Steve Martin and Edie Brickell’s “Bright Star” is a Broadway oddity — and not just because it has a bluegrass score.

No, the weird thing about “Bright Star” is the way it juxtaposes an over-the-top plot with a low-key production and mild-tempered music. The North Carolina–set story fires up Greek-style tragedy while the banjo- and fiddle-heavy tunes gently go plickety-plonk.

Martin and Brickell — who wrote the score and book but aren’t in the show — intertwine two timelines, clearly destined to meet.

One, in 1945, focuses on Billy (A.J. Shively), an aspiring young writer eager to be published in a literary magazine edited by the tart-tongued Alice Murphy (Carmen Cusack, very good but a few watts short of the necessary star power).

The other follows Alice as a young country girl two decades earlier, when she fell in love with the local mucky-muck’s son, Jimmy Ray (Paul Alexander Nolan), and got pregnant.

The show ambles along, alternating between lively hootenannies and lovely ditties — the title song is especially wonderful, performed by Shively and the ensemble with hopeful joy.

But then there’s the fate of Alice’s baby: shocking — and followed by yet another mellow song.

The show’s droll, earnest tone does have its appeal. Fans of Martin’s humor will find evidence of it here, as when Billy tells Alice, “You must be Miss Murphy.”

“I don’t have to be,” she replies, “but I am.”

As a gentle fable, “Bright Star” has a quirky charm, but its stubborn refusal to face up to its dark side diminishes it.

At the Cort Theatre, 138 W. 48th St.; 135 minutes, one intermission.

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