None of the 1,371 musical genres on Spotify describe San Francisco’s Deafheaven. Although some have attempted to pin down the band’s music as “blackgaze”, their vast palette reaches from black and death metal at one end to shoegaze, dream-pop, post-rock and ethereal ambient at the other. With drummer Daniel Tracy’s blast beats sounding like furiously galloping horses, they emerge with a fearsome concoction of pulverising noise and plangent beauty.

This approach has resulted in fans and detractors. Their second album, Sunbather, was Metacritic’s best reviewed of 2013, but the group have been dubbed “false metal”. Although their music has hints of hard rock – and what sound almost like Thin Lizzy riffs hurtle from the mix – they are not really a metal band at all.

Instead, the sextet’s appearance reflects their gleeful mix’n’match: long hair, a Can T-shirt and, for guitar melodicist Kerry McCoy, short hair and spectacles. Sweat-soaked, hair-flailing vocalist George Clarke is the unflinching link with extreme metal. He screams so intensely it is a shock when he speaks in a polite American accent that would charm anybody’s mum.

Much of the set comes from this year’s excellent album Ordinary Corrupt Human Love, which has shades of Mogwai, Sigur Rós and classical music. The sublime Canary Yellow starts as if it’s a lost Cocteau Twins track and ends with the sound of collapsing civilisations. Even at their most bracing – and Dream House, from Sunbather, is certainly that – they never lose their hooks. Clarke’s guttural howl thrills the devotees, although if he were ever to blend in some conventional singing they could potentially appeal to a huge audience.

• At the Classic Grand, Glasgow, on 2 October. Then touring the UK until 5 October.