Herbie Hancock, London Jazz Festival, Royal Festival Hall

A member of Miles Davis's legendary second quintet (“arguably Miles's best ever group” according to the Penguin Jazz Guide); a composer of standards (“Watermelon Man”, “Dolphin Dance”, “Maiden Voyage”, “Cantaloupe Island”) and soundtracks (Antonioni's Blow-Up, Bertrand Tavernier's Round Midnight); winner of over 10 Grammy Awards, the first for hi

s 1983 hit single “Rockit”, the most recent for his magnificent 2007 Joni Mitchell tribute album River: The Joni Letters (one of only two jazz recordings to win the coveted Album of the Year award, the other being Getz/Gilberto over 40 years ago). Whichever way you cut it, pianist Herbie Hancock is one of the lodestars of American music, whose influence reaches out far beyond the narrow confines of jazz. A brilliant extended set from this bona fide jazz icon brought a capacity RFH audience to its feet.

Whether performing material from his matchless back catalogue or his latest release, The Imagine Project, what was especially galvanic about this London Jazz Festival show was the way in which - both in solo and group settings - Hancock breathed new life into everything he played. From the blazing energy and startling complexity of the full-band opener “Actual Proof” (from his 1974 album Thrust) to the self-communing delicacy of his gorgeous solo prelude to John Lennon's “Imagine”, the title track of the new album, his constant search for new expressive arcs was inspiring. More than that, in the age of the anemic X Factor cover version, it was life-affirming.

With two changes from the line-up I saw at the Copenhagen Jazz Festival earlier this year (bassist James Genus replacing Tal Wilkenfeld, drummer Trevor Lawrence Jr replacing Vinnie Colauita), the quintet possessed an extraordinary ability to keep the seething mass of contrapuntal detail in almost perfect balance while coaxing the listener into a state of wide-eyed wonder. This was music-making at an almost superhuman level. Being conversant with a vast array of styles, from post-bop to funk to classical, Herbie - who celebrated his 70th birthday in April - has always been a frontier-breaker, intermingling musical genres in fertile and fascinating ways. Entering the world of The Imagine Project is rather like plugging into his personal iPod: alongside familiar names from pop music, the album also features Anoushka Shankar, Konono No 1, Tinariwen, The Chieftains, Oumou Sangare, Los Lobos and Toumani Diabate.

Thanks to the wonders of technology, the rich textures of the recording were either conjured up from Herbie's hard drive or by the multifaceted keyboard work of Greg Phillinganes. In a striking juxtaposition of Bob Dylan's “The Times, They Are a’Changin’” and Sam Cooke's “A Change is Gonna Come”, the keyboardist stepped into the shoes of The Chieftains and supplied the most life-like sample of Irish uilleann pipes I've heard – believe me, not an easy instrument to mimic.

Vocalist Kristina Train sang gamely in both English and Irish on the Dylan (Lisa Hannigan features on the album) and also contributed some understated fiddle work. Cooke's 1960s single was powered by the unforgettable lead vocal of Phillinganes. From the passionate intensity with which he delivered the opening line, “I was born by the river”, which immediately drew several whoops from the audience, it was evident that something pretty exceptional was on the way.

Thanks to guitarist Lionel Loueke also chipping in with some rather wonderful multilayered backing vocals on “Don't Give Up” - sung here by Phillinganes and Train, on the recording by Pink and John Legend – the textural palette was constantly shifting. From the otherwordly interlude of “Court and Spark” to the powerful block harmonies of “Exodus”, this was a gig full of delightful, ear-catching details.

The powerhouse encore, “Chameleon”, brought people to the front of the stage en masse, either shaking their booty or thrusting iPhones at the musicians. Ever the gentleman, Herbie took it in his stride, walking the length of the RFH platform to shake outstretched hands.

• Full details of this year's festival, which runs until 21 November, are available on the London Jazz Festival website (iPhone users can download their own pocket-sized programme)
• Find The Imagine Project on Amazon