Two years ago, I asked the free jazz pianist Matthew Shipp if he would take part in a concert I was organising in remembrance of Cecil Taylor, who had just died. He said he’d be willing to give a talk, but not to perform. Taylor hadn’t influenced his work, and he didn’t want to encourage the notion that he had. I wasn’t surprised (I’ve known Shipp for more than twenty years). His feelings about Taylor were complicated, and the two men often jousted, especially on the subject of Bill Evans, whom Taylor disparaged as the great white hope of jazz piano, and Shipp reveres. Shipp had also been saddled with the ‘heir of Cecil Taylor’ label for three decades, even though the resemblances in their playing are superficial. The only comparison with Taylor that Shipp ever welcomed was made by a mutual friend, the saxophonist Jemeel Moondoc, who told him: ‘You’re just like Cecil Taylor – you’re both bad motherfuckers.’ 

In an interview with a French journalist, Joseph Jarman compared the Art Ensemble of Chicago, the avant-garde jazz quintet to which he belonged, to ‘a cake made from five ingredients: remove one of the ingredients and the cake no longer exists.’ Jarman, who died earlier this month, at 81, after a long illness, was the ingredient that made the band one of the most aesthetically adventurous groups of its era: he put the 'art' in Art Ensemble.

The last set is over, and the club is almost empty. The bassist has already gone home, the drummer is walking out the door. That leaves the saxophonist and the pianist, but they decide they're not done yet. They have more ideas to exchange, more confidences to share. They begin to play again, only this time just for themselves. Do most saxophone and piano duets start out this way? Surely not, and yet the best of them could fool you, with their intimate, nocturnal ambience, their exploration of 'songs of love and regret', as the saxophonist Marion Brown and the pianist Mal Waldron called their 1986 album. On Random Dances and (A)Tonalities, the new album by the pianist Aruán Ortiz and the reedman Don Byron, the music is unapologetically cerebral, like the title.

Five years ago, the alto saxophonist Miguel Zenón was performing with his quartet at a club in Chicago when he was contacted by Julien Labro, a French accordionist based in Canada. Labro was in town making a record with Spektral, a Chicago-based string quartet that specialises in contemporary music. He had arranged a piece by Zenón, a racing tune called 'El Club de la Serpiente', for the session, and wanted to know if he would have any interest in recording it with them. Zenón went to the studio, and instantly clicked with the quartet. 'The guys from Spektral were really on top of the music, which made the session very fun and easy,' he told me. ('El Club de la Serpiente' appeared on Labro's 2014 album From This Point Forward.) When the Hyde Park Jazz Festival commissioned Zenón to write a work for local musicians, 'naturally I thought of Spektral.'

In May 2002, the free jazz pianist Cecil Taylor performed at the Barbican with the post-minimalist classical ensemble Bang on a Can All-Stars. I managed to slip backstage during the rehearsal. It was tense. Taylor, wearing a dressing gown and pink fluffy slippers, was in the process of firing half the ensemble. Bang on a Can’s keyboard player had already gone, and a procession of other players would soon follow. Their sin seemed to have been to read Taylor’s graphic sketch for how the evening’s music might evolve too literally. With the concert itself underway, Taylor ritualistically shredded his sketch and encouraged the remaining Bang on a Can musicians to do the same: they were going to have to improvise. A hapless guitarist threw a rock riff at Taylor, which he immediately bounced back as an open-ended question: is that the best you can do? Then he turned his back on the ensemble and carved out a cavernous wall of sound with his own drummer, Tony Oxley.

Anouar Brahem first heard jazz when he was studying the oud at the National Conservatory in Tunis in the 1970s. He was astonished that a youthful music of humble origins had evolved in a matter of decades into an art of extraordinary sophistication, through successive waves of innovation; Arabic music struck him as ‘caught in some sort of conformist conservatism in comparison’. He wanted to meld the traditions of the oud with other influences, and to create a vernacular modernism, like the jazz musicians he admired.

In 1962, Richard Abrams, a 32-year-old pianist on the South Side of Chicago, formed a rehearsal group called the Experimental Band. Its purpose was not so much to perform as to provide a laboratory of artistic research and development for young black musicians and composers working in jazz, or what Abrams preferred to call ‘creative music’. Abrams had been electrified by the free jazz revolution launched a few years earlier by Ornette Coleman. As Abrams saw it, the liberation from chord-based improvisation that Coleman had brought about was only a first step. Creative musicians would have to invent new structures to replace the old ones; they would have to re-examine their relationship not only to music, but to sound. Freedom, Coleman's gift, was also a challenge, even a burden: as exhilarating as free jazz was, the hard work of building on its liberties had only begun.

When you’re listening to jazz in, I would argue, its greatest and most significant incarnation, a folk-based, body-based chamber music recorded during the 1950s – Thelonious Monk, Miles Davis, John Coltrane et al – it was probably recorded by Rudy Van Gelder on analogue equipment in his parents’ living room in Hackensack, New Jersey, a room specifically designed for their son’s sound recording and where he made use of hallways and alcoves to tease out acoustic effects. By day, Van Gelder worked as an optometrist in Teaneck. He died yesterday at the age of 91.