According to a frequently repeated anecdote, George Szell, the perfectionist conductor of the Cleveland Orchestra who built that ensemble into one of the world’s best, once had a tiff with Canadian pianist Glenn Gould at a rehearsal, and wouldn’t accompany him afterward. But he continued to engage Gould, before his notorious retirement from the concert stage, to play with his orchestra under other conductors, and when asked why responded, “That nut’s a genius.” That story may be apocryphal, but this new documentary about Gould, whose recordings of Bach were revelatory, whose technique was astonishing and whose oddity was legendary, successfully captures the two sides of the musician—his incredible brilliance and his pronounced, if perhaps deliberately exaggerated, eccentricity.

“Genius Within” covers all the standard Gouldiana—his childhood and early training, his remarkable debut recording of the Goldberg Variations, the tour of the Soviet Union that gave him virtually mythic status in that country, the notorious public contretemps with Leonard Bernstein over their performance of the first Brahms concerto, his renunciation of public performance, his hypochondria, his weird dress, his unusual demeanor at the keyboard, his habit of humming along as he played, and his devotion to technology (including television) in his later years, among other topics. It does so through a wealth of archival footage (interviews with Gould, friends and associates, clips from the television programs he made, film of him rehearsing, recording and concertizing), stills and—on occasion—recreations, particularly scenes of somebody camouflaged in the pianist’s customary overcoat, gloves and beret trudging forlornly down streets, all of it beautifully put together. It ends, moreover, with poignant reminiscences of his untimely death at fifty and footage of his Toronto funeral, which attracted hundreds of mourners, many of whom wept as his second recording of the Goldbergs was played.

But the film adds details about his private life that until now have remained largely unknown—most notably his relationships with women. It includes brief reminiscences from his teenage girlfriend Frances Batchen Barrault and remarks about his last serious friendship with Roxolana Roslak, a soprano whom he accompanied and became close to outside the studio. The major revelation, however, involves his romance with artist Cornelia Foss, the estranged wife of composer Lukas Foss (whom Gould much admired). She separated from her husband and moved in with Gould, along with her two young children Eliza and Christopher. All three of them offer their affectionate yet well-tempered recollections of the time they all spent together.

For directors Michelle Hozer and Peter Raymont, this was obviously a labor of love, and it joins other films about Gould—not only Francois Girard’s “Thirty-Two Short Films About Glenn Gould” (1993) but earlier efforts to capture his elusive genius like Bruno Monsaingeon’s “Glenn Gould Hereafter” (2005)—as worthy contributions to the virtual cult that has built up around the man since his death in 1982. It’s invariably noted that a recording by Gould was included among the items sent into space to serve any other lifeforms that might be out there as examples of the best that human beings are capable of. After watching “Genius Within,” you will probably feel that he deserved that kind of recognition. Fans of Gould—and there are still many—will devour the film, and even the merely curious should find it a fascinating portrait of a unique artist—even if some of his peculiarities might, as is admitted here, have been self-magnified for commercial effect.