Keith Jarrett, Royal Festival Hall, London

Although photography is strictly forbidden tonight, anybody with eyes open will take away a gallery's worth of memorable images in their mind. Keith Jarrett is off his piano stool almost from the moment that he hits the keyboard and at very regular intervals he will arch his body right over the stately grand as if he is about to climb under the lid. He will slowly crouch until he is practically horizontal and extend his right arm to the instrument like a fishing rod, dipping into the choppy sea of sound.

And, in the most thrilling of gestures, he will strike up a dance, feet stomping and shuffling emphatically from side to side as his head rocks sharply back and forth.

It seems improbable that Jarrett suffered a debilitating bout of chronic fatigue syndrome several years ago, but the decision to play three short sets instead of two long ones may be a residual indication of that. In any case, his body is wired with energy and the visual spectacle vividly mirrors the verve and intensity of the music.

Dedicated to the tradition of playing American songbook staples, the "Standards Trio" Jarrett leads tonight is possibly the nearest thing jazz has to a supergroup. The pianist has been performing with double bassist Gary Peacock and drummer Jack DeJohnette for 25 years, and in that time, they've attained a stardom that ensures world tours, high CD sales and great adulation. They are both yardstick and sphere of influence.

Indeed, many artists who have recently made their mark on the piano-trio format, above all Esbjorn Svensson, owe a debt of gratitude to Jarrett for the way he drew on the models of Bud Powell, master of the chordal slalom runs of bebop, and Bill Evans, the architect of crystalline, classical-inflected balladry, to create his own model, one with folk-like melodicism and the elastic metres of the avant-garde.

Jarrett's latest release, Yesterdays, has 1950s bebop and 1940s Broadway standards, but the audience hasn't come to hear "their" tunes. The whole point about a jazz standard is that it can become something else in the hands of great improvisers, so if the band pulls out a Gershwin tune, as they do, then it is the structural transformation and the input of original nuance and detail that make the exercise worthwhile.

Although a bustling surge through "I'm Gonna Laugh You Right out of My Life" provides exhilaration, and "You Belong to Me" impresses for its silken harmonies, the high point of the evening is a majestic take on "Autumn Leaves", in which the combination of Jarrett's ability to create fleeting melodies within his central improvisation and Peacock and DeJohnette's massaging of the pulse to suspend it tantalisingly between 3/4 and 4/4, is superb. Quite seamlessly, the piece shifts into virgin territory, a Latin-flavoured vamp in which a heavily syncopated bass drum becomes the lead voice around which double bass and piano swirl in short, charged lines. Jarrett then stirs a couple of rich, chunky, mid-range chords into a bubbling whirlpool, proving that, for all his gifts as a soloist, he is a devastating accompanist.

The cohesion of that piece held for the whole gig, but what stood out were the moments of great sensitivity on the ballads – the expertly weighted slur of Peacock's bass, the bell-like tinkle of DeJohnette's cymbals and the vaporous, almost whispered quality of Jarrett's melodies, where the notes are slowly caressed rather than pressed into life while the pianist stays steady, head bowed as if deep in prayer.

All of which means the "Standards Trio" has a double meaning. It is about old songs and a new level of excellence to which others must aspire.