CHICAGO — We’re in a strangely busy cycle for musical biopics. Tom Hiddleston plays singer-songwriter Hank Williams, cheatin’ and boozin’ his way through “I Saw the Light,” while Ethan Hawke portrays jazz trumpeter Chet Baker, the cool, forlorn subject of “Born to be Blue.”

Now another, greater jazz trumpeter enters the fray: Miles Davis, the chameleonic visionary at the center of “Miles Ahead.” It’s not the usual biopic. It’s a freewheeling imagining of Davis at a creative crossroads, his mind and the movie toggling between time periods and musical styles. The more you care about the historical record and straight-ahead narrative conventions, the less it’ll appeal to you.

Don Cheadle as Miles Davis in “Miles Ahead.” Brian Douglas, Sony Pictures Classics

Years in development, “Miles Ahead” was produced, co-written and directed by Don Cheadle, who also stars as Davis. For the record: It didn’t happen overnight, but with stealthy technique and rock-steady instincts, Cheadle has asserted himself as one of a handful of American actors who, practically everybody agrees, is great. He improves every project just by being in it, watching, listening, interpreting. Honestly: Do you know anyone who doesn’t admire Don Cheadle? I’d love to hear the reasons.

The Academy Award nominee (for “Hotel Rwanda”) is all over the place, juggling assignments. In Season 5 of the Showtime series “House of Lies,” the 51-year-old Kansas City, Missouri, native continues on his merry way as rascal management consultant Marty Kaan, a J. Pierpont Finch for a new age of corporate blather. Cheadle’s also now firmly a part of the Marvel “Avengers” movie universe, as Rhodey, aka, War Machine, Iron Man’s comrade in arms.

“Miles Ahead” is not that sort of enterprise. For one thing, Cheadle and company made it for a tick under $9 million, which wouldn’t pay for Robert Downey Jr.’s goatee maintenance. For another, it’s not designed to appeal to the widest possible spread of presold fans worldwide. It’s smaller and wilder than that, focusing on a period in Davis’ life in the late ’70s when he’d succumbed to drug-fueled reclusiveness and paranoia, before breaking through to a new career phase back in the public eye.

The movie took many years and several rewrites to find backers.

“Not finding our financing for so long, and hearing so many ‘no’s, gave us a lot of time to work on the script,” Cheadle told me recently over breakfast in Chicago. He also told me that films such as “Run, Lola, Run” (the breathless, time-skipping German thriller) had a more considerable influence on Cheadle’s ideas for “Miles Ahead” than anything in the standard-issue biopic genre.

Cheadle said there’s a misconception about the film’s other major character, a (fictional) music journalist played by Ewan McGregor. The character was there in all the drafts of the “Miles Ahead” script co-written by Cheadle and Steven Baigelman.

“We always knew we wanted a journalist to sort of break into Miles’ life,” Cheadle said, noting that he’s a “composite of several people who didn’t know if they’d be writing a profile of Miles or an obituary.” Cheadle does acknowledge, however, that McGregor got the project off the runway. “We cast the role in a certain way in order to get the financing,” he said. Cheadle and company shot the New York-set “Miles Ahead” in Cincinnati two years ago, just after Todd Haynes filmed “Carol” there.

At the restaurant table, Cheadle and I were not alone. He brought along his high school drama teacher. Now a Chicago-area resident and freelance director, Catherine Davis cast Cheadle in a slew of shows, everything from “Oklahoma!” to “Oliver!” to “The Fantasticks,” back at East High School, part of the Denver public school system. Cheadle’s parents settled the family in Denver when Don was in fifth grade.

“Whenever I come through Chicago, I make sure to see her,” he said of Davis.

Don Cheadle as Miles Davis in “Miles Ahead.”

“He was fabulous,” she replied. “Even then.”

Cheadle again: “We also wrote plays and had a mime show. I don’t know if you saw ‘The Tonight Show’ the other night, but Jimmy Fallon showed a picture from the high school yearbook of me in the mime show.” He turned his head to his right and smiled. “This woman’s a big part of why I’m here right now. It’s not why I invited her to breakfast, though. We were both hungry, is all.”

After a decade of guest and recurring roles on TV and small parts in the movies, Cheadle turned a wider circle of heads in 1995 opposite Denzel Washington in “Devil in a Blue Dress,” the Walter Mosley adaptation directed by Carl Franklin. As Mouse, the gangster from the South who said little but scared everybody, Cheadle made his mark. This was a meaty, nasty, funny role, a lot more interesting than the one he played in 38 episodes of the David E. Kelley quirkfest “Picket Fences.”

The steady, blandish supporting role of the small-town Wisconsin district attorney, Cheadle said, “was a big deal for me at the time, being 12th person on the call sheet. I was the ‘heart’ of the show. The ‘spiritual center,’ and all around me it was, like, this dude’s got a foot fetish, that woman’s baby was born in a cow, and I’m stuck being the ‘soul’ of the piece.” He’s laughing but clearly he has no trouble recalling the frustration he felt as an actor, a generation ago. “Black people, you’re either the beast or the saint.” The protagonist of “Miles Ahead” defies both extremes.

A couple of days after, I called Davis to hear more about the early ’80s Don Cheadle, the one she got to know just before he took the leap and headed west from Denver to the prestigious, progressive California Institute of the Arts.

“In the most subtle and humble way,” she told me of Cheadle’s high school career, “Don was Mister Everything. He was in everything. He was in the a cappella choir, the jazz band, he was in all my shows. He communicated with everyone. He wasn’t quiet as in ‘shy,’ but he was quietly assured in his own accomplishments.” She paused, and added: “I think he just tries to be honest in his work. And he’s done so much that speaks so loudly without him having to brag about it.”

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