For Carly Simon, one word was enough to capture her relationship with Mick Jagger.

“Electricity,” she wrote in her 2015 memoir, “Boys in the Trees.” “That’s what it was.”

And for years, it seemed just one electric spark between the musicians had found its way onto a recording, and onto airwaves across the world.

The Rolling Stones singer did backing vocals for “You’re So Vain,” Simon’s indignant smash hit released in 1972. The subject of the track, the self-absorbed “you,” became an enduring puzzle, as Simon teased possibilities in “dribs and drabs,” as she put it, giving out individual letters of the person’s name, like a trail of bread crumbs for Hansel and Gretel to follow home. Was it the backup singer himself? Her fans said yes, but she said no. Was it David Bowie? Was it Warren Beatty? Was it even anyone famous? She still hasn’t pulled back the brush on all the “Boys in the Trees.”

Alongside that mystery came another. In her memoir, Simon recalled an early-morning studio session in 1972, when she went to the restroom to fix her hair — “mess it up to be like Mick’s” — and returned to find the rock singer sitting at the piano. He began testing out a song, which included the lyrics, “Funny, funny, funny, funny, how love can make you cry.”

He looked at Simon and then back at the piano keys. She became flushed.

“I harmonized with him as it became a chorus, an improvisation that was later searched for and never found among the multitracks at AIR Studios,” Simon wrote.

Never found — until, perhaps, now.

A new duet, never before played in public, was recently discovered on a tape owned by Matt Lee, a Rolling Stones collector in London, the Associated Press reported. The song goes by the title “Fragile,” the AP said, citing Rolling Stones fan websites.

The lyrics recalled by Simon match Lee’s recording, though the two seem to croon the word “change,” not “cry.”

As the closing notes ring out, a female voice utters a gasp: “Good song,” Simon affirmed, according to the AP. Lee said he sent a copy of the song to Rolling Stone magazine, which told him it would transmit it to Simon.

In an interview with the magazine in 2016, Simon stoked speculation about the long-lost duet.

She sang the line she had put in her book, asking, “Does that sound like any Stones song to you?”

The interviewer suggested “Fool to Cry,” a brooding 1976 ballad that finds Jagger seeking solace from his daughter and then his lover. Both rebuff him, deeming him “a fool to cry.”

“Maybe, maybe,” Simon said. “We had this little back and forth at the piano for about an hour.”

But then Paul and Linda McCartney arrived, she said, and the spontaneous collaboration was over. She said she didn’t know what happened to the recording — or whether any trace of it remained. Richard Perry, a producer, had been looking for a tape for years, she said, speculating that it had to be lurking somewhere at Warner Bros.

Although Lee declined to tell the AP where the tape came from, he did offer a review of the duet on Twitter, writing, “It’s super great!”

According to the AP, a small part of the song, including the “funny, funny, funny” lyrics that Simon remembered, can briefly be heard in a documentary about the 1972 Rolling Stones tour. The documentary has never been publicly released.

Lee made his finding two years after “No One Loves You More Than Me,” recorded by the Stones in 1964 and apparently sold at an auction, was located. The band finished a European tour in July and has said a new album is in the works.

Publicists for the two singers didn’t immediately return requests for comment about “Fragile.”

Simon told Rolling Stone in 2016 that she had last seen the lead Stones vocalist at an after-party following an awards show, when saxophonist Bobby Keys picked her up and set her down in front of Jagger. “I was very uncomfortable,” she said. Before that, she had tried to catch his eye at a concert of his in Boston. That was 12 years ago.

In her memoir, she wrote that “for Mick Jagger, all women, including me, were his, by divine right.”

But he wanted something particular from her, she believed. Something as fragile as a Shakespearean romance.

“And if Mick could have his way, it would be Romeo and Juliet tragic,” she wrote. “We couldn’t have each other.”

More from Morning Mix: