Hunter Foster, left, and Kelli O’Hara during a performance of “The Bridges of Madison County” at the Gerald Schoenfeld Theatre in New York. (AP Photo/ Jeffrey Richards Associates, Joan Marcus)

NEW YORK — Were it not for the emotional crescendos Kelli O’Hara achieves with Jason Robert Brown’s swooningly melodic score, the new Broadway version of “The Bridges of Madison County” might feel like a very small show.

As it is, the tale of a desolate Neapolitan immigrant — distracted from her cold Iowa marriage by a hunky visiting magazine photographer — comes across as rather shaky scaffolding, in a sometimes affecting adaptation of Robert James Waller’s best-selling novel that opened Thursday night at the Gerald Schoenfeld Theatre.

But the bony narrative does acquire rewarding flesh whenever O’Hara — veteran of “The Pajama Game,” “South Pacific” and “The Light in the Piazza” — is given a chance to express, in a poignant lyric or hushed speech, the sensual awakening her Francesca Johnson experiences in the presence of the  picture-taker, played by the smoldering Steven Pasquale.

In other words, the love story at the center of this “Bridges,” directed with sensitive command by Bartlett Sher, gives off some bracing sparks, even if some of the plot embellishments dreamed up to broaden the musical’s scope do not feel like anything more than time-filling devices. Any instance in which Marsha Norman’s book segues to the stoic point of view of Francesca’s farmer husband, Bud (Hunter Foster), or keys on their whiny son, Michael (Derek Klena), or whiny daughter, Carolyn (Caitlin Kinnunen), the evening’s electricity fizzles, as if it were in a neighborhood undergoing sporadic blackouts.

It’s a tribute to O’Hara, and to Brown, how well and often they manage to keep the lights on. Affecting a convincingly delicate Italian accent, O’Hara delivers a radiant, self-assured performance, faintly perfumed with the exotic, that distills Francesca’s loneliness as a condition fully worthy of our compassion. No self-pity is engaged in here. The sense of a passionate nature, bottled up in a homey but stultifying farmhouse, is conveyed in O’Hara’s wistful countenance and, just as richly, the songs that Brown (“Parade,” “The Last Five Years”) composes for Francesca. The big-statement numbers like “To Build a Home” vibrantly declare that this a woman whose suffering has meaning and whose pain must somehow be stanched.

The scruffy Pasquale, possessed of a quaking baritone, exudes a romance-novel allure that makes his Robert believable as the answer to a prayer Francesca did not know she was uttering. Their story never quite breaks free of the romance genre, but on the other hand, it’s a far sexier telling of “Bridges” than was illuminated in the 1995 movie with Clint Eastwood and Meryl Streep — a movie that I confess never got to me.

“Bridges” is a musical drama that shares a solemn storytelling tone with such other “serious” modern musicals as Adam Guettel’s “The Light in the Piazza” and Michael John LaChiusa’s “Giant.” It’s also Brown’s most emotionally gripping score, with fleeting tastes of country and folk rock. As a result of his supple compositions and O’Hara’s renditions of them, “Bridges”  leaves you with the feeling that you have something valuable to contemplate.

“The Bridges of Madison County,” book by Marsha Norman, music and lyrics by Jason Robert Brown. Directed by Bartlett Sher. Movement, Danny Mefford; sets, Michael Yeargen; music director, Tom Murray; costumes, Catherine Zuber; lighting, Donald Holder; sound, Jon Weston. With Cass Morgan, Michael X. Martin, Katie Klaus. About 2 hours 40 minutes. Tickets, $59-$225. At Gerald Schoenfeld Theatre, 236 W. 45th St., New York. Visit or call 212-239-6200.