“Frank” is now available on iTunes and VOD. R, 1:35, three and a half stars out of four.

The old rule in Hollywood is that if you have a handsome movie star in the lead role, don’t obscure his features. No mustaches, no beards, no fake noses.

And one would presume that a giant papier-mache head would also be right out.

But that’s what Michael Fassbender wears for nearly all of the running time of “Frank,” a wonderfully dark comedy about a prickly art-rock band and its enigmatic lead singer. Actually, Fassbender’s obscured features may be one of the reasons Lenny Abrahamson’s film never played theatrically in Madison, but this is not one to miss.

We start with Jon (Domhnall Gleeson), a Welsh singer-songwriter of spectacularly mediocre talent, writing tuneful ditties in his head about strangers on the street that nobody will ever hear. He’s also adept at the art peculiar to Twitter of using self-deprecation to hide actual deprecation. (“Ham and cheese panini. #livingthedream”)

One day, Jon lucks into becoming the replacement keyboard player for an art-rock band called Sonorprfbs (they’re not sure how to pronounce it either). The band includes the fabulously hostile theremin player Clara (Maggie Gyllenhaal) and Frank (Michael Fassbender), a lead singer who drones from within that oversize head. With its wide blue eyes, open mouth and neatly-parted haircut, the head makes Frank look like a gigantic version of Davey from those Davey and Goliath stop-motion cartoons that would play after Gumby.

The gig goes well enough that band manager Don (Scoot McNairy) invites Jon up to a remote cabin in Ireland to help the band work on its next album. Jon finds the band dynamics are fragile, as Frank invents new musical instruments and records random sounds (a musical “graph” of cryptic symbols is a great sight gag). Jon yearns to contribute songs to the group, but is cowed by the vicious Clara; perhaps only Gyllenhaal could sell a line like “Keep your fucking hands off my theremin” with such hilarious conviction.

Meanwhile, Jon discovers that Frank seems like a nice guy under the head — or at least he seems nice. One of the things that makes Fassbender’s performances so magnetic is that we can’t see his expressions, so we’re guessing whether he’s as guileless as he seems or is toying with Jon in some way, making him part of some cosmic art project.

Eventually, Jon and Clara come to tussle over the direction of the band, with the fame-seeking Jon hoping to make them rock stars, and Clara focused on making difficult music that only the band can truly comprehend — and sometimes not even them. “Frank” starts off as an oddball, quirky comedy, but definitely starts moving into some darker territory about midway through. In particular, Jon, initially presented to us as sort of a naive innocent wannabe, turns out to have something of a sinister streak in the way he manipulates Frank to take the band down to Austin for a “prestigious” slot at South by Southwest. We start to wonder if Clara is less of a destructive force in the band, and more of a maternal protector for Frank’s fragile psyche.

Some are not going to like this turn, especially when things grow particularly somber as we learn what Frank was like before the mask. But I really appreciated the willingness of Abrahamson and screenwriter Jon Ronson (who wrote a memoir about the real-life musician Frank is modeled on) to push the film into less comfortable areas, to show how art can sometimes save a soul, and sometimes fall short. In particular, the film finally demolishes the old rock ‘n’ roll stereotype that mental illness can bear the fruit of creative genius. I suspect the truth is closer to what one character says: “It slowed him down.”