(L to R): Tift Merrit and Simone Dinnerstein (Lisa-Marie Mazzucco/Lisa-Marie Mazzucco)

When classical pianist Simone Dinnerstein decided to tour with singer-songwriter Tift Merritt, as a kind of exchange program seeking musical connections, she suggested they come onstage and bow first, as they do in the highbrow world.

Merritt said she thought that was odd (“We hadn’t done anything yet”). But it was probably strange, too, for Dinnerstein to be performing in a place where her well-placed notes had to sometimes compete with a fork clanking on a plate.

The Hamilton on Thursday was likely a nicer club than many of the honky-tonks where Merritt plays, and the audience was mostly rapt as the two presented songs from their collaborative album “Night,” issued recently by Sony Classical.

First, Dinnerstein’s precise and deeply felt playing shifted without pause to Merritt’s keenly personal songs, with each sitting quietly during the other’s turn. Even their primary instruments contrasted, with one’s shiny black Yamaha opposite the other’s lovingly beat-up guitar.

Eventually, there were diplomatic forays into each other’s music — muscular chords to back up Merritt’s striking folk-rock observations in “Only in Songs,” and, more jarringly perhaps, Merritt’s harmonica notes above Dinnerstein’s Franz Schubert.

(L to R): Tift Merrit and Simone Dinnerstein (Lisa-Marie Mazzucco/Lisa-Marie Mazzucco)

To accommodate their musical detente, the two commissioned pieces that would merge their musical worlds. Jazz pianist Brad Mehldau and folk songwriter Patty Griffin each provided a piece; Daniel Felsenfeld arranged a song by Leonard Cohen, a writer admired by Merritt and Dinnerstein, with variations on his “Suzanne.”

Jazz often provided the common ground, with the Billie Holiday song “Don’t Explain,” featuring beautiful playing by Dinnerstein, morphing into Henry Purcell’s “Dido’s Lament.” In both, Merritt essentially became a torch singer — clutching the microphone, her guitar gone.

It must have been daunting for Merritt to briefly take Dinnerstein’s seat at the piano for the gospel-tinged “Small Talk Relations” — one of the few departures from their collaborative album.

It was best when they found common ground — Dinnerstein suggested a song performed by countertenor Alfred Deller, “I Will Give My Love an Apple,” that was basically the same song Merritt learned growing up in the South, “I Will Give My Love a Cherry.”

To that, Dinnerstein took to the “extended piano” approach of modern composer George Crumb, a West Virginia native, to pluck the strings under the lid of her piano, in the manner of the old mountain instrument the dulcimer. Also from under the lid, she added key notes to Merritt’s original “Colors.”

Before singing her “Still Not Home,” which mentions bluesman Robert Johnson, Merritt asked Dinnerstein to remind her who she said was the classical equivalent.

“Paganini,” she said.

Catlin is a freelance writer.