On the surface, the hit title track from The Glamorous Life represented the latest changing the guard, as Prince shifted from Vanity 6 to Apollonia 6 to a newfound focus on his eruptive new percussionist girlfriend Sheila E.

But "The Glamorous Life" was more than another star vehicle for Prince's latest flame. Instead, the song – released on May 2, 1984, just a few weeks after Sheila E.'s official introduction on his sexy b-side "Erotic City" – found Prince at the beginning of a deeply rewarding musical collaboration.

Sheila E., whose real name is Sheila Escovedo, arrived as an accomplished performer, having already collaborated with Lionel Richie and Diana Ross, been a member of jazz star George Duke's band and toured with Marvin Gaye. That was in stark contrast with unpolished ingenues like Denise "Vanity" Matthews and Apollonia Kotero – both of whom were better known for modeling and acting before coming into Prince's orbit.

Each would lose Prince's interest in the whirlwind that surrounded 1984's Purple Rain. Matthews, who had a hit with the Prince-written "Nasty Girl" in 1982 as part of Vanity 6, left before the film was made – opening the door for Kotero to take the female lead. Vanity 6 was renamed Apollonia 6 for the script. Once Prince began working with Sheila E., however, he quickly shifted allegiances once more.

"The Glamorous Life," a song about a woman who still longs for romance despite being surrounded by the trappings of success, had originally been slotted for an Apollonia 6 album – and, Kotero says, was inspired in part by her relationship with Prince. Instead, it became Sheila E.'s breakthrough single. "He used to make all these stupid jokes, 'You're the kind of chick who would wear a mink coat in the summertime,'" Apollonia later told Prince's biographer Per Nilsen. "To this day, I don't have my own mink coat! When Sheila came into the scene, Prince took away the song from us and gave it to her."

Tracking for The Glamorous Life began in December 1983 and was over by mid-February 1984. Toward the end, when the sessions were essentially over, the still-unfinished "Glamorous Life" belatedly returned to Prince's creative radar. They completed it together, Sheila E. said.

"'The Glamorous Life' was the last song we worked on," she wrote in her 2014 memoir The Beat of My Own Drum. "In fact, we weren't even going to include it on the album. It started out as an instrumental, and I couldn't think of any lyrics for it at first. Once I got started, though, the words came quickly. … It was very percussive and it had a catchy melody, incorporating all the black keys on the piano so that it almost sounded like a nursery rhyme."

Sheila E. laid down her vocals in a matter of days that April at Sunset Sound in Hollywood. "The Glamorous Life was done in a week," she told Billboard in 2016. "We'd stay up until five and six in the morning recording, go home for a couple of hours, come back and start playing again. Next thing you know, seven days later, the record’s done. That's how to do a record."

Listen to the Long Version of Sheila E.'s 'Glamorous Life'

Turns out, Prince had long wanted to work with Sheila E., whose father Pete Escovedo was a member of Carlos Santana's band. They met when she was just a kid, and he was already impressed.

"He came to the Bay Area to do his first record [1978's For You], because he was influenced by Bay Area music and wanted to record in that studio where Sly [Stone] and Carlos had recorded," Sheila E. told Time in 2014. "So, my dad was in Santana at the time, and they were at the studio, and they were talking about this young kid who was next door recording and producing and playing all the instruments by himself. They were like, 'This kid is amazing.' And I said, ‘Oh, I want to meet him.’ The following year Prince's record came out, so he came back to the Bay Area and San Francisco to perform. And I went backstage to meet him and as I went to introduce myself, I put my hand out, and he saw me in the mirror and he turned around, and he said, 'I already know who you are."

Having consistently encouraged her to make her own record, Prince gave Sheila E.'s debut his full attention, and she likely added vocals to "Erotic City" during those sessions. Prince played all of the instruments on the title song, save for percussion (Sheila E.), sax (Larry Williams) and cello (David Coleman). In fact, though The Glamorous Life was said to have been "directed by Sheila E. and the Starr Company," every track was written, arranged and produced by Prince. He then personally took the finished recordings to his management company, who connected Sheila E. with Warner Bros.

Still, she had more direct input than any other previous protege, and that created a new paradigm after "The Glamorous Life" went No. 1 on the Billboard dance charts, No. 7 on the R&B charts, and No. 28 on the pop charts while earning two Grammy award nominations. By the time Prince returned with 1985's Around the World in a Day, Sheila E. could be found playing drums in place of Bobby Z on "Pop Life." She also appeared on "Life Can Be So Nice" from 1986's Parade, then served as his musical director on tour. Later, she appeared on songs from 1988's Lovesexy and the unreleased Dream Factory, as well.

"I think we influenced each other," Sheila E. told Time. "I influenced him the same way he influenced me. ... That’s the good thing about Prince: you can see how he was influenced by the people around him. I can hear and see it, because I got to live the influence that I had on him as well as the influence he had on me — just being around each other, being able to record all the time and play, and do things that he had never done using live percussion instruments and recording all the time."

She ended up earning the same kind of rare respect Prince afforded established acts like Mavis Staples and George Clinton, who later recorded for his Paisley Park imprint – and that continued even after their relationship ended. She says he proposed to her during a 1987 performance of "Purple Rain," but their romance cooled during the subsequent tour in support of Lovesexy. Sheila E. continued to join Prince on stage, however, until a few years before his 2016 death.

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