But he has his detractors. He's a neo-classicist, they say: safe, backward-looking, a curator of the styles of the past. Presiding at his comfortable base in the Lincoln Center, he gets stick for being less attuned than his brother Branford to what's going on in jazz today.
When the American television series Ken Burns Jazz was aired three years ago, with Marsalis as the prime contemporary spokesman, he was condemned by the jazzerati as being responsible for the fact that the series, which echoed Miles Davis's remark that jazz was dead, was essentially an obituary. The experimental Branford, they said, should have been the guiding light. But one might argue differently: could it be that Wynton's sights are set on wider horizons than those of the masonically-sealed world of avant-garde jazz?
Coming our way later this month is something extraordinary: Marsalis's symphony All Rise, to be performed by his Lincoln Center band, with the London Philharmonic Orchestra and the London Adventist Chorale, and with that august Beethovenian Kurt Masur wielding the baton. Marsalis's symphony, which at 90 minutes is longer than any in the classical canon, would be a great achievement for any classical composer. Coming from this 43-year-old jazz trumpeter - and he wrote it at the age of 36 - it's Herculean.
He has listed the elements in its language: the didgeridoo, ancient Greek music, fugue, the New Orleans funeral cadence, the fiddler's reel, the clave, the naningo, American popular song, Eastern and Near-Eastern scales, and plain old down-home ditties. And he wasn't just striving for "a world-music type of mélange". But that list sells it short: Masur and his orchestra will need to be at the top of their form to do justice to the Mahlerian expressivity and Stravinskian brilliance that Marsalis's score demands. The work reflects a journey based on more than magpie pastiche and taking in three centuries of Western music. At the same time, its 12 movements echo the structure of a 12-bar blues: if it weren't too ill-timed an expression, you might say Marsalis's native New Orleans runs through it like a great meandering river.
I make the mistake of starting my interview by talking about New Orleans, and asking the trumpeter's reaction to recent events. "Deeper than words," he answers, and instantly becomes too choked to speak. When he's recovered, he agrees to recount the genesis of this work.
"Kurt Masur went to one of my concerts in Detroit, and afterwards came backstage and asked me to write for the New York Philharmonic. I thought he was joking. I'd never written any orchestral music, and wasn't known as a composer, even in jazz. So why would this guy approach me? I didn't take him seriously."
But Masur had been serious: he'd loved the "symphonic jazz" tradition, as exemplified by Duke Ellington and Stan Kenton, and, as he told me recently, he'd found it sad that nobody had thought to continue it. "I began trawling through the work of composers in New York, and I realised that very few of them had an independent, individual voice. Most of them were influenced by the Hollywood sound. But when I heard Wynton's music, I realised it was animated by the same kind of feeling as that pervading Ellington and Kenton. He is one of the great jazz musicians, after the tradition of Louis Armstrong and company. I believed he could make history move forward again."
After three years, as Marsalis explains, they met again. "And he asked if I was still afraid to write for the New York Phil. Well, I'm competitive, so when he says that, I say, 'Man, I'm not afraid.' I told him I would try to develop enough technical knowledge to do a piece that was at least passable. So then I wrote a series of pieces - a string quartet to learn about strings, then something for woodwind, then I learnt about the American folk fiddle tradition."
And Masur's admiration grew. "My basic idea was to try to reflect how jazz began - among the black people in Africa, and on the plantations, with gospel and so on. And Wynton simply said, 'I'll think about it.' I could never have imagined that he would use this idea to create a piece of such stunning originality, and such magnitude. At the next meeting he told me what he had in mind, and that it would start very simply. He told me, 'Don't worry, it's growing, it will come' - and then he came to demonstrate three movements on the piano. I was excited. I realised he was deeper than I had thought, and his understanding was absolutely philosophical. He didn't want to make a commercial piece, he wanted to express his feeling, and the feeling of his people."
To get a sense of how classical and jazz bands might fuse, they put the Philharmonic and the Lincoln Center Jazz Orchestra together for a concert in which they would first play Grieg's Peer Gynt and then Duke Ellington's suite inspired by it. Masur says: "It was an amazing evening - we talked first, then demonstrated. 'Anitra's Dance' was so refined in Grieg, and in Duke Ellington's version had such erotic vulgarity - the same melody, but an incredible contrast. And the dance of Peer Gynt's mother was done in the style of a New Orleans funeral. Incredible, going right under the skin."
And when All Rise was premiered - two days after the attacks of 11 September 2001, when America was in shock and shows were being pulled everywhere - it was found to be in near-perfect working order. Masur says: "He hardly needed to change anything, even though it was only just finished as we went into rehearsal."
So Marsalis must have had a sound classical grounding? The trumpeter responds to the question with a potted history of his career, which began with lessons from his jazzman father when he was six. "I didn't get into classical music till I was in high school. I met a guy on a streetcar who gave me a recording of Maurice André playing classical trumpet concerti. Until then I'd only been interested in Clifford Brown and Miles, but I started liked that, so I got some more of his albums, and when I was 14, I won a competition to play the Haydn trumpet concerto at high school. Yeah, I got better quickly."
Then he became a Beethoven fan: "I went to a library and found articles talking about Thayer's life of Beethoven, so I got it out and read it." Thayer's massive tome is the Everest of Beethoven scholarship. "Yeah, but I didn't know it was the summit. I was just a boy in New Orleans, and I didn't know anybody else who liked his music." His school ran a course in symphonic analysis, which * * he diligently followed. Soon he could read a full orchestral score.
In his late teens, he found himself much in demand for classical concerts, and discovered the piccolo trumpet. "I heard Maurice André playing that. At first I thought he was doing it on a regular trumpet, and I was trying to learn it that way; I learnt everything off the record, rather than from music. But a friend brought me a piccolo trumpet, and said that if I learnt how to play it, I could have it. I couldn't get a sound out of it first, but I was determined to play him the last movement of the Brandenburg Concerto No 2. When he came back, I got it."
He went on playing in churches in pieces such as the Messiah. "There weren't a lot of piccolo trumpet players in town then, so I was the one who got called in." When he went on to the Juilliard school of music, he found himself playing Stravinsky, Sibelius and Mahler, while pursuing the line that led to his début with Art Blakey. But he also went to summer camps, where he knocked around with hot-shot classical virtuosi, and drank at the fount of Leonard Bernstein's orchestral wisdom.
How autobiographical is All Rise? Quite a lot, he replies: for example, the opening theme was a song sung to him by his great-uncle Alfonse, who was born in 1883; and the little chant in the second movement was sung to him by his two-year-old son Simeon on a car journey.
But he's at pains to point out that the work is not in any sense the story of black music in America. "It's American music, and true American music has no colour. I may be outspoken on issues of race, and social injustice, but music is different. 'American' music takes in all shades and backgrounds. The racism in our culture makes us separate ourselves, but in fact we are in this all together.
"I grew up in the Afro-American tradition; that may be the foundation of my consciousness. But my principal teacher in high school was white, as was the guy who gave me the Maurice André, who was himself French and white. Masur is German, and his son is a trumpet player. The connections go everywhere."
Even, of course, to England. "To English bands, like the Philip Jones Brass Ensemble, and the whole English brass tradition. All my early records I did with the English Chamber Orchestra, and I love playing with them. They are a link with the tradition that goes all the way back to Handel, and that is now also part of my tradition."
But if his first allegiance remains to jazz, it's for a very good reason. "I don't want to go further and further into the labyrinth of the mind, where the audience can't follow you. The achievement of jazz is that you can come up with something that is abstract, but sounds concrete enough for the average person in the street to dig it."
Marsalis seems surprised that I hear Mahler's voice writ large at one point in All Rise, but he happily admits the Bernstein influences in other movements, and the Stravinskian ones. Then he makes a comment that should give the London Philharmonic pause for thought: "A lot of the time, the way that I hear the music is not the way it's being played. For example, I want all the string players to play like it's fiddle music, but the closest they come to that is what Stravinsky's music sounds like. I'll sing it and you can hear it. I'll write deevee-doodle-deevee... [he sings with an easy swing] but they will play [and he delivers a tamer, more neutered tune]. It sounds like Stravinsky, because they don't have the reference point of fiddle music. And when my jazz band comes in, playing the same melodic shape, it doesn't sound anything like Stravinsky." It's the difference, he says, between violin and fiddle.
Then he chides his classical collaborators on the Sony recording of this work for denaturing a fugue. "I heard the phrasing of that totally differently from the way it was played." He sings, first to demonstrate its swing and energy, and then as though daintily jabbing at the strings. "But it's hard for any string section to sound like a style they haven't heard. This problem will always exist with this work. Like if our jazz band was required to play in the style of Bach; I might manage it, but some would have real trouble. We have that same trouble when we try to play Latin music, which is written like eighth-notes, but is actually in 16th-notes."
One of the most remarkable echoes in this work comes in the middle of the pantheistic final movement, entitled "I AM: Don't you run from me". After an exultant gospel solo and an exuberant big-band riff, the whole thing subsides into a silence broken by staccato parps on the bassoon: is this a reference to the same effect in Beethoven's Ninth? "Right, a very conscious reference." And then, like Beethoven, he brings the sun out? "Yeah, the blues. I wanted it to sound like an elementary school band, but we couldn't pull it off. I wanted it to be inept, but not a parody - because when kids play, they're earnest about it. That's the appeal of their bands. They're trying so hard. But we just sounded like people making themselves mess up." Professionalism can be a disability.
What effect does Marsalis hope this work will have? "I hope it might help players have confidence in our own ways, and not to be afraid of them, as Bernstein showed - things like hoe-downs, fiddle songs, and the art of improvisation, and the New Orleans funeral tradition, and call-and-response church singing, and the fact that the blues run through everything. And in our relationship to European music, in that we don't have to imitate it, it's a part of us, inseparable."
But, alongside New Orleans, it's religion that permeates All Rise, as Marsalis's own commentary indicates: "The tuba preaches, the French horns are the choir, the jazz trumpet is a sister in the back of the church..."
And this prolific sister is now rumoured to be planning, of all things, a Mass, which is yet another idea prompted by Masur. The conductor says: "It arose after I told him about all the Masses I had conducted in my life, and all the different attitudes to God they embody - Beethoven and Mozart and Janacek. And I think he is philosophical enough to do it. I await it eagerly."
So how is it progressing? Marsalis ruminates: "I'm thinking about doing something on the Last Seven Words of Christ." When I mention that those words fired one of Haydn's greatest works, he wants to listen to it straight away. Yes, that Mass could happen.
But now, with the floodwaters receding, Marsalis has found his voice on the subject of New Orleans, and also the obvious way to help. "New Orleans," he says, "is the most unique of American cities, because it is the only one that created its own full culture. It was the original melting-pot of Spanish, French, British, West African and American people. We are resilient, so we are sure that our city will come back."
What this American tragedy provides, he adds, is "an opportunity for the American people to demonstrate to ourselves and to the world that we are one nation determined to overcome our legacies of injustice based on race and class. We need people with their prayers, their pocketbooks, and above all their sense of purpose, to show the world just who the modern American is. This is gut- check time."
Tomorrow, Jazz at Lincoln Center will present a relief benefit concert entitled Higher Ground, which will be televised live to every corner of the United States. Those who have agreed to take the stage include Bill Cosby, Robert De Niro, Renée Fleming, Herbie Hancock, Norah Jones, Bette Midler, Toni Morrison, Paul Simon, Meryl Streep, Robin Williams - and Wynton Marsalis. Yes, presidential stuff.
'All Rise' starts a five-date UK tour on 30 September at Symphony Hall, Birmingham. Its London performance is at the Royal Albert Hall, London SW7, on 2 OctoberReuse content