Coleman grew up in Chicago and came to New York in the late 1970s, busking in the subway and working his way into the city's serious jazz scene. He played with Thad Jones and Dave Holland, and those experiences gave him a foundation in swing and bebop that he would spend the rest of his career pulling apart and reassembling. You can hear that foundation in everything he does — he is never randomly abstract. There is always a logic underneath, even when it sounds slippery.

The M-Base concept he developed in the 1980s with a loose collective of like-minded players — including Cassandra Wilson, Geri Allen, and Greg Osby — was not a genre so much as a shared attitude. The idea was that improvisation should grow out of rhythm and structure the way a plant grows out of soil, not just float on top of a chord chart. The music these players made together was funky and angular, influenced by hip-hop and African rhythmic ideas as much as by bebop. It had an edge without being aggressive.

If you want to understand what Coleman actually sounds like, start with Sine Die (1988) or The Tao of Mad Phat (1993). His alto saxophone tone is dry, fast, and precise — he does not rely on a big romantic sound to carry him. The phrases he plays are long and unpredictable, with accents landing in places that keep you slightly off-balance. It is rhythmically sophisticated without feeling like a math puzzle. You can dance to it, or at least nod your head, even when you cannot quite predict where the next beat is coming from.

He has spent significant time studying West African and Cuban music, as well as ancient Egyptian cosmological systems, and those interests feed directly into the compositions. Some listeners find the theoretical scaffolding around his work a bit much — Coleman has always been willing to explain his ideas at length, and the explanations can be dense. But the music itself does not require a decoder ring. You can just listen and feel how different it is from most contemporary jazz, how much more tightly constructed and yet how open it feels at the same time.

Coleman received a MacArthur Fellowship in 2014, which was one of those moments where an institution finally catches up with what the serious listeners already knew. He has never been a household name, and that is partly because his music asks something of you — not a lot, but something. He rewards patience and repeated listening in a way that casual music rarely does. Put on Harvesting Semblances and Affinities (2010) and give it three or four plays before you decide what you think.