Wynton Marsalis Quintet, Ronnie Scott's

“Wynton Marsalis has had an enormous impact on jazz over the last 40 years,” say the programme notes, “being one of the first artists to perform and compose across the full jazz spectrum from its New Orleans roots to bebop to modern jazz.” Although it seems to bestow an extra precociousness upon the American trumpeter, who was only born in 1961, the first part of that sentence is undoubtedly true. The second part is true too, until the last two words.

That was clear in his set tonight, blues-indebted and swinging – or, occasionally, Latin-tinged – throughout. It was clear in Marsalis’s grunts of “Yeah” and “Uh-huh” and even “What are you waiting for?” when the pianist delayed a solo; jazz Tourette’s that would seem more at home in New Orleans or Harlem of yore. It was clear, even, in the clothing: the whole band wore shirts and ties, only the rhythm section excused jackets.

Wynton’s Neo-Classicism, however, is hardly news. The question is whether it matters. That the most prominent figure in jazz insists on looking at the music only in the rear-view mirror is, arguably, a betrayal of the genre’s very ethos. (And Wynton, founder of the behemoth that is the Jazz at Lincoln Center programme and one of Time magazine’s 25 most influential people, is the most high-profile jazz musician of the last 30 years.) But Wynton was on stage tonight as a trumpeter, and on that level, his traditionalism might not have mattered so much; after all, leaving aside the fact that we might never have had a Louis Armstrong or Dizzy Gillespie if they had taken this sort of curator’s view of the genre, this might be the closest we get to those late, great trumpeters.

The man who famously won two simultaneous Grammy awards, one for Jazz and one for Classical Music, has peerless mastery of his instrument, and his tone and articulation tonight were genuinely dazzling. On the frenetic “First Time”, he negotiated the melodic contours as fast as a skier in a field of moguls. The standards (“April in Paris”, a Django Reinhardt number) were thoughtfully arranged, and the band predictably tight. Saxophonist Walter Blanding matched his leader note for note on "First Time"; pianist Jonathan Batiste was masterful in his use of space (he was delaying that solo for a reason) and dynamic range; drummer Ali Jackson played mischievous games with bar-length subdivisions; Carlos Henriquez pulled off a spectacularly fleet-fingered solo in thumb position. Even the banter was honed: harmony, he suggested, was both horizontal and vertical but “more horizontal than vertical – like most good things in life”.

As the set went on, however, all the good work was undercut by an increasingly serious problem, which may or may not be linked to Marsalis’s purist outlook. The show was enjoyable, and impressive, but at no point was it moving. As a trumpet player rather than jazz ambassador, that emotional bedrock is what Marsalis needs to find if he is ever to sit alongside the heroes he so worships. It may not be a new criticism but it remains valid, although as someone who wishes to see jazz survive as a mainstream, as well as a leftfield, music, there’s little pleasure in saying so.

• Wynton Marsalis Quintet are at Ronnie Scott's, London, until Saturday, 20 August (sold out)
• Find Wynton Marsalis on Amazon