“Hallelujah” is unusual. The man who wrote it, Leonard Cohen, opined that it is “a good song, but too many people sing it.” Its most famous version features not Cohen’s gravelly voice but Jeff Buckley’s nearly angelic one. This biblically saturated meditation on brokenness has become a staple of reality television talent shows. Many know it from the “Shrek” soundtrack.

“Hallelujah” — feel free to hum it as you read — captivates millions because it holds paradox so adroitly, using that ancient Hebrew word to collate the sacred and sensual, what the song calls the “holy and the broken.” References to “the Lord of Song” mingle with passages of erotic longing and the realization that “it all went wrong,” in life and love. There is nothing quite like it.

Now, the song even has its own documentary. “Hallelujah: Leonard Cohen, A Journey, A Song” had its debut at the Tribeca Film Festival and arrived in theaters last week. Directed by Daniel Geller and Danya Goldfine, it uses “Hallelujah” —  written in 1984, when Cohen was 50 years old — to tell the story of how Cohen went from poet to a secular psalmist. 

The documentary touches on Cohen’s roots at Montreal, as the son of schmatta traders who parlayed underwear into wealth. He would gain acclaim as a poet and novelist, a loving rebel against the ordered world into which he had been born. Cohen got a late start as a musician. He was in his early 30s when Judy Collins covered “Suzanne,” and then encouraged him to sing it himself. 

Cohen was famously painstaking in his craft, laboring over verses with a poet’s rectitude. He worked on “Hallelujah” for years, but its unveiling was a disaster. Cohen, middle aged and facing stalled momentum after an off-key album produced by Phil Spector, believed that “Various Positions,” the collection that included “Hallelujah,” would signal his comeback. 

The president of CBS Records, Walter Yetnikoff, felt differently. Famously telling Cohen, “We know you’re great, but we don’t know if you’re any good,” Yetnikoff assured that “Various Positions” was not released in America, effectively sounding its temporary death knell. 

The “Hallelujah” documentary does especially good work in tracing the accidents and byways that took the song from obscurity to ubiquity, demonstrating that inevitability is easy to see when you know how the story ends. This resurrection ran through eccentric influences, East Village serendipity, and the charisma of “Hallelujah” itself, which claimed artists who had never heard of the man who wrote it.  

While much of this trajectory is limned by talking heads — most prominently Rolling Stone journalist Larry “Ratso” Slonam, who was both friend and Boswellian chronicler to Cohen — the most instructive interludes are when we see clips of performances, as the song finds new expression in the throats of performers as diverse as John Cale, Buckley, Rufus Wainwright, Bob Dylan, and Bono.

While it would have been tragic if “Hallelujah” flourished while its creator languished, their renaissances overlapped and were mutually nourishing. For Cohen, a six-year stint in a Zen monastery at Mount Baldy, outside of Los Angeles, was followed by the disclosure that a business partner had swindled him out of much of his savings. 

Driven by what the Greeks called Ananke, or the goddess of necessity, Cohen in his twilight undertook a five-year tour that was an unalloyed success, inscribing his work for a new generation. In stitching together videos of Cohen singing “Hallelujah” everywhere from Helsinki and Dublin to Coachella and Tel Aviv, the film makes the case for Cohen’s song as a global hymn.

The documentary was approved by Cohen just as he turned 80, in 2014, and benefits from extensive access to the Cohen trust. Images of notebooks and jottings bring his creative process to life and remind of just how writerly Cohen was, even and especially as a musician. Footage of Cohen at the monastery and in private offer views inaccessible from the stage. 

This film is less about the life behind the art than how the life is alchemated into the art. Cohen’s private life is not ransacked — his family earns barely a mention — but friends and lovers recall what it was like to watch him work, tinker, square up to his talent, and wrestle it into tune and verse so finely wrought that in the words of the song, “every breath we drew was Hallelujah.”

This reviewer saw “Hallelujah” only a day after taking in “Elvis,” Baz Luhrmann’s new film about the great singer. Cohen and Elvis are studies in contrast, opposites in nearly every way. What they share, however, is immense, and best captured by a verse from Cohen’s “Chelsea Hotel #2,” that great hymn to New York’s perennially endangered bohemians: “We have the music.”