As Cyndi Lauper leaped around singing “Girls Just Want to Have Fun” on The Tonight Show in 1984, it seemed like she might never put down the microphone. After she kicked off her stilettos, danced with her backup singers, sprinted back and forth repeatedly from the monitors at the front of the stage to the drum kit in the rear, and belted out the final refrain enough times to ensure that every spectator would be singing it for the rest of the day, the song only ended with the musicians stumbling one by one to a halt: some of them ready to wrap up, and others apparently willing to continue accompanying Lauper until the end of time.

“If I wasn’t doing this, Johnny, I might’ve been a brain surgeon or a rocket scientist,” she told Johnny Carson afterwards, refastening her heels and adjusting her jewelry. “A visiting professor at Harvard,” he offered in return. Though the host’s response had a note of condescension for this young woman singer who’d just spent the last several minutes exalting the virtues of a good time above all else, it’s clear that she was in on the joke. There would be no rocket science or brain surgery for Cyndi Lauper: not because she was too fizzy and fun-loving to learn how, but because she was born to perform.

There are only three original songs on She’s So Unusual, Lauper’s 1983 debut. Years before its release, she’d been the frontwoman of a cover band. She didn’t need to write songs to express her immense natural talent as a performer. Instead, she used the words of men to illuminate her assertive vision of womanhood, each impassioned yelp a detonation inside its source material. Lauper waffled about ascribing deeper feminist meaning to songs like “Girls Just Want to Have Fun,” but there’s a gravity in her vibrato that’s hard to shake. She brought the weight of her past—her childhood growing up in an abusive home, her battles against male industry gatekeepers—into that music. Her voice walks the line between desperation and the self-assurance she gained from playing in bars night after night. It begs, with its technical skill, to be taken seriously, yet is softened by Lauper’s cartoonish inflections that garnered frequent comparisons to actresses like Bernadette Peters more than contemporary female rockers like Pat Benatar. “That’s all they really want,” she belted on “Girls” with more than a hint of indignation, as if to say, Is that seriously so much to ask?

With She’s So Unusual, Lauper shoehorned rebellion into the familiar, both musically and visually: Who else would play a 1920s song written for the real-life Betty Boop wearing tulle fingerless gloves and a mullet? With her taste for synthesizer-driven disco (she apparently met with Giorgio Moroder once, but he seemed to dislike that she called him “George”), Lauper helped to usher in an electronic era for popular rock. After decades of being rejected by her peers, local bands, and record labels, Lauper wanted not just acceptance, but an embrace, of not just her quirks, but of eccentricity itself. She’s So Unusual imagined a world where women danced through New York in ruffle skirts and combat boots, partied with a sense of purpose, and were just as powerful at their most vulnerable as their most ferocious.

Born and raised working-class in New York City’s outer boroughs, Lauper was too stubborn and strange to succeed at school socially or academically. Her parents, both casually musical, divorced by the time she was five. She and her older sister Ellen spent the rest of their adolescence, in Lauper’s words, “dodging pedophiles and the crazy folks,” including their stepfather and grandfather. Cyndi left home at 17 to live with Ellen on Long Island, where she worked as a “hot walker” for racehorses at Belmont Park, singing Hare Krishna mantras into their ears to calm them down. In her free time, she auditioned for cover bands that traveled the Long Island bar circuit. By 1974, she landed a gig as a backup singer, and was soon asked to step up for brief solos: “Lady Marmalade,” “Tell Me Something Good.” Once it became clear that Lauper’s voice worked best front and center, she became a permanent lead.

Cover bands were an ideal proving ground for Lauper. With her four-octave range and irreverent sense of humor, she reimagined the pop canon, imbuing it with her particular sense of wonder toward the world. Just as she would after finding stardom years later, she twisted other peoples’ words to her own will, cracking songs open to reveal new meanings beneath their popular interpretations. It’s hard to hear her sing Jackie Wilson’s “Baby Workout” and miss how enthralled she seems by her own delivery, adding extra vocal runs as if it’s as easy as breathing. And Lauper’s particularities as a performer offered a counterintuitive kind of universal appeal: If this highly unusual woman with a neon orange buzzcut who spoke like a streetwise Minnie Mouse could convincingly inhabit music from Jefferson Airplane, or the Rolling Stones, or Prince, then maybe those songs were for everyone.

Still, she aspired to more than singing other people’s hits. “If you sing ‘White Rabbit’ one more time, just shoot yourself,” she remembered thinking at the time. By the end of the decade, she had formed her own group, the rockabilly-inspired Blue Angel, with John Turi, a saxophonist from her cover band. Critics loved them; they toured with Hall and Oates and the Human League. Lauper was the kind of singer everyone wanted to sign as a solo artist—“Like Chrissie Hynde and Deborah Harry, Lauper possesses the vocal ability to make her stand out,” Billboard raved at the time—but she held out until Polydor agreed to sign Blue Angel as a full band.

It didn’t quite work out: After a batch of expensive failed demos, a subsequent lawsuit, and a debilitating vocal cyst, Lauper began the 1980s bankrupt and out of the music industry. She started working at Screaming Mimi’s, the Manhattan costume vintage store where she honed her singular sense of style, combining layered neon skirts with punk’s jagged industrial edges. She hired a vocal coach and connected with David Wolff, who became her longtime manager and boyfriend. By 1983, she found herself in the studio with Turi and producer Rick Chertoff, recording her first album under her own name.

Chertoff, an Arista veteran and Clive Davis disciple, saw Lauper as a mouthpiece more than a creative force, someone who could give life to a batch of songs he had been collecting, with his college buddies Rob Hyman and Eric Bazilian of Philadelphia group the Hooters (named after the melodica, of course) backing her up. His selections were scattered: a cult classic from the short-lived pop rock group the Brains (“Money Changes Everything”), a little-known love song by Jules Shears (“All Through the Night”), Prince’s quietly bitter “When You Were Mine.” Lauper’s delivery clearly inflects the latter song’s meaning, her howl supplanting Prince’s coy plausible deniability with an unmistakable sense of raw, real rejection. It was Lauper’s job to make these disparate selections cohere, not just with her singing, but also with her slightly left-of-center musical taste. For She’s So Unusual’s arrangements, she wanted a fusion of synth-pop with reggae and ska; something that sounded like both the Clash and Grace Jones. Just like in her years on the cover circuit, she was forging a voice for herself from the material in front of her.

Not every song Chertoff pitched landed with Lauper. She initially balked at what would become the album’s first single, a throwback rockabilly song from an unknown writer named Robert Hazard called “Girls Just Want to Have Fun.” In the original version, Hazard’s male protagonist blames his listless life on the behavior of the women he knows, who understandably just want to relax after work. To Lauper, the lyrics sounded vapid and misogynistic. With some rewriting (and backing vocals) from Brill Building legend Ellie Greenwich, she found a second life for the song as a generational rallying cry. For Lauper, “Girls Just Want to Have Fun” spoke to the repressed lives of her mother and grandmother, who were barred from any semblance of a social life outside the home. Changing only a few words—instead of Hazard lamenting that “All my girls have got to walk in the sun,” Lauper exclaims, “I want to be the one to walk in the sun”—they transformed the song’s perspective: from that of a moping burnout trying to placate his disappointed parents to a frustrated woman trapped by staid societal expectations of settling down.

Hazard sounded on the verge of tears in his version, his warbling Elvis Costello impression jostled about by the song’s breakneck guitar. Lauper, over synthesizers, gated snares, and a tempo that significantly slows Hazard’s original, sounds triumphant. The more relaxed pace fit Lauper’s delivery, the sound of a woman confidently making her demand for leisure, rather than a boy freaking out about his dating prospects. Her alternating staccato and extended vocals in the song’s opening verse lend a human element with their variations and slight imperfections, balancing out the slick and garish Memorymoog synth. Her vocal hiccups, inspired by Roy Orbison’s, act as the verbal counterpart to the marimba-like synth solo at its center. “Girls” reflected her vision of an electronic ska record, any incongruities between styles patched over by the theatrical flair of her singing.

There is a sad irony in the creation of She’s So Unusual: an album about an ostensibly liberated woman, whose creator was surrounded by men who wanted to control her artistic vision. Even “She Bop,” a thinly veiled ode to self-pleasure that was one of the album’s few original singles, came from a directive from the songwriter Steve Lunt, who insisted that “no other girl has done this before.” So Lauper, who never envisioned herself as a glorified cover singer, was ecstatic when Chertoff asked her and the Hooters team for one more original song to complete the album. She went back to the studio with Hyman, stood next to his piano, and began to sing over a four-chord progression he had put together.

Hyman and Lauper were both dealing with issues in their romantic relationships, the kind of messiness that comes with detangling lives spent together. He referenced a “suitcase of memories” that he carried around with him after his breakup. She thought of the clock Wolff brought back from his mother after he broke hers, its wind-up tick so unbearably loud that she moved it to the bathroom, only to hear it through the walls. The unwinding second hand of the first verse was real, too: Chertoff’s watch had become demagnetized, and he excitedly showed its machinery moving backwards to Lauper and Hyman in the studio. “Time After Time” used these metaphors to capture the sadness of a breakup: the slow-building resentment in a relationship like a metronome that won’t shut off, or the logic-defying bond between two ex-lovers that can erase years in minutes.

Hyman and Lauper originally wrote “Time After Time” with the ska-inspired uptempo groove that drives other She’s So Unusual tracks like “Witness.” But as they continued working, it became clear to them that this song would require a gentler treatment, one inflected with the conflicted feelings of nostalgia, betrayal, hopefulness, and acceptance. That ambiguity is the song’s strength, never fully giving into the sentimental desire for reconciliation or the petty urge to burn bridges. When Miles Davis began to work the song into his set a year after its release, he pulled on those threads, heightening both its triumph and its sadness with his improvisations, just as Lauper made songs her own as a cover singer a decade prior.

The album’s sound was only part of its success. Released the same year as MTV came on the air, She’s So Unusual had a symbiotic relationship with the nascent television channel; Lauper hosted its first-ever New Year’s Eve broadcast to close out 1983. At the time of its release, music videos were a relatively new concept: “Brief, Bizarre Films Rekindle Record Industry’s Hopes,” the Wall Street Journal reported that year. The video for “Girls Just Want to Have Fun” looked like Lauper’s life: volumes of hair and fabric heretofore thought unimaginable (styled by Screaming Mimi’s, of course), New York as its centerpiece, a cameo from her own mother. Though the concept might seem trite today—a singer dancing through the streets with a gaggle of backup dancers—its reimagining of a song away from a simple stage performance was groundbreaking at the time.

The video also featured professional wrestler Lou Albano as Lauper’s disapproving father, the start of a strange PR campaign cooked up by Wolff in which the singer and the wrestler took part in an ongoing staged feud. Lauper credits the wrestling connection with jumpstarting the album’s sales, but from today’s perspective it looks like just another male directive boxing her in: it’s painful to watch her repeatedly credit Albano and his “P.E.G. principles” (politeness, etiquette, and grooming) in interviews and performances around the album.

When Lauper performed on The Tonight Show, after bantering with Carson about her alternate career options, she broke the fourth wall and addressed the crowd directly: “You guys don’t know, but he’s got this whole thing back here,” she said in her over-the-top New York accent. She gestured at Carson’s elaborate set design, apparently fascinated with the artifice of it all, and wanting to bring the audience with her on her journey. She wasn’t some slick industry creation, just a strange kid from Queens, more like the people in the crowd than she was like Carson. She made pop music for outcasts and oddballs: the kind of artist who entered the homes of Americans watching MTV by dancing through the streets of New York and inviting every passerby to join in. Years later, she would win a Tony for her songwriting for Kinky Boots, the unlikely hit musical she wrote with “Time After Time” collaborator Hyman about drag queens and shoe cobblers, applying her career-long belief in the universal appeal of the particular. Lauper succeeded by harnessing the power of the underdog, a quiet majority that she knew was desperate for a voice. As she told Creem in 1984, “There’s a lot of us, aren’t there?”