No wonder subsequent movements have doubled back to the comforting familiarity represented by chords and tunes, for after Taylor's fobiddingly dense improvisations post-modernism was perhaps the only place to go. And although a whole school of improvised music has grown up in response to his free- form experiments in the Sixties, it mostly isn't jazz anymore. Taylor's furious assaults on the keyboard most certainly are. No matter how fractured the arpeggios (you have to see Taylor in action to experience just how powerfully he hits those keys), there's always at least an echo of the jazz tradition to be heard. While he may never play two conventionally congruent notes, the music somehow continues to swing. You may even be able to dance to it, for one of Taylor's greatest influences and most abiding passions is the art of dance. He once said: "I try to imitate on the piano the leaps in space a dancer makes."
Cecil Taylor was born in New York in 1929, to a mother who was both a dancer and a pianist. After taking piano lessons from the age of six, he attended New York College of Music and later the New England Conservatory, where he was influenced by the heavy block-chords of Dave Brubeck's jazz piano playing. Although the influence sounds unlikely, Brubeck told me in an interview that Taylor used to look over his shoulder when he played in New York clubs.
"He said I was the missing link," Brubeck said. "But he didn't say between what and what." For his own part, Taylor has said of Brubeck: "I learned a lot from him. When he's most interesting, he sounds like me." Taylor's recording debut, the album Jazz Advance, made in Boston in 1956 (and produced by Tom Wilson, who would go on to produce Bob Dylan and the Velvet Underground), is a fascinating document. A quartet date with Steve Lacey on soprano sax, it's notable primarily because it showcases Taylor playing tunes, which he does very well. On compositions by Monk and Ellington, and standards such as Cole Porter's "You'd Be So Nice To Come Home To", he swings like the clappers, but the heavily percussive and melodically deconstructive elements of his mature style are there in embryo.
This quartet was the first group to play the Five Spot Cafe in New York, and Taylor was beginning to make a considerable reputation until the increasingly abstract character of his music, and the arrival in New York of Ornette Coleman with his more melodic concept of free jazz, consigned him to the outside berth once again. This, more or less, is where he has remained. A chapter on Taylor in AB Spellman's 1966 book, Four Lives in the Bebop Business, chronicles the years of struggle when he would be lucky to play more than a handful of gigs a year. His relationships with other musicians on the New York "scene" were strained, not only because of his uncompromising music, but also because he was a gay man in a largely homophobic jazz community. Perhaps as a result, he has tended to perform most often as a soloist, although he was involved with other "New Thing" players such as Jimmy Lyons, Albert Ayler and Sonny Murray in the Sixties, and these days he sometimes plays in the "Feel Trio" with bassist William Parker and the British drummer Tony Oxley.
Some of Taylor's most fruitful musical relationships have been with drummers, and Sunday's London date with Max Roach is therefore a tantalising prospect. Each will perform a solo set before coming together for the second half of the performance. They've played together before, but not for years.
Despite his principled refusal to compromise his art, it's hard not to see Taylor's outsider status as largely self-willed. He appears to enjoy the role, and has probably profited from it, especially in Europe and Japan, where his rare appearances command large fees. Like Ornette Coleman, he has attained the almost mythical stature of a genius or guru figure, where eccentricity isn't just permitted but comes with the turf. Thus Taylor's performances are often strange affairs, part music and part theatre, with gnomic poetic outbursts scattered among his improvisations. And as geniuses are allowed to do anything they like, the audience is unlikely to ask for its money back.
As if to confirm his wayward genius, Taylor has been leading the British press a merry dance these past few weeks. The first time I phone his number in New York, his assistant or partner or whoever answers. "Yes, he's here, but he's rather sour this morning," he says. Then, "No, wait a minute, he's coming to the phone now." The deep tones of Taylor's voice follow. He's sorry, but he's having breakfast. Can I try later? I do, but the promised interview never happens. It's been rumoured that Taylor wants cash for questions, and the promoter's offer of a fancy meal in London apparently isn't enough to make him talk.
In contrast to Taylor, Max Roach is approachable, if a little forbidding. When I interviewed him last year at his apartment on Central Park West, in a room decorated with African masks, Roach answered questions patiently from the lofty perspective of someone who isn't just speaking for himself, but for jazz in general. Incredibly, he's only five years older than Cecil Taylor but while the pianist has come to represent the end of the line, Roach has travelled the whole journey. Along with Charlie Parker and Dizzy Gillespie, he helped invent bebop before forming, with Clifford Brown in 1954, the first great hard-bop group. In the years since, he has kept pace with each succeeding development in jazz while retaining an essential identity as the most intelligent of all drummers.
When it comes to the unfettered freedom that Cecil Taylor's playing appears to represent, Roach is more cautious, always keeping one eye on the past. "You're free to pick and choose but the concepts that you pick and choose must be as profound as those you learn from," he says. "Segregation, as convoluted as it seemed, kept the music in that rarefied atmosphere of creativity that was profoundly exhibited by Lester Young, Louis Armstrong, Dizzy Gillespie and so forth, and the public knew exactly how to respond. Then, when the music began to branch out to the rest of the world, it seemed you could do anything, but it was never that. You had responsibility to the people who came before you. You could never just do anything."
So, on Sunday, the old sage (aged 74) and the young rebel (68) do battle on the Barbican stage. The great irony is that both these OAPs are still on the jazz train and rattling along into the future, while Wynton Marsalis and his generation are travelling in the opposite direction, trying, perhaps, to get back to the comforting certainties of the age of steam.
Taylor and Roach play the Barbican, London EC1, on Sunday (0171-638 8891)