Some time last spring, not for the first time, I thanked God for Kim Gordon. Along with Lorde, St. Vincent, and Joan Jett, Gordon, a founding member of the band Sonic Youth, had agreed to perform with the surviving members of Nirvana (Dave Grohl, Krist Novoselic, and Pat Smear) as part of the ceremony for that band’s induction into the Rock and Roll Hall of Fame. The choice to have only women stand in for Kurt Cobain felt in keeping with a band defined by inversion—a vigorous, kinetic kind of inversion, where the movement between one thing and its opposite is so dogged, and occurs at such speed, that a third, separate thing emerges from the blur.

The performances with Lorde, St. Vincent, and Jett had an odd, denatured quality that left both song and singer exposed, missing the viscera of the thing and, in effect, the point. For her number, though, Gordon chose “Aneurysm,” not a hit but a B-side, released on the 1992 compilation “Incesticide.” Wearing a black-and-white striped minidress of the sort she favored in the early nineties, Gordon seemed to pull the song from her guts and trap it in her throat, her body switching, bouncing, and lurching to get it free. “Love you so much it makes me sick,” she spat, “Uhhhhhh-huhhhh.” Not a singer, exactly, Gordon was perhaps the only hope for a song like “Aneurysm,” which in the absence of its author requires less a vocalist than a medium for translation.

In the final pages of “Girl in a Band,” Gordon’s sober, ruminative new memoir, she recalls that night. One of her first appearances following her split from her husband and former bandmate, Thurston Moore, for Gordon the performance became “a four-minute-long explosion of grief,” a purge involving both “the furious sadness” of Cobain’s death, twenty years earlier, and the recent end of her nearly thirty-year marriage, her band, and whomever she was inside of both. Afterward, Gordon reports with some pride, Michael Stipe told her that her singing was “the most punk-rock thing to ever happen, or that probably ever will happen, at this event.”

Stipe’s compliment doesn’t work without the dig—“at this event,” that is to say, as part of the institutionalization of an art form designed to tear down institutions, or at least send a steady stream of guitar and cigarette butts their way. (Stipe’s former band, REM, was inducted in 2007.) Cobain “would have hated being a part of” the Hall of Fame business, Gordon reminds us, and yet there they all were, and there we all were, and there I was, feeling saved, but from what?

“Girl in a Band” is in some ways a curious title for Gordon’s memoir. For a kid discovering Sonic Youth in the nineties, a big part of the point of Kim Gordon was that she was a grown woman, a bellwether, it seemed, of the first rock movement within which women would claim an essential place. An artist who saw music as a way to join and perhaps even direct a larger cultural conversation, Gordon sees now that her sense of a secret, mutually reinforcing world of men influenced her creative decisions, that she joined a band in order to “be inside that male dynamic, not staring in through a closed window but looking out.”

Through the smudgy glass that separates musicians from music journalists, Gordon was nevertheless treated as a novelty. “What’s it like to be a girl in a band?” they all asked. How should she know? “Girl in a Band” can be read as a prolonged consideration of that question, the book’s lamentations for lost or never fully known relationships, decades, movements, and identities keenly of a piece with the era it documents in the greatest depth.

“Did the 1990s ever exist?” Experimental music is now a genre, she writes, and one finds songs from the eighties and nineties bundled indiscriminately and sold as a product called The Past. What about the struggle, “hard-won and unself-conscious … through the obstacles of drugs and greed, past clubs of overly burnished bodies and buff teeth,” to do something separate, disheveled, and true? Did it really happen that way? Does it matter? Gordon’s question, part of a late chapter on “where music has gone, where it’s been, how it’s evolved,” seems at odds with her gimlet distrust of rock mythologizing. Which makes it a fitting lament for an era whose conflicted relationship to popular mythology formed the basis of a late—if not rock music’s final—mass cult.

Gordon describes feeling an immediate kinship with Kurt Cobain, “one of those mutual I-can-tell-you-are-a-super-sensitive-and-emotional-person-too sorts of connections.” It was also something of a maternal bond, and she writes tenderly of it and of Kurt himself. Their shared self-consciousness about adopting a public persona, and their sensitivity to rock-and-roll clichés, puts a unique pressure on the attempt to tell their stories.

“Kurt Cobain: Montage of Heck” (airing on May 4th on HBO), the first authorized documentary portrait of its subject, offers a study of how the anti-mythology mythology surrounding Gordon and Cobain took shape, and found its patron saint. Directed by Brett Morgen, the film makes abundant and often striking use of private footage, writing, and recordings—primary materials that, together with animation, kitsch-heavy montage, raw and imaginatively reworked versions of Cobain’s songs, and interviews with family and friends, form a kind of bio-collage of a man whose life and art, so perilously fused, seemed always at the point of flying apart.

Both Gordon and Cobain emerged from their childhoods with a morbid fear of embarrassment. Gordon describes the ridicule and humiliation she suffered under the spell of her charismatic, mentally ill older brother, Keller; Cobain’s mother, Wendy, claims that his father, Don, belittled and shamed him. His parents’ split mortified seven-year-old Kurt, so fervent was his attachment to the image, the fantasy, of the perfect family. To be embarrassed was to suffer a betrayal, and to betray one’s self. Multiple interviewees point out that Cobain experienced shame as the ultimate threat.

As a songwriter, he returned often to this formative breach, as in “Sliver” and “School,” songs of childhood innocence giving way to rage; lyrics of primal tenderness and disgust set to what Cobain calls “a very powerful, high-energy rock and roll.” He was a perfectionist, his mother says: he had to sing the best, play the best, and be loved the most. Embarrassing qualities, all, for an aspiring punk rocker. “Learn not to play the guitar,” Cobain wrote, in a list of self-admonishments. No chance of unlearning his generation’s tormented relationship to ambition, fame, success, authenticity, influence, performance—a self-consciousness so pervasive that its transcendence occurred against crushing odds, in moments that felt holy as a result.

One such moment: a Christmas scene, shot on home video, from the late eighties, of a family milling about a tree-decked room, genial, cups in hand. The camera pans to catch an entrance, and suddenly there, amid the shoulder pads and squared-off hairstyles, stands Kurt Cobain, a vision of smiling, deeply shocking beauty.

Cobain was appearing in actual documentaries even before true fame arrived. “1991: The Year Punk Broke” documents Nirvana’s stint opening for Sonic Youth on a brief European tour, a month before the release of “Nevermind,” which went on to top the Billboard charts and sell upward of thirty million copies.