A spin through “Tapestry” — the Carole King record with those chart-topping hits such as “It’s Too Late” and “So Far Away” — is no less satisfying today than it was decades ago. Happily, it’s an equally rich thrill to sit for the new musical “Beautiful,” which tracks the Brooklyn-born songwriter’s early life and career up until the making of that seminal LP.

“Beautiful” is a must-see if you’re a King fan, or you’re fascinated by the music business during a potent time when chart hits were coming out of cubicles in places like the Brill Building and 1650 Broadway, where King and husband Gerry Goffin set up shop.

With Tony-nominee Jessie Mueller (“On a Clear Day…”) as the four-time Grammy winner, “Beautiful” has just opened at the Stephen Sondheim Theatre, on the heels of its world premiere in San Francisco. It’s directed by Marc Bruni (“Old Jews …”), with a book by Douglas McGrath (the screenplay for “Bullets Over Broadway”), who had input from all the major players in the story, King included.

“Beautiful” is bookended by scenes at Carnegie Hall during a live performance in the wake of the “Tapestry” phenomenon. The device gives Mueller space to explain that life doesn’t always go the way you want: “And sometimes when it doesn’t, you find something beautiful,” she says, addressing the audience from behind a grand piano, curly hair and a blue print dress evoking so many earth mother images of the semi-reclusive legend.

Even after hawking her first hit songs as a teen, what King wanted was the suburban dream. What she got was more complicated, and “Beautiful” does a swell job breaking it down. First, it’s the story of her marriage at 17 to Goffin (a brooding Jake Epstein, who was a bipolar musician on TV’s “Degrassi: The Next Generation”). It also chronicles one of the great affectionate rivalries in the music industry, which pitted King and Goffin against Barry Mann and Cynthia Weil (Jarrod Spector and Anika Larsen), the duo on the other side of their office wall.

Under the eye of music publisher Don Kirshner (Jeb Brown, with the right balance of slickness and decency), the foursome produced the soundtrack for a generation, mass producing hits for The Chiffons (“One Fine Day”), The Shirelles (“Will You Love Me Tomorrow”) and The Drifters (“Some Kind of Wonderful”), and even Little Eva (“The Locomotion”), who was King and Goffin’s babysitter.

With an understated performance, Mueller, seen recently in the Roundabout’s “Drood,” establishes herself among the elite of Broadway leading ladies. The actress, 30, doesn’t sound much like King, but she makes each song her own while respecting the original imprint. She has lovely chemistry with Epstein, who you can’t help but feel a bit sorry for: he’s on his game, but Goffin, who is said to have suffered from manic depression, comes off mostly as a wounded misanthrope.

Spector, who notched 1,500 performances as Frankie Valli in “Jersey Boys,” plays Mann as a confident hypochondriac willing to wait for Weil while she figures out her path. Larsen is bubbly and brainy as lyricist Weil, from the moment she arrives at Kirshner’s office looking for work, flooring a gobsmacked Kirshner with her assertiveness.

Bruni, who has been associate director for Tony winners “Anything Goes” and “The Pajama Game,” constructs some delightful segues: We’re privy to the water-cooler insecurities of the songwriting duos, whose nervous words hang in the air even as singers emerge to wow us with polished versions of the songs those writers were just fretting over. Josh Davis and Kevin Duda do a bang-up tribute to The Righteous Brothers.

If there’s an oversimplification in McGrath’s story, it’s that we’re left to think the trauma in King’s life was just the tumultuous marriage. “A Natural Woman,” King’s 2012 memoir and a source for some of “Beautiful,” is a more thorough look at the soaring ups and downs in her life. A scene set at the Bitter End, where King is pushed to make an early solo performance, gives Mueller a small chance to convey some of that oft-depicted struggle with self-confidence.

Executive producer Sherry Kondor, one of two daughters born to King and Goffin, has said she doesn’t expect her mom to sit through “Beautiful.” King walked out of an early reading, feeling, apparently, that living through her turbulent first marriage once was quite enough. Should King slip into a back row of the Sondheim one evening, she’s apt to be pleased with Mueller’s humble portrayal, which reminds us “Tapestry” came from someplace very much between bitter and sweet.

“Beautiful,” with an open-ended run at the Stephen Sondheim Theatre, 124 W. 43rd St. Tickets: $75-$152. Telecharge.com or 212-239-6200.

Follow Robert Kahn on Twitter@RobertKahn