Recorded in 1984, it was on the only Cohen album rejected by his record company. Virtually no one noticed when the song did come out on an independent label. Since then, through dozens of cover versions, high-profile performances and appearances on TV or movie soundtracks, “Hallelujah” has become a modern standard.

Author Alan Light reflected upon that while at Yom Kippur services in Manhattan two years ago, as he saw congregants in tears when the choir sang “Hallelujah.” His curiosity led him to write “The Holy or the Broken,” about the song’s trajectory, about Cohen and about its most celebrated singer, the late Jeff Buckley. The book is out Tuesday.

“At a time when everything has fragmented so dramatically, it’s sort of heartening to see that this song can connect as universally as it did,” Light said.

Cohen labored over “Hallelujah,” filling a notebook with some 80 verses before recording. The song has Biblical references, but Cohen’s stated goal was to give a nonreligious context to hallelujah, an expression of praise. Some of those hallelujah moments are clearly sexual, given a lyric like “she tied you to a kitchen chair … and from your lips she drew the hallelujah.” The author’s droll humor is present throughout in lines like “you don’t really care for music, do you?”

Musically (and Cohen’s lyrics even describe the melody), the verses build slowly to a release in the chorus, which is simply the title word repeated four times.

Cohen saw his composition as joyous, yet its placement on “ER,” “The West Wing,” “House” and many other TV and movie soundtracks has become a nearly universal signal of a sad moment. It is played at weddings, funerals, school concerts and all manner of religious services, the chorus lifting it into the realm of the spiritual.

The song’s malleability is one key to its success, Light said. Cohen recorded four verses but sent several more to John Cale when Cale recorded “Hallelujah” for a 1991 tribute album. Seven were published in Cohen’s 1993 book of lyrics and poetry. Verses can be dropped or given greater emphasis depending on the interpreter. And most everyone knows “Hallelujah” from an interpreter, from Buckley to Bono, from k.d. lang to Susan Boyle, to seemingly half the contestants in TV music competitions.

That sets it apart from other modern standards, like “Imagine” or “Bridge Over Troubled Water,” where greatness was apparent almost instantly and the original recording remains the definitive version.

Buckley’s recording was a milestone; half Cohen’s age when he made it, Buckley’s take was more romantic and yearning than the reflective original. The song’s inclusion on the “Shrek” soundtrack, its repeated replaying on VH1 after the 2001 terrorist attacks and 2010 versions by lang at the Winter Olympics and Justin Timberlake at a telethon for Haitian earthquake relief were other key moments for its visibility.

Light can’t recall when he first heard it. His favorite version is by Cohen in concert at the 2009 Coachella festival, easily found on YouTube.

Credit one of the world’s greatest living songwriters for first recognizing the potential of “Hallelujah.” Bob Dylan performed it twice in concert during the mid-1980s, once in Cohen’s native Canada.

“They’re not very good but are heartfelt in a certain way,” Light said. “I’m sure hardly anybody at the time who heard Dylan sing it knew what it was.”

In writing a book on a single song, Light joins a very specific and small category of literature. Other notable examples include Dave Marsh’s book on “Louie Louie,” Robert Harwood’s on “St. James Infirmary” and Ted Anthony’s on “House of the Rising Sun” (Anthony is an Associated Press employee).

There is always a bigger story to tell. Harwood said that in writing about a song, an author must explain the environment in which the song appeared and how the song grew, changed and metamorphosed.

“That sort of information is more likely to have been discarded when it comes to popular culture than, say, if it was a historic political moment,” Harwood said. “… In the end, though, popular culture is the story of our times.”

Veteran music industry chronicler Light’s recognition of the times in which “Hallelujah” first appeared play into him giving a pass to Columbia Records executives for rejecting the song. Madonna, Michael Jackson, Bruce Springsteen and Prince were at their peaks and selling boatloads of albums in 1984.

Cohen, then a 50-year-old singer-songwriter whose sales were steadily fading, would not have been a priority.

“At the time, they were just trying to print up enough copies of Born in the USA to keep up with demand,” Light said.

One of Light’s key interviews came late, when Bono agreed to speak about U2’s little-known version. Light had just finished a draft of the book where he talks about the recording not being particularly good.

“What if he says how proud of it he is and I have to rework the whole thing?” he said.