The playwright Kathy Hendrickson had been wanting to produce her script for “Lock 10” for years. Working with director K Tanzer, with whom she founded the New York-based Exhibit A Performance Group, Ms. Hendrickson had been developing concepts about theater, movement, and improvisation. As a longtime music fan and a native of Minnesota, Ms. Hendrickson also was fascinated with the historical influence of the Mississippi River in the development of jazz.

All these tangents flow together in “Lock 10,” which opens Sunday for a two-night run at Joe’s Pub. Conceived as the live staging of a radio play in 1930, the production already has a few layers of meaning built into it, but doesn’t stop there.

“There’s a lot of jazz in the show, and the show is about music, so I always thought I’d have a live jazz band onstage,” Ms. Hendrickson said. But she didn’t want music as background or interlude, and she didn’t exactly want to revisit the sounds of the emergent Swing Era, which become essential to a drama about the reverberations of radical black culture in a Midwestern river town in 1936.

Enter Ken Vandermark. The 44-year-old Chicago saxophonist, winner of a 1999 McArthur Fellowship, struck Ms. Hendrickson as a perfect choice for the show. He’s been a tireless presence on an international scene where post-Coltrane jazz, pure improvisation, and contemporary chamber music blur together. And he was a longtime friend who would be fun to collaborate with, if he could find gaps in a busy touring schedule.

There was a catch, though. “He told us, ‘If you want someone to play covers, I’m not your guy,'” Ms. Hendrickson said. “And then we told him, ‘No, we thought of you because you’re not that guy.'” Instead, Mr. Vandermark composed an original score for the piece, which he will perform with the percussionist John Herndon (best known for his work as a member of post-rock innovators Tortoise) and electronics whiz Christof Kurzmann. The musicians will themselves be part of the play, as much as the nine actors in the cast. “It’s a totally different kind of thing for me to do,” Mr. Vandermark said. He’s worked with dance and spoken text before, but not like this. “Kathy and K were open to letting me work the way I like to, which is why I agreed.”

In the end, the idea that stuck was to create music that would feel as surprising to an audience in 2008 as Bix Beiderbecke would have sounded 70 years earlier. Accordingly, Mr. Vandermark decided to ditch familiar bass-drum-horn-piano configurations.

“This isn’t going to be a score about early jazz, so I wanted to remove any of those associations from the outset,” he said. “The surface of the play suggests one thing, but as soon as things are set in motion, a whole lot of other information is coming at the audience.”

The other major challenge for Mr. Vandermark, who only began rehearsals with the cast two days ago, was to create music that is notably distinct from his own established work as a composer for such groups as the Vandermark 5 and the Chicago Tentet (fronted by one of his mentors, the German saxophonist Peter Brotzmann). “I’ve tried to think of music I wouldn’t normally arrive at,” he said. “I wrote a solo percussion piece for John to play, and I’ve never done that before. I’m really trying to lean toward something that is far away from a jazz sensibility, but that still has some melodic elements to remain attractive. It will be interesting to see what gets pushed into the forefront.”

“Lock 10” will be performed Saturday and Sunday at 7 p.m. at Joe’s Pub (425 Lafayette St., between East 4th Street and Astor Place, 212-967-7555).