At the age of 74, Canadian poet and troubadour Leonard Cohen started a world tour — his band in matching fedora, with backup singers, many of whom had been with him for years and with a seemingly endless and boundless itinerary.

And “years” were how long this venture went on, five years of performing his ornate, soulful, introspective ballads and laments on a valedictory tour, a victory lap, revered everywhere he played, every show building to that one transcendent moment, that one song with every night’s crowd singing along to what a fellow singer calls “a modern prayer,” “a church moment” at the end of every single concert.

Cohen gave this tune everything he had, night after night — leaning into it one night, laying back on it the next — honoring a singular composition that he recognized had given him everything, and delivered that “everything” late in life, when the “elder” that he’d longed to become could appreciate it.

“Hallelujah: Leonard Cohen, a Journey, a Song” isn’t really a new Leonard Cohen bio-documentary, although it has plenty of footage of his early career, prefiguring his transition from privileged Montreal poet to self-taught singer-songwriter. Folk songbird Judy Collins was among his mentors in making that leap. And we hear other bits of his personal history and track his entire career through this Daniel Geller and Dayna Goldfine film.

But what they focus on is the thing that made him, not his Tom-Waits-without-the-gravel baritone or his Anthony Bourdain-the-prototype dash and good looks. It’s that one song.

“Hallelujah” took him seven years to write and re-write, tinkering and expanding and contracting the scale of this magnum opus as he saw fit over the decades after its 1984 introduction on an album his U.S. record label refused to release here. His friend and favorite journalist, Larry “Ratso” Sloman of “Rolling Stone” and other publications, recalls Cohen turning out “150-180” verses of “Hallelujah,” notebook after notebook filled with variations of Cohen’s blending of “the holy with the horny,” an epic song deconstructing how that song was built.

“It goes like this, the fourth, the fifth
The minor fall, the major lift
The baffled king composing ‘Hallelujah’…”

The Jewish Cohen was singing about Old Testament King David struggling to compose a song built around that ancient word of praise in that opening verse. But it’s easy to see himself — seven years struggling, never gaining commercial success and notoriety until his 60s and 70s — as an equally baffled “king.”

The bafflement extends to the song’s journey to glory. An unreleased album, a 1984 music video (glimpsed here) that did nothing for it, a gorgeous melody with glorious lyrics destined for the dustbin.

But Bob Dylan started playing it in concert. Velvet Underground alumnus John Cale took hold of it and performed it in a spare, solo piano and voice version. Jeff Buckley found it and gave it a bracing blast of sexualized youth. “Shrek” came along and Dreamworks got Rufus Wainright to record a streamlined version of it. “American Idol” and other singing competition shows had singers take it on. Eric Church covered it. Kate McKinnon performed it as a funeral dirge on “Saturday Night Live” the week the disgraced ex-president took the White House.

The song itself may be over-performed and indeed over-exposed, something Cohen fretted about late in life. But how can any singer resist a melody that prompts an almost Pavlovian response in tens of millions of listeners, the tears starting long before the chorus?

“It’s become it’s own thing,” Brandi Carlile marvels. “Universal.”

Geller and Goldfine’s film breezes through that history and attaches the tune — Cohen’s friend John Lissauer wrote the moving, funereal arrangement — to Cohen’s life as a “spiritual seeker,” a Zen student who spoke Hebrew and absorbed “the charged speech” and song “I heard in the synagogue growing up.”

We hear from Cohen’s rabbi and get a handle on how the song fits within Cohen’s faith, and where it sits in his life-long discography, “a mature man chronicling his life” via his musical “conversations with eternity,” struggling with love and spiritual meaning to the very end.

And through it all, we see the many guises of Cohen on camera, Canadian TV in the ’60s, struggling to find his place as a folk bard in the pop singer-songwriting of the ’70s, clinging to a career as he aged into the ’80s and ’90s, warm and playful interviews, recollections of mistakes (working with Phil Spector and his “Wall of Sound”), hints at heartbreak.

“Hallelujah” may not get as deep into Cohen’s life story as the earlier Cohen doc “I’m Your Man.” It doesn’t dig deep into the song itself, with the filmmakers content to show scores upon scores of performances of the tune, never having anyone parse the lyrics and break down its construction.

But narrowing the focus to this song elevates the film and its subject, and makes a fascinating window into one creative life, lived in curiosity, looking for answers and groping — for seven years — just to come up with a song that explains it all.

Rating: unrated

Cast: Leonard Cohen, Judy Collins, John Cale, Sharon Robinson, John Lissauer, Brandi Carlile, Adrienne Clarkson, Jeff Buckley, Rufus Wainright, Vicky Jenson, Glen Hansard, Eric Church, Clive Davis and Larry “Ratso” Sloman.

Credits: Scripted and directed by Daniel Geller and Dayna Goldfine. A Sony Pictures Classics

Running time: 1:55