One night this summer, Alicia Keys fell asleep listening to show tunes.

She was on vacation following a five-week concert tour, but her mind was still at work. For 12 years, she has been developing “Hell’s Kitchen,” a musical based on her adolescence in a then-gritty New York neighborhood, and at the top of her to-do list was writing a new song for the actor playing the main character’s mother.

So she took a nap with her headphones on, listening to a playlist of theatrical mom songs (think “Rose’s Turn” from “Gypsy” and “Little Girls” from “Annie”). When she woke up, she could feel the rhythm. She could hear the chords. She could see the title.

She ducked into a closet and began to sing into her phone. She hopped online, doing a little research to strengthen her lyrics. And then, when she returned to New York, she began to write, in the wee hours after the meetings and the calls and the rehearsals, noodling at an upright piano in her Chelsea recording studio.

“This is occupying a lot of space in my mind,” Keys said about the musical.

“Hell’s Kitchen” is to begin an off-Broadway run Oct. 24 at Public Theater. Even though Keys is not in it, demand is high: Each time more tickets go on sale, they are snatched up.

“I am thinking a lot about ‘Hell’s Kitchen,’ and obviously, the goal for it to be tremendously beloved and really something that comes into the world in a way that is just like a storm, an incredible storm,” Keys said. “And the goal, obviously, is to transfer to Broadway. So that’s heavy on my mind.”

With 15 Grammys, five No. 1 albums and about 5 billion song streams, Keys is an unusual figure in the music world — a classically trained pianist turned R&B singer-songwriter who signed a recording contract as a teenager and remains, at age 42, determined, driven and resolutely in control of her creative and commercial life.

Her musical, “Hell’s Kitchen,” is unusual too, in ways that seem promising. Unlike many biographical jukebox shows chronicling childhood to celebrity, this one is both focused and fictionalized, depicting a few months in the life of a 17-year-old named Ali.

“This is not Tina Turner, this is not the Temptations, this is not MJ, this is not Carole King — although all of those are phenomenal,” Keys said, referring to shows about pop stars. “It’s really so much more about relationships and identity and trying to find who you are, which I think is a continuous theme in all of our lives: Who are we? Who do we want to be? Who are we becoming?”

In “Hell’s Kitchen,” Ali, like Keys, is the daughter of a white mother and a Black father and is growing up in Manhattan Plaza, a subsidized housing development just outside Times Square where 70% of the units are for performing artists.

The supporting characters — a hyper-protective single mother, a life-changing piano teacher, an older boyfriend and an unreliable father — are based on figures in Keys’ own upbringing.

“We’ve highly fictionalized the specifics,” said Kristoffer Diaz, a playwright and librettist who has been working with Keys on the show for more than a decade.

Along the way, Keys and Diaz have been joined by Broadway veteran Michael Greif, who directed “Dear Evan Hansen,” and by choreographer Camille A. Brown, an in-demand dance-maker.

“Hell’s Kitchen” is, in the eyes of its creative team, a mother-daughter love story. Keys’ identity, as a person and as a songwriter, was shaped by the city in the 1990s, and that informs the show’s sounds (like bucket drumming) and movement (with echoes of social dances like the Running Man).

The score, played by a band that will include a pianist visible to the audience even when actors pretend to be tickling the ivories, features Keys’ best known hits: “Fallin’,” “No One,” “Girl on Fire,” “If I Ain’t Got You,” and, of course, “Empire State of Mind,” her 2009 collaboration with Jay-Z that has become an inescapable New York City anthem. Keys said she has written four new songs for the show but that even existing songs have a new sound because they have been rearranged.

“The songs that you think you know,” she said, “you never heard like this.”

When Keys was a child, her mother, Terria Joseph, was a struggling actor — that’s how she qualified to live at Manhattan Plaza — who took survival jobs, particularly as a paralegal, while trying to find work as a performer. (Keys’ father, a flight attendant, did not live with them and was mostly not around; though Keys was close to her paternal grandparents, she was often estranged from her father. Now, she says, they are good.)

Keys would tag along to auditions and rehearsals when her mother couldn’t afford a babysitter; when there was enough money, they would stand in line at the TKTS booth and buy discount theater tickets.

Her mother recalls an early trip to “Cats,” and Keys remembers “Miss Saigon,” but the show that stands out is “Rent,” in part because it’s about AIDS, which hit Manhattan Plaza, with its high population of gay artists, hard. “Rent,” like “Hell’s Kitchen,” was directed by Greif.

She was valedictorian of her graduating class at the city’s Professional Performing Arts School and attended Columbia University for a month before dropping out to pursue music.

In 2001, with the release of “Fallin’ ” and boosted by an appearance on “The Oprah Winfrey Show,” her career took off.

Keys has continued to see theater when she can, and in 2011, she co-produced a Broadway play, “Stick Fly,” about an affluent Black family wrestling with race and class.

“Stick Fly,” Keys said, “ignited this desire in me, across all mediums in regards to storytelling, to be able to start to hear, feel and see stories that I know exist, but in so many ways the world doesn’t see.” And when she started cooking up “Hell’s Kitchen,” she had audacious goals.

“Because I have all the experience with seeing theater since a kid, I just was really ready to reinvent theater, too,” she said. “I just felt like there was so much to bring, so many worlds to collide and cross. I almost felt obligated to create that piece that would be something that people who absolutely can’t stand musical theater would love.”

Rather than finding Broadway producers to finance and shepherd “Hell’s Kitchen,” thus far she is doing so herself, retaining the rights to its commercial future.

“I want to own my story,” she said. “And I deserve to.”

She consults, and is heard, on every strategic and creative choice: writing, casting, staging, marketing.

“For the first time in my life,” she said. “I’m doing something exactly right.”

She explained that with previous projects, “I didn’t start out right but kind of ended up right.”

But this time, she said, “I didn’t want to go out and get too diluted and get too many partners. We have all the right partners, all the right minds. It’s the right mixture of experience and also newness that I think is important to continue to create a new world.”