NEW YORK—How Washington theater lights Joy Zinoman and Holly Twyford came to make their New York debuts with the breathlessly spare playlets of Samuel Beckett is a story that has to be told with music.

The music, in this instance, is cerebrally Beckett-worthy: a series of experimental compositions, commissioned by a New York classical ensemble and written as responses to three of the Nobel-winning playwright’s later short pieces. The result is “Sounding Beckett,” an intriguing platform for a playwright’s stark emotional landscape and the feelings it arouses in contemporary listeners—in this case, a passel of living composers.

The 75-minute production, running through Sunday at off-Broadway’s Classic Stage Company in Greenwich Village, exposes to Manhattan a stage director and three actors who occupy a top echelon in D.C. theater. The Washington-based Twyford is joined in this endeavor by veteran actors Ted van Griethuysen and Phillip Goodwin, both well known in the nation’s capital for their frequent appearances with Shakespeare Theatre Company and the company that Zinoman founded, Studio Theatre. Van Griethuysen lives in Connecticut, and New York-based Goodwin, is seen regularly on the stages of the city.

They’ve surfaced here, in collaboration with the Cygnus Ensemble, in a high-toned affair bringing together two artistic forms that rarely share a stage, let alone fall into any sort of meaningful conversation. With the six Cygnus musicians stationed in an illuminated row to the left of the performance space, the theater and new-music pieces alternate on the stage to give voice to three Beckett plays — “Footfalls,” “Ohio Impromptu” and “Catastrophe” — and the music it coaxes out of composers such as Laura Schwendinger, Laura Kaminsky and John Halle. (Six composers in all — two per play — received commissions.

The unusual project began in a more modest form in March at the Library of Congress, where Cygnus music director William Anderson and Zinoman created a shorter program, similar in style, built around only one of the Beckett plays, “Ohio Impromptu,” to launch a New Music concert series at the library. That was that, until Anderson called Zinoman, who has been in semi-retirement since leaving Studio Theatre in 2010. “He said, ‘Joy, would you consider doing this again, New York?’ ” Zinoman recalls. “I said, ‘Bill, it’s an 11-minute play. What do you mean, do it in New York?’ And he said, ‘What if we choose two more, to go with it?’”

A foundation connected with Cygnus financed the New York mounting, which leased the playhouse on East 13th Street for the two-week run, Zinoman says. But conjoining original music and the work of the modernist master was tricky. Beckett, author of absurdist classics such as “Waiting for Godot” and “Krapp’s Last Tape” and who died in 1989, was rigorous about how he wanted future versions of his plays staged. He left instructions prohibiting the addition of musical accompaniment to his work, says Zinoman, who counts him among the dramatists she most admires. (She ran into a bit of trouble herself with his estate back in 1998, when her vivacious staging of “Godot” took some liberties with language and design.)