On Dec. 4, 1956, an amazing musical harmonic convergence occurred when four of the giants of early rock ’n’ roll and rockabilly just happened to be in the same Memphis studio at the same time.

Carl Perkins, of “Blue Suede Shoes” fame, was in the Sun Records studio recording some new material. Accompanying him on piano was a young, energetic and still unknown Jerry Lee Lewis.

Johnny Cash, who’d had a recent hit on Sun with “I Walk the Line,” dropped in to hear Perkins. So did a young former Sun recording artist who was by then a star on RCA Records: Elvis Presley.

As often happens when musicians get together around instruments and equipment, they held an impromptu jam session. Sun Records owner Sam Phillips left a tape running and recorded the session. Then he called a reporter from the Memphis Press-Scimitar and had him come to the studio with a photographer.

In the next day’s paper, the headline for the story and accompanying photo of the four musicians read “Million Dollar Quartet.”

Half-a-century later, that session would morph into a Tony Award-winning Broadway musical with the same title.

As part of the Broadway Across America series, “Million Dollar Quartet” is coming to the Mahalia Jackson Theater from Tuesday through April 21 for a run of eight shows, six in the evening and two Saturday and Sunday matinees. As popular entertainment is fond of doing, considerable artistic license is taken with the facts.

During their session, the four musical icons sang mostly gospel songs and country standards, and few or none of their own records. (Lewis was still a year away from his own recording debut.)

But rather than let boring facts stand in the way, the writers and production team for the musical saw an opportunity to showcase these Rock ’n’ Roll Hall of Famers’ greatest hits, nearly 20 of them spanning the mid- to late ’50s rock ’n’ roll era.

“We took actual events that happened that night, plus 18 months of other actual events and put them into one night to give some dramatic tension,” said the show’s director, Eric Schaeffer. “But all the events were true, and they happened. In some sense we make it more theatrical but, as entertainment, it works.”

The show is billed as “an irresistible tale of broken promises, secrets, betrayal and celebrations.” The songs are an eclectic mix of the legendary singers’ rock, gospel, R&B and country hits. Some of the better-known numbers include “Blue Suede Shoes,” “Sixteen Tons,” “Great Balls of Fire,” “Matchbox,” “Folsom Prison Blues,” “I Walk the Line,” “Whole Lotta Shakin’ Goin’ On” and “Hound Dog.”

Two of the gospel songs in the show actually were sung during that impromptu session, “Down by the Riverside” and “Peace in the Valley.” Some of what Lewis said on tape about the four “playing the devil’s music” is repeated by his character in the show.

And there’s some authentic sibling joking between the bass player at the session, Perkins’ brother Jay, and Perkins.

Two songs, “Fever” and “I Hear you Knockin’ ” are sung by a woman given the pseudonym “Dyanne.” According to Schaeffer, she is a prototype for a Las Vegas showgirl named Marilyn Evans, Elvis’ girlfriend who was present at the session but didn’t sing.

In the uncropped version of the original Million Dollar Quartet photo, she is seen perched on the piano.

The cast includes James Barry (Perkins), David Elkins (Cash), Ben Goddard (Lewis) and Cody Slaughter (Elvis).

Vince Nappo plays Phillips. Also featured are Kelly Lamont as Dyanne, and musicians Billy Shaffer (Fluke, drums) and Corey Kaiser (Jay Perkins, bass). Rounding out the company are Katie Barton, Austin Cook, Scott Moreau, John Michael Presney, David Sonneborn and Billy Woodward.

“The audience is going to be rocked and up on their feet dancing,” Schaeffer promised.