THE LAST time Anthony Braxton came to Glasgow, he lost four saxophones. It was the end of a lengthy tour and he’d had rotten luck with the airport luggage handlers. “Remember?” says Taylor Ho Bynum, a cornet player/flügelhornist/trombonist who studied with Braxton and who was performing with him on that 2005 tour. “Remember how you started off the trip with five horns and ended up with one?” In the background I hear Braxton chuckling at the recollection. The two musicians are at his house in Connecticut, drinking Caol Ila in the afternoon to prepare for their interview with the Scottish press. “After this election I might be moving to Scotland,” Braxton jokes, though I suspect he’d stick to his word if the unthinkable happens. Incidentally, the very substantial silver lining of all those airline cock-ups was a recording of the Braxton gig at Glasgow's CCA on June 23, 2005, released by Leo Records as a double-CD set and called simply Trio Glasgow.

Braxton is a 71-year-old saxophonist and composer who has made huge contributions to jazz over his 50-year career but who has spent most of that time taking umbrage with the term. “As a black man with a saxophone,” says Bynum, “he is most often lumped into the category, regardless of whether he is leading a quartet or conducting an opera!” Bynum suggests that Braxton and his peers “exploded those definitions from the very beginning”, because the music they played drew on way too many traditions (jazz, improv, various strains of contemporary classical) to fit into one label. And it was a two way thing: Braxton was cold-shouldered by arbiters of the neo-conservative jazz establishment like Wynton Marsalis because his unbound sounds didn’t quote the right trumpet solos, didn’t stick to the right modes, didn’t swing the way they wanted it to.

Braxton can totally swing – listen to his albums of jazz standards, including one pointedly titled In the Tradition – and you’ll get gorgeously fractured, husky proof that he can take on the traditionalist at their own game. He’s got a wry sense of humour when it comes to satisfying our appetite for hearing the old classics. In his piece Echo Echo Mirror House Music, performers test out various methods of sound production using cartographic scores while simultaneously shuffling through iPods that contain Braxton’s entire discography. Neat dig at the archive junkies.

He grew up in Chicago, and it was hearing Ahmad Jamal’s record At The Pershing that provided his early epiphany moment. At high school he played bebop and show tunes; he did a stint in the army in the 1960s before fellow saxophonist Roscoe Mitchell got him involved in the Association for the Advancement of Creative Musicians, a black artists’ collective in south Chicago that would become a pioneering force in American avant-garde culture and racial politics. It was through the AACM that he met kindred spirits like trumpeter Wadada Leo Smith and violinist Leroy Jenkins. This was an environment, he has described, where “no one was so much concerned with labels,” where “everybody came from different directions and eventually they went and continued in their own directions. It was very interesting, and nobody came out sounding alike.”

Certainly nobody came out sounding like Braxton. Was it the sheer omnivorousness of his musical appetite that set him apart? He was into Hildegard von Bingen, Edgar Varese and La Monte Young as much as Charlie Parker, Dave Brubeck and John Coltrane. In 1969, his groundbreaking album For Alto – first ever full-length album for unaccompanied saxophone – was inspired by the solo piano works of Schoenberg and Stockhausen and included dedications to early Philip Glass and John Cage. The album is still a monumental listen, and tracks like the 20-minute megalith Composition 8B still sound the absolute progenitor of successive generations of solo saxophone intense-ovists. Think Peter Brotzmann or Evan Parker, or the younger guard like Mats Gustafsson, Mette Rasmussen, even Colin Stetson.

Frustrated with the American music industry – its type-casting of black musicians as jazz cats, its lack of financial support for anything but straight-up jazz combos – Braxton went to Paris and found himself drawn to electronic studios like Boulez’s IRCAM. “If not for the wonderful people of Western Europe,” he has said, “I would have no career at all in music. […] it was the Europeans who gave me an opportunity to actually play.” But it was Braxton’s curiosity that drove him on, ignoring the conventions that said he was “too black” for classical music and “too cerebral” – which is to say “too white” – for jazz. He refused to limit himself to one form, one instrument, one tradition, one set of parameters, and instead sought new contexts for improvisation and new challenges for composition. He wrote works for a hundred tubas and wonky Sousa marches. He launched a roving cycle of operas called Trillium that take the shape of Socratic-style philosophical dialogues. He wrote for ensembles big and small, always investigating the social dynamics of musical interaction.

And instead of the term "jazz" he chose to label himself a "creative musician" and, says Bynum, “prefers the term ‘trans-idiomatic’ – embracing the influence of multiple musical styles, while avoiding the stylistic definitions and restrictions of all of them.” Above all, he wanted options. “What I got most out of contemporary classical music is the fact that the composer has so many different mediums that he can work in,” he says, “and that keeps his activity up.” During our conversation he tells me that he “always wanted everything to be a fresh encounter for myself as a composer.” It reminds me of the old Ezra Pound axiom: KEEP IT NEW.

This month the BBC Scottish Symphony Orchestra and conductor Ilan Volkov perform a concert of works by Braxton, Bynum and saxophonist James Fei. The two Braxton works are Composition No 27, which he describes as “a transformation post-Schoenberg,” and Composition No 63, “conceived as a concerto for two improvisors and chamber ensemble” and inspired by Stockhausen’s Kontra-Punkte as well as Dave Brubeck’s I’m in a Dancing Mood. Stockhausen and Brubeck? It’s a classic Braxton combination. “The Brubeck composition passes through many different states,” he tells me, “starting with a Latin feel and going from there. Composition 63 similarly establishes many different domains. I hope it provides an interesting sequence for the friendly listener and for the musicians.”

Braxton has admitted a tendency to be a recluse, to retreat in dismay about the state of the world and the limitations of America’s commercial culture industry. But his Tri-Centric Foundation is all about connections – “a community of actually interacting human beings,” he calls it. “I wanna keep learning,” he tells me. “My Tri-Centric Construct is a system of becoming, not a system of arriving. I wanna keep getting into new debt, not relying on old debt.” He recently retired from university teaching and has big plans for writing, reading, consolidating his unique musical-philosophical systems.

Our conversation ends in a jubilant shout-out to the commercially overlooked. “I tell you this: my proudest experiences have been in the underground, not the overground. So I wanna say hurray for the underground!” I remember one of my favourite Braxton quotes, spoken in an interview in Toronto in 1973. “It’s all over the planet,” the young Braxton said. “You go and look in the alleys and under the doorways, in the coal mines – they’re there, lurking in the shadows: a significant amount of people in different parts of the planet who are genuinely creative. And I associate and attach myself to that.”

The BBC Scottish Symphony Orchestra plays the music of Anthony Braxton on November 19 at City Halls, Glasgow