her hair hangs in a sharp dark bob. Her custom electric guitar shines in the light. For the next two hours, her pop genius is blasted loud – Those solos! Her voice! That bass! – but it's also embedded in careful details. Clark performs in micro movements – one beckoning finger, one tapping foot – to ensure that some three thousand people hang on her every hyper-realised breath. Above her head, a screen displays the video art from recent album Masseduction with lurid, stylish drama; screen-Clark stares out at us, unblinking, as bedazzled boxing gloves pummel her cheeks.

She opens with Sugarboy, a song that cracks open any correlation between gender and performative storytelling: 'I am a lot like you (boys!) / I am alone like you (girls!)' she states, pumping a single fist and exploring the ways in which listeners try to find themselves in her, revelling in the fakery and the magic. It feels both a warning and a comfort. Then – a guitar solo, the first of many. Surely Clark is this generation’s guitar hero, and she shreds with violent, disorientating detachment.

Behind her are four sparkling panels, as if enormous glitter balls have been steam-rolled flat. Her drummer and synth player are both dressed in utilitarian boiler suits, beige masks and blonde bowl-cut wigs. Bassist and vocalist Toko Yasuda dances neatly to the right of Clark. The 20 song set skims ten years and four albums of St. Vincent, darting from older singles like Year of the Tiger to the dystopian crush of this year’s Fear the Future. In-between, the lights fade to black and Clark vanishes from view, reappearing seconds later like a faulty hologram – but this time with a different guitar in a different neon hue.

The Playhouse is an odd venue for one of pop’s brightest, oddest stars. The audience feels cowed by the room’s plush interior and are too timid to stand until the show’s halfway over. Twice Clark has tried to incite movement, but it takes the unmistakable opening bars of Digital Witness to persuade people to take the plunge. It starts as a trickle – tentative dancing under the supervision of stewards – but by Rattlesnake the room is carefree, bouncing between the velvet seats.

A noisily demanded encore begins with newer song Smoking Section. Staging vulnerability, she croons under a single spotlight: 'Sometimes I feel like an inland ocean / Too big to be a lake, too small to be an attraction.' The lyric is a precise capturing of an artist in full power, aware that she’s unlike any other. On this penultimate night of the Festivals, Edinburgh’s crowd scrambles to please her, to make up for lost time. The Edinburgh International Festival brought glittering pop gifts to the capital this summer – all we need now is proper space to dance.