It may be a while before Thom Yorke becomes known as the king of movie music, but he’s off to a fast start, now that he’s finally started accepting film assignments, at least from friends. Last year, he scored and wrote songs for “Suspiria,” and now he’s followed that up with “Daily Battles,” an original ballad written for “Motherless Brooklyn,” which premiered over Labor Day weekend at the Telluride Film Festival. Edward Norton not only stars in but also wrote and directed the film, finding its jigsaw falling into place after he approached his pal Yorke about making a contribution.

“We go back to the mid-‘90s,” Norton told Variety after the film’s sold-out Telluride premiere. “I saw Radiohead play in a small club in New York, and we had mutual friends and became friends. So it’s been over 20 years that we’ve known each other, but this was the first time I sort of had the nerve to really ask him to do something.”

Two different recordings of “Daily Battles” appear in the film and have just been released as digital singles — one with Yorke singing and a co-credited Flea playing trumped as well as bass, and then a jazz instrumental version with the trumpeter Wynton Marsalis as headliner. (Marsalis also performs some ‘50s jazz covers and on Daniel Pemberton’s score for the film.)

Yorke also contributed to the screenplay, although he didn’t know it. “There are funny little Easter eggs,” Norton says. “When Lionel [the character he portrays, who deals with Tourette syndrome] is describing his head to Laura [played by Gugu Mbatha-Rawand], he says, ‘It’s got to have everything in its right place.’ That was one of my little nods to Thom.”

Norton says he had no compunctions about asking the frontman of as post-modern and increasingly electronic-leaning a group as Radiohead to pen a period piece for him. Beyond believing Yorke was up to the task stylistically, the actor-writer-director also wanted to bring in the musician’s inherent sense of disconnection to represent a lead character, Lionel, who both suffers from and benefits from Tourette’s, making him a highly unlikely gumshoe in this noir homage.

“Thom is a real musicologist,” Norton says.” He loves jazz and his taste and expertise in music are incredibly erudite and wide-ranging.” For ”Motherless Brooklyn,” “I think what I said to him was that I felt the condition of Lionel’s brain is one that is in some ways analogous to the kind of music Thom makes. It has sentiment and longing and is human, but it’s also this chaotic, dissonant space in which, like his music, things loop in reverse and rewind. And essentially what I said to him was, ‘I want a ballad in the old-world sense that reflects his anguish, and in some ways the larger anguish of living in dark times.’ He talked about that dark Billie Holiday ballad ‘Strange Fruit’ and things like that, and read the script and just went off and came up with this song that was to me immediately very affecting, and even affected my sense of some of the latent themes in the film, in some ways.”

Asked to cite a particular lyric, Norton says, “There’s a line: ‘You’re on parade for daily battles; the other side, it has no face.’ The song encompasses, I think, not just the personal struggle with personal daily battles, but also the larger struggle of living within oppressive times, or feelings of the futility of pushing against forces you can’t win against. And Thom to me has always straddled incredibly interpersonal longing and turmoil with the challenge of living in the modern age. And I think that added a great dimension to the tonality of the film.”

Yorke’s version first appears over a montage in which Norton’s character comes home and, seemingly with a sense self-loathing, examines his own tics in a mirror. Later, the Marsalis arrangement appears in a more peaceful setting, as Lionel and his African-American almost-love-interest, do a slow dance at a jazz club in Harlem.

“I don’t know if people (at the premiere) picked up on it, but the song that occurs when Lionel and Laura dance is Wynton doing Thom’s song as if arranged by Miles Davis, in the style of the mid-‘50s. The moment is so emotionally important, we were concerned about distracting from it with an (existing) ballad.” When it came to the idea of adapting “Daily Battles,” Norton says that “it was sort of both” his idea and Marsalis’. “I think I might have suggested it to him. But then when he heard it, he went, ‘Oh, yeah, we can make a very nice Miles Davis version of this.’”

The song was turned in early enough for Norton to incorporate the title into the dialogue. “I put it into the scene with Laura in the car when she says, ‘We’ve all got our daily battles.’ He had read the script, but somehow Thom captured something in the song that wasn’t actually in the film (to that point). It actually affected my sense of what their relationship was about, which is the idea of ultimately Laura having an agency on Lionel that gets him to look beyond the struggles he lives within and think about bigger things. It was amazing to have that affect it while we still had time to incorporate it into the emotional development of that relationship. His song actually elevated my sense of what their relationship was formed in, because it wasn’t a traditional romance.”

Yorke’s contribution is just one aspect of the jazz-heavy film, which has Marsalis’ band doing Mingus covers and the like in the Harlem club scenes (with all of the real musicians on stage except for the trumpeter himself) and also a score by Daniel Pemberton that features Marsalis as well. “I can’t say enough about Daniel Pemberton,” Norton says. “I think he’s one of the great talents working in film music right now.”