In the tradition of “Percepto” and “Odorama,” director Gary Hustwit’s “Eno” comes with a gimmick. Granted, it’s unlike that used for William Castle’s “The Tingler” (1959), wherein buzzers were applied to selected seats in movie theaters in order to simulate the sensation caused by the title monster. Nor is it like the scratch-and-sniff card that accompanied John Waters’s “Polyester” (1981), a cinematic aid meant to embellish the film’s mise en scène. Mr. Hustwit’s gimmick is less kitschy but just as conducive to the film’s subject. 

Brian Eno is a musician whose contributions to the broader culture will be familiar even if you’re not sure how to place the name. He was a founding member of the glam rock outfit Roxy Music, and a collaborative producer who’s worked with musicians like John Cale, David Bowie, Talking Heads, Devo, Paul Simon, and U2. Mr. Eno’s backlog of solo albums is impressive. So, too, is his ability to synthesize a daunting array of prescribed adjectives into a three-second sound — that is to say, the opening chime of Windows 95.

Mr. Eno’s role as the exemplar of ambient music is, I think, the most far-reaching of his accomplishments. Although there were precedents to his 1978 album, “Ambient 1; Music for Airports,” the project helped to codify the genre. “Soundscaping” abjures the niceties of structure, lyrics, and compression for free-floating accumulations of texture and sound, usually achieved on electronic instruments. 

In Mr. Eno’s estimation, ambient music “must be as ignorable as it is interesting.” His finest album, “Another Green World” (1975), isn’t ignorable at all and plenty interesting, being an amalgam of moody grandeur, sweeping symphonics, and pop-wise know-how. After almost 50 years the record retains its strange beauty.

Chance incident is a mainstay of Mr. Eno’s approach. Along with artist Peter Schmidt, he created Oblique Strategies, a set of 100 or so cards that feature suggestions meant to jog or waylay the creative process. “Disconnect from desire” is one option; “Give way to your worst impulse,” another. There’s a scene in Mr. Hustwit’s movie in which Mr. Eno recounts how he and David Bowie picked radically different strategies for one particular song. The result retained the eccentricity of the situation without revealing the contradiction at the heart of its making. It’s a funny moment.

When approached with the idea of a documentary biopic, Mr. Eno proved reluctant: He wanted no part of a hagiography. Then Mr. Hustwit and a colleague, Brendan Dawes, invented a software system that allowed for “a film [that] can continue to change and evolve over the coming months and years.” Mr. Eno signed on with, one imagines, the glee of a child let loose in a candy store. His is an intellect that likes to be surprised.

There is a grudging nod to order in that the scenes bookending the movie will remain constant. The rest of the time “Eno” is interrupted by glitchy shifts of coding that serve as transitions from one part of his life and career to another. On paper, this sounds annoying; in the theater, it works brilliantly. The approach is less higgledy-piggledy than you might think if only because it goes to confirm the constancy of the man. Mr. Hustwit knows when the sum of the pieces are the whole.

At age 76, Mr. Eno is far from the image of a vampiric androgyne he cultivated in the early 1970s. He’s a droll and self-effacing gent, an avant-garde country squire as happy to potter around in his garden as he is to push buttons in the studio. Mr. Hustwit stacks the deck with rare footage from back in the day — concert films, television appearances, like that — with contemporary interviews held at the artist’s picturesque British estate. 

At several moments in the film, Mr. Eno complains of being peckish — the consequence, one supposes, of the filmmaker’s incessant attention. Get the poor man his tea: “Eno” is an outstanding achievement.