Revered because of his role as the pianist in the revolutionary John Coltrane Quartet in the Sixties, and also as leader of a series of brilliant recordings for the Blue Note label in the same period, McCoy Tyner, 59, is an authentic repository of the great tradition; a kind of much-loved carriage-clock in the heritage industry of jazz. His appearance at the Royal Festival Hall on Monday was, therefore, an opportunity for more than a little ancestor worship, and he performed to huge affection and applause.

Tyner has grown into this elder-statesman role as if to the manner born, his slicked-back hair (with the contemporary touch of a little top-knot pony-tail), pencil moustache and generous figure making him look the very image of the old-style piano-man band-leader, part Earl Hines, part Count Basie. Stylistically too, he has slipped into the past a bit, favouring a mainstream approach rather than the uncompromising Modernism that won him his spurs. Thankfully, he can still make the piano talk.

Way back when, Tyner's thing was producing rolling waves of continuously ecstatic notes that washed tumultuously against the shore of Coltrane's saxophone Inventions, buoyed up by the relentless attack of Elvin Jones' drumming. Now, playing in a trio, the waves continue to roll and the technique is the same, only less so. His signature-sound is still gloriously apparent: he smacks the bottom of the keyboard with an open left palm while his right hand pummels the treble-register ribs with a rolling, tremolo-heavy motion that almost begins to bounce the Steinway along the stage. Glorious stuff - but not exactly new any more. Also, like most big stars of a certain age, Tyner defers to his band more and more as the performance progresses, and Avery Sharpe's marvellously fluid (if a little over-twangy) bass solos and Aaron Scott's fine drumming take up more slack than is strictly necessary. Tyner still has it all right, he just lets it out more slowly these days, an incremental release of a wonderful gift that one wants - unreasonable though it may be - to be smothered with all of the time.

Later that night at Ronnie Scott's, as a perfect corrective to Tyner's rather prematurely-aged approach, the alto-saxophonist Kenny Garrett (Miles Davis's last sax-man) produced the kind of continuously energetic and astoundingly inventive jazz that you can easily forget still exists. With a full-on rhythm section and a repertoire of themes played flat-out at impossibly fast tempos, Garrett took the chord changes like a champion hurdler in a heroic performance that showcased both his impeccable technique and his beautiful, Parker-esque, tone. His version of Coltrane's "Giant Steps" is not to be missed. It can be heard at the club until Saturday, although this will be a very hot ticket indeed.

The Contemporary Music Network tour by Lawrence "Butch" Morris, which came to an end at the QEH as part of the Festival this week, was extraordinary on many counts. Leading a 23-piece band of British free-improvisers through a programme showcasing Morris's method of "conduction" (there's no music, but Morris conducts the band through a series of semaphore-like gestures designed to bring out the musicians' individual qualities), the results were, initially at least, compellingly good. Eventually, however, it was the instruments rather than the players or the conductor who seemed to win out, with the quirky, DIY noises of tuba-farts, sampler-deck mutterings and ethereal glissandi from sundry string-driven things making the most impact. Faced with the imposed dictatorship of the conducter, the proletariat of the orchestra had, it seemed, gone all bolshie and rebelled. It was Animal Farm all over again.