During one of several candid, articulate, and compulsively watchable interview segments in Ron Mann’s splendid 1981 documentary “Imagine the Sound,” the trumpet player Bill Dixon references the halcyon days in the early 1960s when he was based on Bank Street in the West Village. Though he was living and working in an ad hoc musical community that included Ornette Coleman and Eric Dolphy, Mr. Dixon recalls those years as a time of hot-house productivity for artists of every inclination.

Part of a scene that fostered everything from club gigs to loft gigs to musical collaborations with the influential Judson Dance Theater, Mr. Dixon makes Mayor Wagner-era New York sound as if it were in the midst of a creative gold rush. At one point, he says with amusement and wonder, “I played with a painting.”

But “Imagine the Sound” is anything but nostalgic. Inspired by the music and ideas of Mr. Dixon, pianists Cecil Taylor and Paul Bley, and tenor sax player Archie Shepp, Mr. Mann created a uniquely vivid, muscularly impressionistic film that is one of the great music documentaries of all time. Recently restored from the original 16 mm negative, digitally remixed from analog tape, and transferred to high definition wide screen, “Imagine the Sound” made its return at this year’s South by Southwest Film Festival and will show at Anthology Film Archives tomorrow and Sunday. The cinema’s century-long embrace of music has not produced a smarter, handsomer, or more lucid love child.

The music that Messrs. Taylor, Bley, Shepp, and Dixon play has become known as “free jazz.” An alternative to melodically based improvisational playing, free jazz was pioneered in the mid-1950s and peaked in the ’60s via records and performances by Coleman, Dolphy, John Coltrane, Albert Ayler, and the musicians in Mr. Mann’s film. Like many turning points in 20th-century American music, what these men did both begs and eludes classification. Whether you called it “free jazz,” “the new thing,” “out jazz,” or “energy music,” says Mr. Taylor, who dominates the documentary’s four-man showcase, the musician’s obligation was “to change the environment that music has been traditionally played in.”

And changing the environment of music documentaries is precisely what “Imagine the Sound” does. Rather than capture live performances in a traditional nightclub environment, Mr. Mann and production designer Sandy Kybartas framed each player (solo in Mr. Taylor’s and Mr. Bley’s case, backed by their bands in Mr. Shepp’s and Mr. Dixon’s) in studio situations that allowed the filmmakers complete freedom to visually improvise as well. Using multiple cameras, Mr. Mann’s crew tracks, isolates, and scrutinizes the players with such dexterity and freedom that the director plunges the film audience deeper into a free-form musical whirlwind than they could achieve in a filmed club setting.

The only rule for each performance was that an individual piece of music had to be confined to 10 minutes, the length of time that a 400-fit magazine of 16 mm film allows. It’s one of those technical limitations that become an advantage. Rather than limiting the performers (though Mr. Dixon looks at his watch more than once), the 10-minute rule ensures that screen time is shared equally among the four men and that the musically unindoctrinated viewer doesn’t get left behind on longer flights of tonal imagination.

Seated at a bone-white piano, Mr. Taylor, dressed in gray sweats, a white wool watch cap, and filthy sneakers, sprays out cascades of notes with such speed and off-kilter accuracy that I wondered for a moment whether the screener I watched had sped up. The camera swoops and glides through the room, painted white like the piano, arching out over the instrument’s sound board, drifting back through the microphones, and finding Mr. Taylor’s hands as they simultaneously pose and solve musical riddles by coaxing combinations of notes and tempos with an uncanny combination of controlled intelligence and complete abandon.

In contrast to Mr. Taylor’s clean room, Mr. Bley performs against a black backdrop. Although he insists in one interview segment that what he does is founded on “a disdain for the known,” when he plays both piano keys and strings, Mr. Bley’s improvisations subtly usher the spirits of more traditional blues-based musical idioms into the room.

Mr. Shepp powerfully leads and generously lays out, offering space and time to his band. During one performance, Mr. Mann takes an informal but astute editorial solo himself by seamlessly splicing footage of Mr. Shepp and his group listening to a recorded playback of the composition that a few edits ago they were performing, before cutting back to the live performance.

One of the pleasures of the musical avenue he’s chosen, says Mr. Taylor, is that “you see all of art as a potential harvesting area.” What the art of music in “Imagine the Sound” garners from the art of filmmaking, and vice versa, is fruitful indeed.