London Jazz Festival

If it walks like a duck and quacks like a duck, don't just call it a bird

This year's London Jazz Festival has been notable for two things: the absence of a raft of big American names – the Wayne Shorters, the Marsalis brothers, the Chick Coreas – and a curious lack of confidence in jazz itself. The festival programme says it was always supposed to be "a jazz festival that didn't have just jazz in it", but from some of the publicity it sounded like you'd be lucky to find any at all. The arts overlord of the Evening Standard, one of the festival's sponsors, heralded its opening with a remarkably silly article in which he crowed that the line-up was "approximately two-thirds world ... Some may regret world's displacement of jazz," he wrote, but "a healthy society must celebrate diversity in the belief that it will bring about cultural regeneration." The author, Norman Lebrecht, is a distinguished classical music scholar. No doubt next year we can look forward to him suggesting the Proms play their part in "cultural regeneration" by telling the stuffy old symphony orchestras to make way for groovin' Norman's world music ensembles.

World music may be all very well (I stress "may be" – there is not space here to discuss it), but in future can we just render unto jazz what belongs to jazz, and let world music devotees bang their drums elsewhere? Jazz is underfunded and underappreciated, and the way to attract new recruits is not by getting people along under false pretences – not that "don't worry, it's not really a jazz festival" is much of a rallying cry. The organisers would have done well to sweep away the world element and instead adopt the approach of the Cheltenham Jazz Festival, which featured the likes of Christian McBride, John Scofield, Dave Holland and Abdullah Ibrahim, unambiguously stars in the jazz firmament.

Even if the Lebrecht crowd didn't want you to know it, there was some rather good jazz at this year's festival. The Pizza Express Jazz Club in Soho concentrated on the European scene, featuring amongst others the Italian altoist Rosario Giuliani (best known here for his work with Guy Barker), and the beguiling French saxophonist Julien Lourau. The latter's simple, dignified melodies are crafted from the dust of a timeless Mediterranean landscape, drawing from Spain and Southern France on one side and the Maghreb on the other. He opened one set with a single electrifying accented note, like a sharply raised eyebrow, just as he does on his latest album, The Rise. It ushered in a tune of two parts: one slow and on the beat, the swing squeezed and displaced as though the band were pushing on the lid of a jack-in-the box, the other let off the leash, Lourau leading his quartet rushing up and down the winding streets of a Provencal town.

Brad Mehldau's trio at the Royal Festival Hall was as infuriating and compelling as ever. The pianist dabs away at the keyboard like a butterfly on an ice rink, barely ever rising above mezzo-piano. You really have to listen to hear him above Larry Grenadier's boomy double bass (I don't know why he chooses to use such an indistinct tone) and Jorge Rossy clattering around the kit. Mehldau loves deconstructing standards, and this time he gave Harold Arlen's "Get Happy" the treatment. The trio pulled in three directions, leaving the melody hanging by a thread in the middle, while Mehldau provided a fantastic Jarrett-esque cadenza. They hardly ever swing, they're not bothered about producing strong tunes of their own – there are so many reasons why Mehldau's concept should fail, and yet in concert it is utterly mesmerising. Even before Mehldau started, the British pianist Julian Joseph was rolling his name around his mouth. "Braaaad Mehldau," he was saying to himself from his seat behind me. "Brayed Mehldau."

Sharing a bill with Mehldau was the US saxophonist Chris Potter. Reversing the usual pattern, his quartet live was not a patch on the superb studio album they've just made. Unfocussed and uninteresting, they sounded as if they were coasting, expecting to knock the London audience dead with their punchy New York sound although they were only going through the motions. It showed.

The festival finishes tonight with what should be a very special concert by saxophonist Lee Konitz, a true jazz legend, and the chance to see the wonderful drummer Billy Hart in the cosy confines of the Vortex. I'd advise Mr Lebrecht to go along. He might learn something about this crazy jass music.

Brad Mehldau, Lee Konitz: BBC Radio 3, Monday 7.30pm