Back in Britain to introduce a growing network of fans to their fifth studio album, Prog, the Bad Plus were on ebullient form at the Jazz Café on Wednesday. The trio of David King (drums), Reid Anderson (double bass) and Ethan Iverson (piano), from Minnesota and Wisconsin, have snagged the affection of an audience that stretches well beyond the usual confines of the jazz crowd, thanks in no small part to their habit of including a handful of songs with a pop and rock provenance in their sets.

The latest numbers to undergo the treatment were the Tears For Fears hit Everybody Wants to Rule The World – a version that stuck comparatively faithfully to the rather twee original – and Life on Mars, which underwent a quite extraordinary mauling. Having tested the structure of David Bowie’s song to the point of destruction with an arrangement that started off drifting like gossamer, they somehow moulded it back into shape for a marvellously grandiloquent conclusion.

While Iverson’s piano playing supplied a seamless mixture of the classic and the avant-garde and Anderson’s bass playing provided a secure anchor, it was the irrepressible drumming of King that commanded most attention.

Playing every part of the kit, including rims, cymbal stands, snare strap and an assortment of children’s toys in a constant flurry of limbs, he pushed the music along with a creative eagerness that was compelling to watch.

The bulk of the set was comprised of compositions by each of the three musicians, all of them (songs and musicians) introduced with scrupulous attention to detail and dry humour by Iverson. King’s 1980 World Champion, about an Olympic skiing star, was full of humorous twists, while Iverson’s Old Money, a “political piece”, took a seriously discombobulated turn before a bass solo gathered the song back together.

But the best numbers of the night were a catchy little rocker called Beryl Loves to Dance and a breathtaking industrial-funk workout, Physical Cities, both composed by Anderson. Combining advanced mathematics with high drama, the long series of stabbing, staccato beats at the end of Physical Cities were executed with a skill and synchronisation that was little short of telepathic.

— The Bad Plus play the Edinburgh International Jazz Festival, July 31

Editor's choice

• The 100 Best Films of the Decade
• 70 facts you didn't know about Marvel
• The 50 Biggest Movies Of 2010