“Everything you touch turns to sh*t!” the icy words spat by Jean (Carey Mulligan, giving a beautifully bitter performance) linger in the even icier New York air. “You’re like King Midas’s idiot brother.”

This witty, biting criticism is directed at Llewyn Davis (Oscar Isaac) having just been told he’s potentially the father of Jean’s — his close friend’s girlfriend’s — unborn child. And it’s an unfortunately accurate reflection of the Coen Brothers’ titular character. Nothing can possibly go right for him.

The hazy, smoke-filled bars and woolen-clad, bearded folk singers may suggest a nostalgic reflection on the Greenwich music scene of the 1960s. Yet the Coen Brothers inject their idiosyncratic tragedy-laden humor and humanity to provide a touching insight into this often-mythicized era of American music. And it’s all through the eyes of one of their most engaging characters to date.

“Inside Llewyn Davis” paints a living portrait of Davis. Through his inability to maintain friendships, his attempts to remain sincere to his craft and his attempts to avoid becoming the dreaded “careerist” musician, he all the while tries to make ends meet. Though it might be hubristic, it’s this integrity and idealism that encourages the audience to continually root for him, even though he manages to infuriate anyone and everyone he encounters.

Davis, however, appears to sit comfortably in this role of deadbeat artistic rogue, roaming from couch to couch. He informs his disinterested nephew, after an argument with his sister, that “your uncle’s a bad man” without even an ounce of regret.

The Coens succeed in capturing this week in the life of Davis with an intimate stillness, lingering on Davis’ failures and documenting the stagnant nature of his existence. Nothing is achieved. There are no dramatic realizations or character arcs. Yet it’s his failures that make him so believable and empathetic. Great restraint is demonstrated so as not to patronize the audience by allowing the narrative to tell you how to judge their central protagonist with grand and predictable revelations. But then again, these are the brothers who brought the world such unique anti-heroes as The Dude in “The Big Lebowski” and H.I. McDunnough in the woefully underappreciated film “Raising Arizona”.

New York is similarly photographed in a somewhat less-than romantic light — there are no sweeping Woody Allen-esque love-letter shots of the Big Apple. Instead, the audience is placed at ground level, among the dirt and winter slush, to bear the brunt of this unforgiving environment alongside Davis. The camera navigates through cramped Greenwich apartments, framing awkward interactions between Llewyn and the various characters he annoys. That said, there is still unquestionable beauty in the grimy, snow-speckled alleyways and the smoke-filled folk clubs into which we are led.

Like “O Brother, Where Art Thou?,” it’s easy to view “Inside Llewyn Davis” as much as an ode to a musical epoch as an unorthodox odyssey. All but one of the musical inclusions are performed live by the various actors, and the notable absence of music otherwise supplies greater gravitas to the few performances the audience is gifted. This is where the film, and also Oscar Isaac as Davis, shine the brightest. The renditions given by Isaac provide the most delicate and touching moments of the film, granting the audience (both on screen and in the movie theatres) a glimpse of his vulnerability, his artistry and also the craft for which he has sacrificed so much.

The film ends where it began, emphasizing the circular monotony of Davis’ situation as a committed singer-songwriter in ’60s New York. A brief glimpse of this musician, suspiciously sounding and looking like a young Bob Dylan, might suggest that perhaps times are a-changin’.