“Do we have any fans with a falsetto voice?” Jonathan Higgs asks a packed Hackney hall, seeking solidarity. The Everything Everything frontman gets cheers of support, but as the high-voiced poster child of indie’s quasi-New Complexity – the increasingly arena-friendly, math-rock movement where bands such as Foals, Alt-J and Django Django merge guitar intricacies, fiddly afrobeats and electro clicks and whistles – he’s virtually unsingalongable.

His natural range is a rich, soulful warble, but when he pops into his falsetto, his tongue-twister raps make itchy older tracks such as Cough Cough and Schoolin’ sound as if they’re tripping over themselves in their rush for the future.

It’s led to comprehension issues before. That a song such as MY KZ, UR BF resembles Heaven 17 mentally disintegrating at an ayahuasca ceremony, for instance, has tended to cloud its concerns about drone warfare. So for the new songs from forthcoming third album Get To Heaven, Everything Everything slow the pace to let the politics peek out. The brooding, euphoric The Wheel (Is Turning Now) casts Nigel Farage as a fake faith healer, Regret mirrors the fickle fate of girls tempted out to Syria and the Radiohead-ish Fortune 500 has Higgs as a downtrodden dealer of retribution on a murderous rampage through trading floors and palace halls. 2015 seems so bleak that recent intense single Distant Past yearns for pre-history, Higgs dreaming of “blood dripping down my sunken monkey chin”.

In their urgency to be understood, Everything Everything occasionally tumble into Noel Fielding-esque surrealism. Tackling modern helplessness with the line: “It’s alright to feel like a fat child in a pushchair” on the emotional epic, No Reptiles, prompts hilarity, as if designed to baffle a super-intelligence that’s escaped on to the internet just long enough for us to turn the damn thing off. But with frenetic pop genius like Kemosabe and Photoshop Handsome abounding, Everything Everything should soon mean all things to all people.