Cheltenham Jazz Festival, Town Hall/Everyman Theatre, Cheltenham

Masterclass in style and substance

Now into its seventh year, the crowds are increasingly drawn to the elegant Georgian terraces of Cheltenham for the International Jazz Festival, and deservedly so. The organisers sugared the pill for those wary of jazz by opening on Thursday night with the ubiquitous Jools Holland and his Rhythm and Blues Orchestra. Quite why anyone thinks Mr Holland has any jazz credentials whatever is one of life's great mysteries, but the real show began on Friday night with the Randy Brecker Sextet. Brecker is one of the world's foremost session trumpeters, and often granted less respect as a jazz player because of that, but he has an easy proficiency and is a formidable hard-bopper. He was on relaxed form, effortlessly and unintentionally showing up the British players in his band. His generosity was evident in the time he allowed them to solo, and in the fascinating masterclass he gave the next morning, where his constructive criticisms of the youthful musicians were kindly and diplomatically put.

Brecker was followed on stage at the Everyman Theatre by the Mike Stern Quartet. A former Miles Davis collaborator, Stern on guitar formed a burnished metal and oil combination with the tenor saxophone heavyweight Bob Franceschini. This quartet, including Lincoln Goines on electric bass and Lionel Cordew on drums, had all the exhilaration of a racing car revving up, tyres spinning and burning, as they wrung the juice out of a series of superb jazz rock numbers. You could file it under fusion, but it had none of the designer-suited smoothness and emptiness that that word can imply. This outstanding band had heart and balls.

Saturday evening began as a more cerebral affair, with Britain's own John Surman and then Marty Ehrlich's Traveller's Tales. Ehrlich's thoughtful compositions were given plenty of space to breathe, the leader (on alto sax – sadly he'd left his bass clarinet at home) paired with Tony Malaby on tenor sax, and rhythm section of drums and acoustic bass guitar. At times challenging, you'd need a few stamps on your passport before embarking on these travels; but it proved a very rewarding journey.

Delayed by 25 minutes, Christian McBride's band later played a storming set that was the highlight of this critic's visit. Still only 30, the Philadelphian McBride deserves every accolade he has won for his handling of the electric and double basses. He has reached a level of virtuosity that is possibly unparalleled. Not that he over-uses it, a temptation the Danish master double bassist Niels-Henning Orsted-Pedersen regularly succumbs to when he plays live. McBride has an imposing command of every technique – pizzicato, bowing (I have never heard a melody bowed as well on double bass as on his lovely ballad, "Lullaby for a Ladybug"), plectrum, and judicious use of sustain, echo and wah-wah pedals.

With his clever reworkings of jazz numbers and tunes by Steely Dan and Sting, this winningly un-self-important young genius provides one answer to the omnipresent question of where the future of jazz lies.

McBride's keyboardist, Geoff Keezer, is also astonishingly good, and to be commended for reclaiming the rhodes piano and even the Moog synthesiser for jazz use (he had both alongside a more conventional grand piano). Keezer's inventiveness and authority, which he also displayed on Sunday in an impressionistic lunchtime set with London's Gerard Presencer, bear comparisons with Herbie Hancock.

So there was plenty on offer at the festival, the main acts being supplemented by the Jerwood Rising Stars (of which the excellent Presencer on flugelhorn was one), a fringe festival, and a programme from Trinity College of Music. Congratulations to Tony Dudley-Evans, the festival director, for assembling such a fine list of acts.

One observation, probably of no great relevance. The American visitors were distinguished by two factors: their greater conviction in performance, and their more interesting appearance – McBride, Brecker, Franceschini and Ehrlich all wore hats – either Moroccan or baseball – and the chin of McBride's saxophonist, Ron Blake, was decorated with a beard like a liquorice bootlace. Could the two factors be linked?