January 3, 2014 12:52 PM EST

They had fame, reams of money and fans willing to do wild, unmentionable things just to breathe the same air — but in its September 24, 1971 issue, LIFE magazine illustrated a different side of the lives of rock stars. Like other mere mortals, they often came from humble backgrounds, with moms and dads who bragged about them, fussed over them, called them on their nonsense and worried about them every single day.

Assigned to take portraits of the artists at home with their sweetly square folks, photographer John Olson traveled from the suburbs of London to Brooklyn to the Bay Area, capturing in his work the love that bridged any cultural and generational divides that existed between his subjects.

Here, LIFE.com brings back Olson’s nostalgia-sparking photos — Marvel at the decor! Gaze in wonder at the shag carpets and bell-bottoms! — and shares his memories of hanging out with pop culture icons of the Sixties and Seventies, as well as their mums and their dads.

John Olson on Frank Zappa: “Everyone had told me that Frank Zappa was going to be really difficult, and he couldn’t have been more professional,” Olson told LIFE.com.

Zappa on His Parents: “My father has ambitions to be an actor,” Frank told LIFE. “He secretly wants to be on TV.”

Zappa’s Mom on Zappa: “The thing that makes me mad about Frank is that his hair is curlier than mine — and blacker.”

Grace Slick: Grace Slick’s mom Virginia Wing, wrote LIFE, was a “soft-spoken suburban matron” — pretty much the opposite of her wild child. “Grace and I have different sets of moral values,” Mrs. Wing told LIFE, “but she’s her own person, and we understand each other.”

Elton John: In 1970, Elton John was just three albums into his prolific career, and still had countless hits — “Rocket Man,” “Daniel,” “Bennie and the Jets” and “Candle in the Wind” among them — in his future. “When he was four years old,” his mother said of her prodigiously talented son, “we used to put him to bed in the day and get him up to play at night for parties.”

Ginger Baker: The world knew him as Ginger, on account of his red hair, but his mother christened him Peter, and to her he was always “my Pete.” As she told LIFE magazine: “He would bring people over and they would say, ‘You realize your son is brilliant,’ and I’d say, ‘Is he? I wish he was a bit more brilliant at keeping his room tidy.'”

John Olson on Ginger Baker: “I had worked with lots of these musicians before,” Olson told LIFE.com, “and the first go-round some of them had been really difficult. But when they were with their parents, they were totally different people. Baker, who had been terribly obnoxious before, acted like a grown-up. I don’t think it had anything to do with respect for me, so it must have been the parents.”

Joe Cocker: Facial contortions, flailing arms, gallons of sweat: the blues singer poured all that and more into his passionate performances. But off stage, LIFE observed, “he is cool and withdrawn — a temperamental mixture of Harold Cocker, his civil servant father who preferred gardening to posing with his famous son, and his outgoing, chatty mother.”

David Crosby: With his parents divorced, the “Crosby” of Crosby, Stills, Nash & Young posed with his father Floyd, an Oscar-winning cinematographer, in the Ojai, Calif., home Floyd shared with his second wife in 1970. “In the last few years we’ve become good friends,” David told LIFE magazine. “What I like best about him is that he seems to feel no need for me to be like him, so we’re not offended by each other’s differences. Like he knows I get high. He doesn’t do it and he doesn’t approve of it, but he doesn’t inflict his values on me.”

Jackson 5: Unlike the other stars featured in LIFE’s story, the Jackson brothers — Michael, Marlon, Tito, Jermaine and Jackie — experienced fame as kids, and still lived with their parents (father/manager Joe and mother Katherine). At the time of LIFE’s shoot, they were the hottest act in pop, skyrocketing in 1970 with “ABC” and “I’ll Be There,” and had just moved into an expansive new house.

“It was very controlled,” Olson says of the photo shoot that resulted in the September, 24, 1971 LIFE cover. “As I remember, they followed my requests to a T, and were incredibly polite. The dad was pretty stern.” Indeed, Joe — who had been a crane operator in Gary, Indiana, just three years before — hinted at the relentless drive toward fame about which Michael would later voice such ambivalence. “It wasn’t hard to know they could go on to be professionals,” Joe told LIFE of his young sons. “They won practically all the talent shows and I wasn’t surprised when they did make it.”

Donovan: His parents’ love of Scottish and English folk music inspired the same in their son, the singer/songwriter behind such hits as “Season of the Witch” and “Mellow Yellow.” But by the time of his photo session with Olson, Donovan’s fruitful partnership with record producer Mickie Most had soured and his career was in decline. Perhaps as a result, Donovan was the only musician Olson photographed who was left out of the story that LIFE eventually published.

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