"You're just going to have to go with this." So says zoned-out band manager Don (an unrecognizable Scoot McNairy) to eager-beaver new keyboardist Jon (Domnhall Gleeson) at the outset of Lenny Abrahamson's brazenly strange, frequently brilliant new film "Frank." He may as well be speaking to the audience: a black comedy that runs the gamut from gentle whimsy to balls-out absurdism, "Frank" certainly demands a lot of acceptance from its viewers – and not just for the cardinal aesthetic sin of encasing Michael Fassbender's regal mug in a fiberglass fishbowl painted to resemble Dora the Explorer's unsavory older brother. Some will certainly go with it; others will find it flying right over their regular-sized heads.

To be fair, the "Fassbender in a giant head" hook is a cute, blurb-friendly entry point into a film whose chief provocations and curiosities run far darker and deeper than that; what initially seems a high-concept goof-off becomes more humanly moving as the gimmick progresses, though "Frank's" concessions to realism remain few and far between. It is, then, exactly the collaboration one might have expected from Abrahamson, the Irish humanist noted for such modestly scaled, emotionally rich character studies as "Garage" and "What Richard Did," and Jon Ronson, the wonky Welsh humourist whose work last reached the screen in "The Men Who Stare at Goats" – if one were to imagine anything at all from those paired sensibilities. (Oscar-nominated screenwriter Peter Straughan adapted Ronson's skew-whiff style in "Goats"; here, they share script duty on a more sophisticated oddity.)

What emerges, then, from the jokey premise and faintly Kaurismaki-esque sight gags – or sound gags for that matter, as when Maggie Gyllenhaal covers "I Want to Marry a Lighthouse Keeper" with torchy intensity – is a complex, compassionate study of varying degrees of mental illness, and the ways it can both prompt and impede creative prowess, and not just for Fassbender's fragile title character. No romanticized celebration of savant syndrome here: "If anything, it slows him down," observe Frank's parents of his singular psychology, and indeed, "Frank" also works as a wicked satire on our own fixation with tortured artistry.

Certainly, Jon believes he could do with a bit more suffering for his art. An aspiring but profoundly ungifted songwriter living with his parents in a dead-end English coastal town, he can draw lyrical inspiration only from his mundane surroundings. Rescuing him from a life of chip-shop lyrics and markedly dull tweeting (his dismal command of hashtags is one of the film's best running jokes) are a visiting indie band, The Soronprfbs – a strenuously avant-garde outfit fronted by Fassbender's false-headed enigma. Appointed without ceremony as a replacement member when their keyboardist attempts suicide, Jon is initially dazzled by their unpronounceable name, impenetrable sound and perversely difficult working process.

Frank, for his part, declares him "cherishable," unperturbed by his lack of evident musical talent. His fellow band members, however, are less convinced – notably Clara (a perma-scowling Gyllenhaal), whose evident infatuation with Frank rivals Jon's own. Over 18 months spent holed up in a rural recording studio, the band members squabble for creative control over their new album and, eventually, over Frank himself – whose already dubious grasp on reality is further loosened as Jon introduced The Soronprfbs to social media and they go unexpectedly viral. "I always dreamed that one day I'd have a band member who shared my vision of creating extremely likable music," Frank gushes to Jon – yet as he begins composing with an audience in mind, perhaps for the first time, the deterioration of his work and mental state is alarmingly swift.

As written on paper, this could all play out as a straightforward backstage drama: even the film's greatest single quirk, That Head, serves as a valid symbol of the protective disguise donned by many an out-there performer. The difference it and Bowie's Aladdin Sane glitter-bolt, of course, is that the head never comes off. (UK viewers, meanwhile, will know of the Frank figure's real-life inspiration: comedian Chris Sievey's moon-faced Frank Sidebottom persona.) But if "Frank" is, at least to some extent, a story of finding security, not to mention artistic identity, in affectations, it's fitting that the film should have a few of its own.

Pleasingly and perhaps surprisingly, given the extremities of the material, the cast plays crazy with cool, measured aplomb. Gleeson, rapidly developing into one of our most endearing everyman actors, is just guileless and dorky enough to convince us that he himself is convinced; Gyllenhaal, meanwhile, nails an all-too-rare comic performance as the band's sleekest, most volatile presence.

Even those unmoved by the film's admittedly oblique emotional subtext, meanwhile, should appreciate it as a virtuoso showcase for Fassbender, exuding eerie frontman magnetism even with his face invisible for the bulk of the film. Turns out he can hold a tune, too: it's one of the film's great joys that the band's music isn't treated merely as joke fodder. Landing somewhere between My Bloody Valentine and Morrissey, the film's original compositions are abrasive and difficult and somewhat inexplicably lovely – all words that apply to different stages of "Frank," a film that suggests we might labor as hard to love art as we do to create it.