Holly Twyford, Ted van Griethuysen and Philip Goodwin in “Catastrophe” as part of “Sounding Beckett,” presented Sept. 14-23 at the Classic Stage Company in New York City. (Jeremy Tressler/Jeremy Tressler)

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?’”

Holly Twyford in “Footfalls” as part of “Sounding Beckett.” (Jeremy Tressler)

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.)

Commissioning stand-alone work that would convey the composer’s own reactions to one of the three selected plays, all written between 1975 and 1982, was the solution. “They’re united in poetic and rhetorical devices,” says Zinoman, who made the choices. “Footfalls” portrays an aged woman (Twyford), pacing in precise movements along a shaft of light, as her mother (the voice of Kathleen Chalfant) in controlling fashion, coaxes her on. In “Ohio Impromptu,” identically attired men (Goodwin and Van Griethuysen) sit at a table, as one reads from a story that, in the manner of “Krapp’s Last Tape,” disturbs the other to a mysterious degree. And in the satirical “Catastrophe,” an imperious theater director (Goodwin) orders a sunny minion (Twyford) to manipulate a silent, shivering actor (Van Griethuysen), seemingly forced to play the role of the director’s mannequin.

“These plays are about the divided self, and the comfort of grief and what it’s like to become an individual,” says Zinoman, who, it turns out, merely took a sabbatical from theater after she departed Studio. She and her husband, Murray, a career U.S. Foreign Service officer, have traveled the world since then and have more trips in mind. But she also continues to teach at Studio and in the spring will direct Amy Herzog’s “4000 Miles” there.

“I really like to direct plays,” she says. “It’s like sailing down the Mekong to cave with 1,000 Buddhas in it,” she adds, applying an analogy about a recent excursion to the task of staging Beckett.

The musical breaks — two separate programs of three pieces each alternate from performance to performance — are not meant to intrude. “The music stands side-by-side with the plays,” Zinoman says. “There’s no bleeding between the two things.”

For Twyford, who’s mesmerizing in “Footfalls’’ —Goodwin and van Griethuysen are equivalently riveting in “Ohio Impromptu” — working in New York for a short spell is stimulating, but mostly because of the project.

“When I first read this, I had no idea what to make of it,” she says of “Footfalls.” “What was fascinating working on it with Joy is that she was so interested in trying to put it into a realistic context. You had to figure out how to take this to a real place.

Philip Goodwin and Holly Twyford in “Catastrophe” as part of “Sounding Beckett.” (Jeremy Tressler)

As for this real place and the New York audiences that are new to her as an actress, Twyford doesn’t sense much of a difference. “Frankly,” she says, “a theater is a theater.”