Wherever you currently land on the subject of the Bee Gees (Forgotten glitter gods? Perpetual punchline?), director Frank Marshall’s thorough and beautifully appreciative HBO documentary “The Bee Gees: How Can You Mend a Broken Heart” will get you where you need to be — which, I can practically promise, is a sublime state of awe.

An exemplary lesson in how to make a revealing rockumentary, “The Bee Gees” (premiering Saturday) will satisfy lifelong skeptics and loyal fans. It’s less of the usual tract (we had them all wrong!) and more of a reckoning with the profound degree of artistry and accomplishment that should be the last word on any Bee Gees story. The movie is also a unique consideration of the phenomenon of rise and fall, and how one learns to live with it.

Spending almost no time on a deep probe of the biographical 1950s family dynamics of the Gibbs of Brisbane, Australia, it instead heads straight into the recurring theme of success and fame as a matter of raw determination: Hugh Gibb, the father of Barry and twins Robin and Maurice, was a musician who simply believed his sons’ harmonizing vocals and knack for songwriting deserved as much or more attention than, say, the Beatles. He wrote to Beatles manager Brian Epstein and offered up his cheerfully ambitious offspring; Epstein handed them over to a subordinate, Robert Stigwood, and the rest is pop-music history.

But what kind of history and why? This is where Marshall’s film succeeds. With archival footage and music cues that will invariably lure you out of your chair (or have you choked up during those achingly perfect chord progressions in the band’s ballads), “The Bee Gees” insists the Gibbs’ musicianship and prolonged success is as impressive as anyone in the rock pantheon. The film also has an adept awareness that such statements are always up for careful review and heated debate. No greater authority than Barry Gibb himself, the band’s sole survivor at 74, can confirm the ways in which celebrity stories, and images, change with time.

“I am beginning to recognize the fact that nothing is true,” he says at the film’s opening. “Nothing. It’s all down to perception. My immediate family is gone, but that’s life. It’s the same thing in every family, that someone will be left in the end. [At] this time in life, I have fantastic memories, but everybody’s memories are different. So they’re just my memories, you know?”

In other words, “The Bee Gees” is years too late to present the fullest possible account, relying on past documentary interviews with Maurice (who died in 2003) and Robin (who died in 2012) to supplement the narrative of a band that continually recalibrated itself to radio’s whims. Inspired by the work of others (including Otis Redding and the Mills Brothers) in a time when appropriation was just part of the game, their greatest gift to music could have started and ended with the writing and recording of their much-covered 1967 hit ballad “To Love Somebody.

The footage and music from the band’s initial dalliance with fame is as much or more fascinating than the “Saturday Night Fever” superstardom that lurked ahead. As noted by Coldplay singer Chris Martin, who considers himself something of an expert on pop-star backlash, the Bee Gees were among the first groups to understand that long careers in the recording industry come with stretches that are as low as any high. Ego clashes were complicated by familial resentments. Oasis’s Noel Gallagher observes that making music with family members is “the greatest strength and the greatest weakness you can have.” Bee Gees fan Nick Jonas agrees: “Brothers, in general, is a very complicated thing.” One wishes the movie went even more deeply on this — the depth with which Barry, Robin and Maurice loved one another comes through; the darker moments often don’t.

Robin briefly went solo and wouldn’t talk to Barry. (The good-humored Maurice says he always had to be the “Mr. Fix-It” between the two.) The 1970s dawned with another big hit (“How Can You Mend a Broken Heart”), but, even reunited, the brothers yearned to find a new sound. The supportive Stigwood, who by now had his own label at Atlantic, urged the Bee Gees to do what his other big client, Eric Clapton, had done — move to Miami and experiment.

“Those guys were actually an R&B band that hadn’t really worked that out yet,” Clapton observes.

It is here that "The Bee Gees" makes an enlightening argument for the kind of musicianship that happens at the studio control board. It's not so much about manipulation as it is a startling degree of precision and perfectionism. "Jive Talkin'," a revelatory new Bee Gees hit in 1975, was divined from the rhythm produced by car tires speeding across a Miami bridge. Working with producer Arif Mardin on the song "Nights on Broadway," Barry was pushed to improvise near the song's end, eliciting a sonic falsetto he never knew he had. ("Blamin' it all! Blame it on the nights on Broadway!") That, more than anything, put the Bee Gees' stamp on popular culture — and again borrowed heavily, the film notes, from such bands as the Spinners and Stylistics.

Their new sound leads, of course, to a level of fame and riches the brothers never imagined. Stigwood asked the band to add some songs to the soundtrack of a movie he was producing about the flourishing disco scene in Brooklyn. To persuade the studio to release “Saturday Night Fever” in as many theaters as possible, Stigwood promised to attach a No. 1 hit to it in advance, leaving it to the Bee Gees to come up with “the best love song you’ve ever written.” They delivered, with “How Deep Is Your Love,” followed by “Stayin’ Alive” and “Night Fever,” on a double album that eventually sold 45 million copies.

In the relentless pursuit of hits, the Gibbs were remarkably unfazed by popularity. Rather than reject it or treat it in an aloof manner, they always seemed to acquiesce to it. The point, after all, is to be adored.

Living in their own glitzy bubble, they were completely unaware, while performing in Oakland on July 12, 1979, that a belligerent rock DJ in Chicago, Steve Dahl, had summoned tens of thousands of listeners to a White Sox doubleheader at Comiskey Park for a “Disco Demolition Night” rally. Fans could get into the game for 98 cents if they brought a disco album to add to a heap that was to be blown to smithereens in the outfield. Plenty of those albums were Bee Gees records; Dahl used to inhale helium on the air to do a mocking imitation of the band.

The event ended, deplorably, in a riotous melee that police had to break up. House music pioneer Vince Lawrence, who was working that night as a teenage usher, remembers seeing a disproportionate number of Black artists in the album pile. For many, Dahl’s “Disco Sucks!” movement took on the pall of a fascist uprising. “It was a book burning. It was a racist, homophobic book burning,” Lawrence says. “And the Bee Gees got caught up in that, because they were part of that culture that was lifting a lot of people up.”

The brothers were hurt and confused by the sudden backlash; record companies started dropping disco acts, and everyone’s gaze was about to turn toward MTV. Asked about it then, Barry grew testy with an interviewer and looked angrily into the camera: “Does anybody mind if [the Bee Gees] exist in the ’80s, thank you?”

Yet “The Bee Gees” hardly ends on a note of bitterness. The brothers reinvented themselves once more, this time as master collaborators and surefire love-song wizards writing for others, including Barbra Streisand (“Guilty,” “A Woman in Love”), Dionne Warwick (“Heartbreaker”), and Dolly Parton and Kenny Rogers (“Islands in the Stream”). Respect came in due time (including a Rock & Roll Hall of Fame induction in 1997), as did a recurring theme of loss.

“I can’t honestly come to terms with the fact that [Robin, Maurice and their younger brother Andy] are not here anymore. I’ve never been able to do that,” Barry says. “I’d rather have them here and no hits at all.”

The Bee Gees: How Can You Mend a Broken Heart (110 minutes) premieres Saturday at 8 p.m. on HBO.