Saxophonist Steve Coleman plays with his band Five Elements Sunday, April 5.

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In his classic 1973 book “The Anxiety of Influence,” the prodigious literary critic Harold Bloom argues that great poets define themselves through an Oedipal struggle in which they misread the work of their predecessors to find their own distinctive voice.

Maybe the collaborative nature of jazz serves as an antidote to anxiety, because the most creative improvisers embrace and build on their influences rather than symbolically killing them. And no jazz artist better embodies the way a powerful musical personality can nourish widely divergent approaches than alto saxophonist Steve Coleman, who performs with his band Five Elements on Sunday at the Triple Door.

Few of the players inspired by Coleman sound anything like him, but his conceptual rigor connects with Cuban drummer Dafnis Prieto, pianist Vijay Iyer and altoist Miguel Zenon (who recently became the youngest jazz musician ever awarded a MacArthur “Genius” Fellowship).

“Musicians are looking at the people who have the more personal concepts and ideas, stuff you can’t get off the shelf,” says Coleman, 52, downplaying his role as a jazz guru. “What happens is there are a lot of private get-togethers that the public never sees. Miguel is one of those guys.

“Even though we’ve only ever done two gigs, we’ve gotten together a lot.”

As Coleman sees it, he’s just part of a process that’s been going on in jazz since the beginning. Born and raised on Chicago’s South Side, he started playing the alto in his midteens and grew up in thrall to the great Parker altoists, Charlie and Maceo.

Deeply influenced by the improvisational concepts of landmark Chicago tenor saxophonist Von Freeman, Coleman made the move to New York in 1978 and soon landed a job with the Thad Jones-Mel Lewis Orchestra, the era’s definitive big band. At the same time, he started working with avant-garde patriarchs Cecil Taylor and Sam Rivers.

Over the past two decades, he’s turned his band Five Elements into an improviser’s academy, attracting a steady flow of exceptional young musicians.

The ensemble’s latest incarnation features stellar 22-year-old drummer Marcus Gilmore (grandson of drum legend Roy Haynes); bassist Thomas Morgan; vocalist Jen Shyu; and Jonathan Finlayson, who came under the altoist’s wing as a high school student, when Coleman was teaching at the University of California, Berkeley.

“The first time I went over to his home he talked about music for three or four hours and I listened,” Finlayson says. “At that age it was great. I was looking for something. Aside from the challenge of a hard set of chord changes or a tricky melody, playing in four/four time over jazz changes wasn’t going to be the end-all for me. It was miraculous that Steve came along and introduced me to this whole other world.”

For Coleman, the pulse, or clave as he calls it, borrowing from Afro-Cuban music, is the organizing principle. He’s developed an extensive body of compositions, and is constantly generating new music, but his bands don’t play a repertoire of tunes. Rather, there are bits and pieces of compositions that serve as sign posts when rhythmic cycles converge.

“We don’t work on improvisation, because everybody knows how to improvise,” Coleman says. “What we work on is the language itself. How things fit together, how to answer. It’s just like church. The preacher says, ‘I’ve been to the mountain top!’ They answer ‘Amen!’ ‘And I’ve seen the Promised Land!’ ‘Amen!’ It’s call and response, which has been going on since Africa, since forever. It’s just that we have our own call and response patterns.”

Andrew Gilbert: