NEW YORK — The prospect of Jonny Greenwood — the notoriously spotlight-averse Radiohead multi-instrumentalist and classical composer — in a tux at the Oscars is especially tantalizing to "Phantom Thread" director Paul Thomas Anderson.

"He said, 'Either you come and you're dressed like an idiot, and that'd be brilliant. Or you come and you have to say something on stage, which would also be brilliant. So win-win for me,' " Greenwood said. "It's a kind of abuse, really, the way he treats me."

Just as Daniel Day-Lewis' obsessive fashion designer Reynolds Woodcock and his muse, Alma (Vicky Krieps), carve out their own twisted harmony in Anderson's sublime comic romance, so too have Greenwood and Anderson found an idiosyncratic equilibrium.

"Phantom Thread" is their fifth film together. Since 2007's "There Will Be Blood," Greenwood has scored all of Anderson's films (2012's "The Master," 2014's "Inherent Vice"). In 2015's "Junun," Anderson documented Greenwood's trip to India to play with Shye Ben Tzur and the Rajasthan Express.

What makes them such a good match?

"(Anderson) has faith in me, and he likes making fun of me," Greenwood said. "I think they're the two prongs of the perfect relationship, really."

"Phantom Thread" marks a new crescendo for their collaboration and for Greenwood as a composer. The film is up for six Oscars, including best score — Greenwood's first Academy Awards nomination. That, in itself, rights what many consider a grave wrong.

Greenwood's shrieking, unearthly music for "There Will Be Blood" is widely considered among the best film scores of the last two decades. But it was ruled ineligible for the Oscars because it was based partly on pre-existing music: Greenwood's "Popcorn Superhet Receiver," a harrowing, dissonant piece in which Greenwood instructed the string section to play with guitar picks.

"Phantom Thread" is a warped love story, and it called for a more traditional orchestral score full of warmth and romance. Those are qualities not only uncommon to Greenwood's previous film work, but much of Radiohead's fraught and restless catalog, too.

When Greenwood sent Anderson more typically dark music for the first scene, Anderson pushed him to write something more romantic. On the finished score, the first sounds you hear are 32 strings at once.

"A lot of the music I've done for other films has been quite mournful or frightening," Greenwood said. "I was a bit uptight about it and awkward about the fact that it's all genuine. What I kept thinking about is that feeling you get when you go to see a concert and you hear an orchestra start. Everyone gets quiet and the orchestra starts playing and you hear what the strings sound like in real life. It's amazing. It's like nothing else."

Greenwood's initial forays into classical began with arrangements for Radiohead songs but has steadily grown. He has grown more comfortable in his second act, which — despite the magnitude of Radiohead's achievements — is verging on overtaking his first.

"I suppose I'm more confident that stuff I've got on paper will sound how I imagine it will sound. I used to have to guess a lot more," Greenwood said. "There's still an element of that. I'm just a bit less cautious about it and more excited ... that's not the word. What's the word? Addicted, I suppose."

What Greenwood returns to again and again is the thrill of a live orchestra — the complexity, the variation. Radiohead will find songs through constant reworking and experimentation, but Greenwood's classical work is solitary, on paper, leading up to a handful of days recording with an orchestra: "And then, suddenly, it's alive," he said.

Anderson called Greenwood "equal parts authentic musical genius and total faker."

"He won't push gently into something that doesn't come naturally. He needs to find a legitimate way into something rather than just jukeboxing. The music he came up with is just deeply felt — by him, clearly," Anderson said. "He can access something inside him and get it to come out though his fingers into his instruments. It's weird. He can even make Toca Band on his phone sound like something spectacular and moving."

A few nights before the Academy Awards, the "Phantom Thread" score will be played live alongside a screening of the film, one of a series of such concerts. When Greenwood spoke last week, he was intrigued but noncommittal about attending the Oscars.

But last week, Anderson confirmed in an email that his dream of seeing a formally attired Greenwood on the red carpet will indeed be realized.

"He's coming!" Anderson wrote. "I have confirmation!"