McCoy Tyner, Barbican, London

There is living history in the hands of McCoy Tyner. He was an original member of John Coltrane's seminal quartet, playing piano with them from 1960 to 1965. He later made more than 80 albums as a bandleader and composer.

The 72-year-old last played London in 2007, and for this London Jazz Festival celebration of 50 years of Impulse! Records, his trio of bassist Gerald Cannon and drummer Joe Farnsworth was joined by American tenor saxophonist Chris Potter and singer Jose James for a set re-imagining the album Coltrane made with singer Johnny Hartman in March 1963.

Tyner, of course, was on those original sessions – all but one of the six released cuts were done in a single take – and here, four of the songs are featured, alongside instrumental outings of great energy and finesse. The opening "Fly with the Wind" clocks in at 16 minutes of creative group invention, with Tyner setting out the theme before the band strides in. Potter and Tyner chase the tune as if it had wings, with Potter's extended, inventive soloing producing not so much sheets of sound as cascading ribbons of the stuff. Joe Farnsworth's pulse is as deft as heart surgery, and there's a high-quality weave in Cannon's handiwork.

Tyner's hard-hitting, lyrical playing is interrupted mid-flow when he picks out a number of the audience bothering him with a movie camera. "PLEASE!" he implores, before taking it back to the top with a furious energy that belies his apparent physical frailty. The following "Blues on the Corner" (from seminal 1960s album The Real McCoy) was drawn, he says, from his home neighbourhood – great jazz players tend to live on the corner, it seems, as well as on the edge. And like the lyrical ballad that follows, with its spiral of a tune rising, step by step, like stairs to a lover's room, this is music that gives out more oxygen than it sucks in – it's giddyingly good.

Singer Jose James appears for "Autumn Serenade", and a lovely "Dedicated to You", a ballad in which bass and drums ease in like a slow train and Potter's sax unfurls in nocturnal slow motion. "You are too Beautiful" ups the tempo, before a final, aching ballad in "My One and Only Love", and a great, weeping solo from Potter. Jose James then departs, and Tyner closes with a piece of Ellington, and his own "African Village", a propulsive, energetic and triumphant finale.