This account is excerpted from Walk This Way: Run-DMC, Aerosmith, and the Song that Changed American Music Forever,” which will be released Feb. 5.

The album was finished, everyone agreed, and yet Rick Rubin couldn’t shake the feeling something was missing. It was more than a song. Rubin found himself getting almost philosophical as he considered the state of hip-hop in 1986. It wasn’t merely that so many misunderstood it. What frustrated Rubin most is how many smart people didn’t even view it as music. The missing piece would be the bridge in the erector set of his musical imagination.

“I was looking for a way to bridge that gap in the story of finding a piece of music that was familiar and already hip-hop friendly so that on the hip-hop side it would make sense and on the non-hip-hop side you’d see it wasn’t so far away,” he said.

The idea of melding rock and rap wasn’t foreign territory for Rubin. In 1984, he had sampled the central riff of AC/DC’s “Back in Black” for “Rock Hard,” the debut Def Jam single from the Beastie Boys. One night early in 1986, Rubin called up Tim Sommer, the former NYU radio jock, and told him, “I need a white rock song that can be turned into a rap song.”

“And we spent about ten or fifteen minutes on the phone, shooting around ideas,” said Sommer. “We kept on coming back to ‘Back in Black’ by AC/DC, but the Beastie Boys had recorded a version. Then Rick goes, ‘How about “Walk This Way”?’”

Strangely enough, that’s not the only account of how Aerosmith and Run-DMC came together. In 2010, Sue Cummings, a onetime Spin editor — and Sommer’s former girlfriend — wrote a short piece for the magazine with the headline: “Spin introduces Run-DMC to Aerosmith.”

In that piece, Cummings claims she was the one who thought of the idea.

“I called Rick Rubin,” Cummings wrote. “‘Can you give me a tape of Run-DMC? I’m going to Boston to meet Aerosmith.’ ‘That would be incredible!’ he replied.

“When I met up with the band, I proposed the collaboration. Aerosmith had never heard of Run-DMC when I handed them that cassette, but they were willing to take the risk of working with a new artist.”

Years later, Cummings conceded that everyone could be right. She and Sommer and Rubin were close and spent a lot of time together, whether going to see Anthrax or Slayer at L’Amour or just chatting.

“Back then, we would talk on the phone every day,” she said. “I talked to Tim. I talked to Rick. I don’t dispute that Tim suggested it to him, but I suggested it to him, too. It might have been that Tim and I thought of it.”

Whoever actually suggested the idea, it clearly made sense in Rubin’s sonic imagination. He wasn’t interested in the kind of flashy hair-metal licks that had become popular with Def Leppard, Bon Jovi and Quiet Riot. He had, in fact, grumbled to Sommer about the guitar sound on “Rock Box” and “King of Rock.” His vision wasn’t to simply mix rap and rock. Technically, Kurtis Blow did that back in 1980 with his weirdly off-key croon of Bachman-Turner Overdrive’s “Takin’ Care of Business.”

“It’s one thing to say, ‘We’re going to mix rap and rock,’” said Sommer. “That wasn’t his vision. His vision was mixing rap and this heavy riffing that one gets from Sabbath or Blue Öyster Cult or Aerosmith. That’s very different. What Rick said is, ‘I’m going to take this definitively unfunky white music and I’m going to take that and mix that with rap.’ That was the experiment of the Beasties and to a lesser extent the experiment of Run-DMC. It’s an oversimplification to say mixing rap and rock. Anybody can do that. What Rick wanted was a specific kind of rock. That meathead kind of rock.”

Aerosmith had been one of Rubin’s favorites in high school. He followed them closely enough to go see the Joe Perry Project play live in 1979. He even made an aborted attempt to help the reunited band record a few new songs. (A bootleg of those sloppy demos, Love Me Like a Bird Dog, suggests they were done in early 1987, though everybody involved believes it was before “Walk This Way.” No records of the session seem to exist.)

To get “Walk” rolling, Rubin decided to call Aerosmith’s representative at Geffen to pitch his idea.

By 1986, John Kalodner was a kind of insider star, known as much for his golden touch with bands as for his look — the white suits, thick beard and sunglasses made famous by John Lennon. Kalodner’s disinterest in drugs also set him apart. He didn’t need any chemicals to inspire self-confidence. On records he influenced, Kalodner claimed a special title starting with Foreigner’s 1978 self-titled debut.

John Kalodner: John Kalodner.

By the time Rubin called, David Geffen, famous for launching the Eagles, Linda Ronstadt, Jackson Browne and Joni Mitchell on Asylum Records in the 1970s, had launched a new label, Geffen Records. In 1980, he hired Kalodner as the first artists and repertoire executive.

There were successes, particularly Asia, but his signing of the reformed Aerosmith was not turning out to be one of them.

As the summer of 1986 rolled around, even the slickest publicist couldn’t have spun Done with Mirrors into anything less than a bomb. The album opened in June at 190 on the Billboard 200. What’s worse, Classics Live, a sluggish smorgasbord released by Columbia as part of Aerosmith’s exit deal, hovered in the Top 100. Kalodner, the bearded A&R guru, suddenly found himself worried about his job.

Then Rubin called.

It sounded intriguing, and sometime during the winter of 1986, Kalodner decided to stop by Def Jam’s office to hear out the young producer. He admits he wasn’t expecting to find that Rubin’s headquarters was a dorm room.

“It looked like a bum slept there, and here’s this guy who looks like some young schlub,” said Kalodner. “Except he spoke so clearly and he had such a clear vision of what he wanted to do.”

Kalodner knew nothing about rap. He wasn’t about to pretend he did. But as famous as he would become for pushing what he described as “corporate rock” — groups like Aerosmith, Nelson and Whitesnake — he wasn’t above appreciating an innovative musical idea that cut against the grain. He did, after all, sign XTC and Siouxsie and the Banshees. He also had some questions for Rubin.

“I think I said to him, ‘Do the schwartzes even know who Aerosmith is?’” remembered Kalodner, invoking a Yiddish word that’s either derogatory (at best) or racist (at worst). “I don’t know if I’m proud of it, but it’s what I said to Rick.”

Then he told him he thought it was a great idea. He did wonder whether it could work.

“I thought in my head, ‘Good luck to you working with two people who are higher than a kite,’” said Kalodner.

The next call went to Collins. He needed Aerosmith’s manager on his side. He also needed Collins to talk to the band.

The manager admits he was as clueless as Kalodner. It could be a great idea or it could be a disaster. He deferred to the record exec and presented the idea. Reaction, as he remembered it, was mixed. Tyler immediately sounded game. Today, he talks of the early ’80s, living at the Gorham Hotel with his twenty-dollar-a-day allowance.

“I loved rap,” he said. “I used to go looking for drugs on Ninth Avenue and I would go over to midtown or downtown and there would be guys on the corner selling cassettes of their music. I’d give them a buck, two bucks, and that was the beginning of me noticing what was going on in New York at the time.”

Whitford, Hamilton and Kramer were down on the idea. At least that’s what Collins and Kalodner remembered. Over time, the record executive has taken to referring to them dismissively as the LI3, or the less important three.

“They were always against everything,” Kalodner said. “They were against doing ‘I Don’t Want to Miss a Thing.’”

But Hamilton, looking back, didn’t remember having any reservations about Run-DMC.

“I definitely had a feeling of being left out,” he said.

“Like, can’t we all go?” Whitford added.

But Rubin only needed two. He had Tyler. He also needed Perry. The guitarist wasn’t necessarily against the pitch. He just wasn’t sure. Then, a thirteen-year-old kid with a growing collection of cassettes entered the conversation.

Perry’s divorce from his wife, Elissa, had gone through and, during the making of a video for the Project’s last-ditch third record, he had met Billie Paulette Montgomery, a model who didn’t know a thing about Aerosmith. They began to date, and got married in 1985.

It was her son, Aaron, who found himself providing guidance to Perry one day.

“Joe was curious,” Billie remembered. “He went into Aaron’s room and asked him about it. Aaron was trying to show him how you break-dance. Aaron got into it as much as a Jewish white kid could. He rolled around on the floor and kicked his feet up.”

“I was so into rap,” said Aaron. “I’ve always had an eclectic taste in music, because growing up, my mom was a young mom and she knew a lot of artists, musicians around the area. She was more into the punk rock scene. I got turned on to a lot of college radio. That’s where I would hear Doug E. Fresh, the Sugarhill Gang, and that first Run-DMC album.”

Perry also had reservations about the band’s fans. Maybe they wouldn’t get it. But there was a certain logic to it. He grew up with the blues.

“I heard a direct connection between what they were doing and the blues,” he said. “All you had to do was have a boom box and some talent. And a way to express yourself, which is what they were doing, on the street corner. Which is what blues was. They’d be on the street in the day or in the juke joint at night. They were singing about living wherever they were living, and to me, it was like a direct connection.”

The one thing missing, Perry would say later about his stepson’s rap tapes, was easy for him to get his hands on. The only thing missing: His guitar.