A soundtrack is an essential part of a movie, so it’s appropriate that the “live documentary” “The Love Song of R. Buckminster Fuller” has a live soundtrack.

When filmmaker Sam Green brings the show to the Contemporary Arts Center Friday night, he’ll have rock band Yo La Tengo with him, who’ll play the soundtrack live as it has for the two years that the show has been staged.

Green is a San Francisco-based filmmaker whose 2004 feature-length documentary “The Weather Underground” was an Academy Award nominee. His “live documentary” process mixes film, monologue, and music in a form of performance art.

Green’s most recent live documentary based on The Guinness Book of World Records is titled “The Measure of All Things,” but “The Love Song of R. Buckminster Fuller” remains in demand, with shows scheduled into next year.

Fuller was a neo-futurist architect and thinker best known for the geodesic dome — a series of triangular plates assembled to create a dome. One of the best known examples is Spaceship Earth at Disneyworld’s Epcot Center, but Green contends that there is a lot more to Fuller than the symbol of a Jetsons-like future that never came.

He loved people, Green says, and he believed that the way the geodesic dome could help manage resources could help raise people’s standards of living.

“Even if the inventions themselves seem out of date or naive, the bigger ideas are relevant,” Green said.

Performing “The Love Song of R. Buckminster Fuller” for the last two years has affected how Green thinks about Fuller. When the project began, he understood Fuller as an intellectual, but over time, he came to see the man more clearly.

“There’s this kooky, free-spirited guy who loves humanity who’s going to dedicate himself to making the world a better place,” Green said. “He also had within him a huge egomaniac; that’s part of who he was.”

Yo La Tengo became involved in the project because Green was a fan. The band’s broad musical interests range from garage rock to bossa nova to guitar noise freak outs to peaceful drones, so it made sense for the project. Guitarist Ira Kaplan explained how the band’s collaboration with Green worked to the website Consequence of Sound.

“We had a couple of pretty intense sessions where we would play things and get instant feedback,” Kaplan said. “The music came together a little faster and with a little more emotional intensity in the creative process. There were times when Sam couldn’t hear things that we could hear, and we’d finally say, ‘Let us do what we’re going to do’ and ‘I think it’s going to be OK.’ And then the opposite would happen. Sam would just say no, this isn’t how he hears this certain piece. We were moving very quickly. I’m very happy with how it came out.”

The live soundtrack affects how Green delivers his narration. Unintentionally, he adapts his speaking cadence to the band’s rhythms while onstage, and they’ll tweak some ideas before the performance.

“Sometimes they’ll say to me, ‘Can you wait until we come around a full measure before you say this?’ and I’m totally into that,” Green said. “I love thinking of this as a musical experience.”

Just as the music affected Green’s performance, the demands of his presentation required Yo La Tengo to make some changes too.

“When you record something for a soundtrack, you don’t have to play it a second time,” Kaplan told Consequence of Sound. “You play something you like, and if the director likes it, you’re done. Here we played it, and if we liked it, we had to then learn how to play it again.”

Yo La Tengo’s presence has been a large part of the appeal of “The Love Song of R. Buckminster Fuller.” The band usually plays Tipitina’s when in New Orleans, so it has a substantial audience on its own. When Green took the show to Miami earlier this year, the audience demanded an encore — something that had not happened before in the Fuller show.

“Their music has a very emotional tone to it,” he said.

The audience affects Green’s delivery as much as the band does. He tries to tweak the text for each performance to include relevant local references when possible, and he has lines that he is still trying to find the exactly right expression for. If he gets laughs, he tends to go with them rather than try to wrestle the audience to a more sober place.

“When people laugh, they’re more relaxed and okay with a piece,” he said. “If you can get people to laugh, they open up and everything works better. It’s easier to get serious stuff across using humor.”

Although the show is titled “The Love Song of R. Buckminster Fuller,” Green admits that his affection for Fuller isn’t unconditional.

“A part of me cringes a little bit because he was somebody who believed entirely in technology,” Green said. “The extreme example of this was his design to put a dome over midtown Manhattan, since it would save money on snow plowing costs.”