Making a name for oneself at the Algonquin Hotel’s legendary Oak Room — home, over the years, to Harry Connick Jr., Diana Krall, and Andrea Marcovicci, among countless other luminaries — can be tough going. But Tajlei Levis and John Mercurio are about to try. On January 28, Ms. Levis and Mr. Mercurio will open “Glimpses of the Moon,” the first musical conceived expressly for the hotel’s intimate, wood-paneled supper club.

In 2006, Ms. Levis and Mr. Mercurio invited the entertainment director at the storied hotel, Barbara McGurn, to attend a performance of a musical, set in 1940s Manhattan, that they had written for the Fringe Festival. Ms. McGurn was intrigued by the idea of staging a New York-specific period piece in the Oak Room, but their Fringe Festival production featured 13 jitterbugging performers, and the intimate room, which seats just 80 guests at candlelit tables on either side of a grand piano, couldn’t accommodate the unwieldy cast.

So, Ms. Levis and Mr. Mercurio suggested they write a musical specifically for the hotel’s famous cabaret venue, and Ms. McGurn agreed to the concept.

At that point, Ms. Levis, who contributed the book and lyrics to this partnership, and Mr. Mercurio, who wrote the music, set about gathering ideas for the new piece. To take advantage of the Algonquin’s glamorous history, they aimed to set the musical in the hotel’s 1920s heyday, the decade of the famous “Round Table,” a daily gathering of young literary smart alecks, including Alexander Woollcott, Harold Ross, Robert Benchley, and, most famously, Dorothy Parker. The group set the standard for literary style and, among other things, gave rise to the New Yorker magazine.

Ms. Levis cuddled up last winter with Henry James, F. Scott Fitzgerald, and other writers of the Jazz Age, looking for source material upon which to base the project. Finally, she hit upon an Edith Wharton novel she had read many years earlier, “The Glimpses of the Moon.” One of Wharton’s lesser-known works today, it was a huge commercial success in 1922. But it was never a critical success, perhaps because Wharton wrote “Glimpses” when she was financially strapped, and sales were the priority. A dark undercurrent bubbles below the surface of Wharton’s breeziest prose, though, on the whole, as Ms. Levis said, “This is jazzy, funny Edith Wharton.”

“It’s got a great kind of musical comedy setup,” the director, Marc Bruni, said, citing “the idea of these two people who decide to get married and live off the gifts that their rich friends give them.” The protagonists, Susy Branch and Nick Lansing, make a business agreement that supposedly lasts one year, to be terminated earlier if either person finds a better (i.e., richer) match. It’s a light-hearted take on the escape that proves to be no escape, one of Wharton’s habitual themes. “It’s not chock-a-block with plot,” as Mr. Mercurio puts it, so there’s room to musicalize.

Ms. Levis, Mr. Mercurio, and Mr. Bruni all agreed the story would work as the basis for the Oak Room project. And when the team presented two songs on speculation to Ms. McGurn, she gave them the go-ahead.

As a nod to the location, Ms. Levis explained, Nick and Susy visit the Oak Room in one scene and listen to a cabaret singer, who will be played, each week, by a different guest star. (Susan Lucci and Alison Fraser are currently on tap.) Mr. Mercurio plans to incorporate a multiple reed player (saxophone, clarinet, flute) in addition to the piano, but any more musicians would take valuable playing space away from the actors who dance, as well as sing, in the production.

Their adaptation takes place in New York and the vicinity, with much of the action at “jazz-infused, martini-soaked parties,” in Mr. Mercurio’s words. A description that will, no doubt, apply to the “Glimpses” atmosphere itself.