One of the great jazz bands of the past half-century, comparable in class and curiosity (if not box-office clout) with the 60s groups of Miles Davis or John Coltrane, has been the Art Ensemble of Chicago. The 1960s offspring of that city’s civil rights-inspired Association for the Advancement of Creative Musicians, they have been devoted to fusing Africa’s traditions, western art forms, improv, blues and rock under their banner of “great black music, ancient to the future”. A big, mixed-genre lineup led by septuagenarians Roscoe Mitchell (reeds) and Famoudou Don Moye (drums) tell that story in a thrilling 50th anniversary show for the London jazz festival, which also commemorates the band’s late co-founders Lester Bowie, Joseph Jarman and Malachi Favors Maghostut.

They begin with a preparatory Art Ensemble habit – the whole group standing motionless, facing stage left. A long opening deep-strings drone hums until a staccato summons from Mitchell’s soprano sax, and a stretch of churning strings free-improv ends with a jubilant groove on a tuba hook, which guest tenor saxophonist Shabaka Hutchings whoops and wriggles through in a scalding solo. Mitchell’s own banshee pitch-bends and circular-breathing detours are highlights, as are rising young UK/South African star Abel Selaocoe’s spellbinding vocal and cello-improv soliloquy over a percussion clamour led by Moye’s congas, and Hugh Ragin’s valediction to original Art Ensemble trumpeter Lester Bowie, in whistling high tones and windily bluesy slurs.

The sidelong Art Ensemble theme Odwalla brings cheers, as does the band’s joyously funky encore, led by exciting young bassist Junius Paul. On the way out, the hallways echo with people singing Odwalla in rightful gratitude for a special night.