Not since Claude Rains made his debut in “The Invisible Man,” in which his face wasn’t shown until the film’s final frame, has an actor been so visually constrained by a character as Michael Fassbender is as the title figure in “Frank,” a quirky, weirdly funny tale with an underlying layer of deep melancholy, about the fragility not only of art but of the human psyche.

The enigmatic Frank is the lead singer-songwriter of an avant-garde British band that calls itself by the unpronounceable name of Soronprfbs, and their highly unorthodox, often chaotic numbers are certainly not designed to appeal to whatever listeners can be attracted to their hole-in-the-wall gigs. The group’s oddity is accentuated, however, by another fact: Frank wears a giant mask—a papier-mache head painted with wide eyes, slick black hair and a cartoonish open mouth, giving the thing a look of vague astonishment. (Just think of the Jack-in-the-Box commercial.) He doesn’t just don the mask on stage; he wears it constantly, even—as one amusing moment will demonstrate—when he’s in the shower.

As difficult as it might be to believe, the character is based on a real person, an English punk rocker and performance artist named Chris Sievey, who gave the name Frank Sidebottom to his bizarre creation. But scripters Jon Ronson and Peter Straughan use that circumstance merely as springboard for their screenplay, which builds imaginatively on Ronson’s experience as a substitute keyboardist in Sievey’s band.

The story is told from the perspective of Ronson surrogate Jon (Domhnall Gleeson), depicted as a nerdy young man with a dull office job who’s obsessed with the idea of becoming a songwriter and is constantly spinning out dreary beginnings of insipid tunes on his computer. One day while taking his lunch on the beach, he observes a man carted off by the police after having tried to drown himself in the surf. The poor soul turns out to be the Soronprfbs’ keyboardist, and since the band has a gig that night, Jon is immediately recruited as a temp replacement despite his woeful lack of expertise. The performance is a disaster, but Jon’s invited to stay on with the group for what he expects to be another day or two; but instead he’s driven to a remote retreat, where he and his new colleagues—Frank; spacey manager Don (Scott McNairy); hostile theremin player Clara (Maggie Gyllenhaal); grim percussionist Nana (Carla Azar); and snooty French bassist Baraque (Francois Civil)—will remain in isolation for as long as it takes to record what’s foreseen as a ground-breaking CD.

The stay will stretch into months, during which Jon spends his savings on the band’s needs while desperately trying to pen some songs on his own. But he also yearns to help the group win the popular recognition he believes Frank deserves, and begins blogging about their efforts, winning a group of admirers that, however small, greatly outnumbers the few sad souls who once had followed Jon’s personal postings. Eventually the blog will earn the Soronprfbs an invitation to the South by Southwest Festival in Austin. But that’s only the culmination of the tension that Ronson, Straughan, the cast and director Lenny Abrahamson draw between, on the one hand, the goal of creating a pure expression of individualistic artistic drive, however insular and unappreciated it might be, and the drive for worldly success on the other. When Jon’s dream wins out, it inevitably leads to a disaster that unmasks Frank and threatens to destroy him and the small, supportive reality he’d constructed around himself.

“Frank” is certainly an odd film, and some viewers may find it difficult to tune in to its peculiar wavelength. But for those who can, it will prove a delightfully unusual tale that speaks to the chasm between genius and mediocrity in much the same way that “Amadeus” did, but adds the poignant observation that sometimes what makes someone appear exceptional is a matter not of extraordinary ability but mental distress. And it affords a choice opportunity for Fassbender to show his skill in using his body, as well as his voice, to convey emotion even in the absence of facial expression—though when unmasked in the final reel, his morose countenance adds to the impact. Gleeson presents a perfect contrast as the simpleton who sports equal measures of eagerness and naivete, while Gyllenhaal adds a striking tone of bitter realism as the person who understands Frank better than anyone else. An equally important contribution comes from Stephen Rennicks, whose music strikes the precise chords the story demands. The film is modestly mounted, but James Mather’s camerawork is evocative, especially in the long middle section at the recording retreat, and Nathan Nugent’s editing gives it an arresting rhythm.

The distinctiveness of “Frank” makes it difficult to categorize. It also makes it easy to appreciate in an age when most movies come off like assembly-line products.