The most likely byproducts of combining classical and pop music are prissiness and tedium. But during their hour-long Wednesday set at the National Museum of Women in the Arts, Juilliard-trained pianist ­Simone Dinnerstein and indie folkie Tift Merritt never went all Emerson, Lake and Palmer on the crowd.

The odd couple, who will soon be recording their first album together, professed envy for each other’s upbringing: Dinnerstein comes from Brooklyn; Merritt grew up in Raleigh, N.C., although on this night, she claimed Appalachia for the purpose of widening the cultural divide between the duet partners. Merritt confessed she can barely read music, while Dinnerstein said she’d never improvised at the keyboard before hooking up with the Dixiefied singer/songwriter.

Yet, as things turned out, the most precious moments in the hour-long set were also among the best. Merritt blew on a pair of harmonicas to add a taste of hickory to Dinnerstein’s take on Schubert’s “Nacht und Traume.” During a medley of reworked old-timey folk songs, Dinnerstein got off her stool and under the hood of her pristine Steinway Grand and hammered its strings like a dulcimer to accompany Merritt’s strumming of a beat-up acoustic guitar. Dinnerstein told the crowd that packed the museum’s fancy-shmancy theater that this song cycle was intended to expose the ties that bind the music of Elizabethan England and rural 20th-century America.

Merritt took a seat stage left while Dinnerstein played what she described as “variations on Leonard Cohen’s ‘Suzanne,’ ” an all-instrumental piece that brought out the melodic similarities between the original and Jimmy Webb’s “MacArthur Park.”

Merritt faithfully covered Cat Stevens’s “Trouble,” a dose of melancholia from the soundtrack of 1971’s “Harold and Maude,” then climaxed with what she called the “painful woman” portion of the show with Billie Holiday’s standing-by-her-philandering-man blues song “Don’t Explain.”

For an encore, Dinnerstein threw in classical chords wherever she thought they fit as Merritt sang “I Can See Clearly Now,” the 1972 AM-radio smash that will uplift a crowd’s mood no matter how highfalutin the setting or delivery.

McKenna is a freelance writer.