Wynton Marsalis: Miles Davis? He was a rock star

The old kind of jazz is the only real kind, claims Wynton Marsalis. Sholto Byrnes is not convinced

Wynton Marsalis leans over the desk towards me, a smile both encouraging and warning on his face. "When I read your article I'm going to say, 'Yeah, you're my man. You understood. Unlike many of the others, you understood.'"

His has been a career of effortless achievement: performing the Haydn Trumpet Concerto with the New Orleans Philharmonic Orchestra and recording with Art Blakey's legendary finishing school, the Jazz Messengers, while still in his teens. And becoming the first artist to win Grammies in both the jazz and classical categories when he was only 22. In the intervening two decades he has released numerous albums, ventured into orchestral composition (winning the Pulitzer Prize for his Blood On The Fields oratorio), and now sits upon a mighty throne as director of Jazz @ Lincoln Center – a job which puts him in control of programming at the New York venue with a budget and powers of patronage unequalled in jazz history. But despite all this, the world's most famous and powerful jazz musician feels seriously misunderstood.

He blames it on the critics. An attempt to enquire what he feels about the criticism levelled at him by the saxophonist David Murray, who said that great jazz musicians were out of work because they don't play in Wynton-approved styles, gets Marsalis very agitated. His already fast speech speeds up, and he interrupts before I can finish the sentence. "Every four years there's another issue. There's another controversy, but it's never really controversial. What is the controversy?" he demands. "What's the controversy now – what is it? Man, it's like a thousand times, controversy!"

Of course, he knows really why he is a controversial figure. Leave aside his own trumpet-playing, which is universally praised, and Marsalis is seen as the standard bearer for those who want to codify jazz as America's classical music, and whose focus is on recreating the music of the past rather than innovating. Given that many feel that innovation is the very essence of jazz, that's a controversial position. But he doesn't see it that way.

"My experience with people on a day to day basis is beautiful," he says, "it's like a dream. Construction workers call out to me when I walk by, people come and bring me pies, they work overtime at weekends." There's no doubting he has a public, although it's not as overwhelmingly positive as he suggests. "Who are you going to interview?" asked the US Immigration official when I arrived in New York to meet Marsalis. "He speaks too much – tell Wynton that from me," were his parting words, a sentiment echoed by a member of Oscar Peterson's quartet I spoke to that evening.

The contradiction at the heart of Wynton Marsalis is that he is relentless in his pursuit of his vision of jazz (he gives me a long and comprehensive definition, but basically it must swing in the "ding-ding-a-ding" sense of the word), yet refuses to accept that his public utterances and his role at the Lincon Center should be seen as anyone's business but his own. In fact, his position as an arbiter of what constitutes jazz is so commanding that everything he does has consequences. During our interview he denies his authority time and again – "it's not for me to say whether it's right or wrong" – when it's perfectly obvious he has strong opinions on almost all areas. He is unafraid to judge, but is wary which of his judgements he reveals, hiding behind a bland wall of "it's not my place to say...". Flashes of what he really thinks come out when he's pushed. After stressing his good relations with David Murray (Marsalis plays basketball with Murray's son, Mingus) he concedes the point: "Did some people lose some gigs because I don't like their style of music? Maybe that's true, maybe that's false, I don't know. But that's not controversial to me."

When I ask if he felt hurt by the comments Miles Davis and the avant-garde trumpeter Lester Bowie made about him (Davis: "that motherfucker's not sharing a stage with me". Bowie: "everybody knows this cat ain't got it") he replies "not at all." He then goes on to describe Davis as "a genius who decided to go into rock, and was on the bandstand looking like, basically, a buffoon", and Bowie as "another guy who never really could play."

These judgements are not wholly without truth. Unfortunately, such forthright condemnations of post-Sixties developments (which Marsalis would deny were jazz) have come to define him as a purveyor of negativity rather than a celebrator, or curator, of jazz history. He is intensely frustrated that the focus is always on what he doesn't do rather than what he does do. Speaking about Ken Burns's mammoth television series Jazz, which was criticised for detailing the early years but skipping through the last 40, Marsalis could be talking about himself. "It's like I come to your house and you lay out a banquet for me and then I'm mad because I don't like the cigar you gave me at the end. Maybe the cigar wasn't that good, but why should that dominate the conversation about the meal?" And then, in a statement that does reflect the divide between him and his critics over post-Sixties jazz: "Maybe you went through that meal just to get the cigar. Me, I wasn't going to smoke that cigar at all."

He does deserve garlands for bringing the music of Ellington, Armstrong and Blakey to new audiences, and his idea that such music should be seen as the bedrock repertory of jazz has much to commend it. It's when he goes beyond this that he starts getting into trouble again. Many contemporary artists in all fields argue that their work has merit irrespective of its popular appeal. When I put this point to Marsalis in the jazz context he is not impressed. "Why subject me to it then?" he says. "Play it in your house. I want people to like what I'm playing."

Such an argument would have confined almost every wave of innovators to their homes, but it's consistent with Marsalis's generally conservative views. Towards the end of our interview he inveighs against rap and hip-hop record companies. "They take your drawers off for you, they show your ass, they sell bullshit, they call themselves 'niggaz' and the women 'bitches' and 'hos' and it's fine with everybody." He adds, voice laden with sarcasm: "It's just our style, cutting edge." But can't people still make their own choices through the possession of a moral sense? "We don't all have that. That's what the essence of decadence is. Civilisation is an effort."

Marsalis is beginning to sound like a member of the Bush administration, only with better grammar. It's no surprise that he considers the more formal Thirties to be "a golden era in American culture for dress, for music, for many things".

"Unlike many of the others, you understood." Yes, I think I do understand. I'm not sure I'm "his man" and I'm not sure I agree with his views. But I do admire his convictions and the work he's doing in jazz education. And to my surprise, I do find myself more "his man" at the end of the interview than I was at the beginning. Marsalis performs a valuable role in jazz, and if he wasn't so combative, that might be more widely recognised.

Wynton Marsalis and the Lincoln Center Jazz Orchestra: Usher Hall, Edinburgh (0131 228 1155), Saturday and on tour. Final date: Barbican Centre, London EC1 (020 7638 8891), 30 January