The filmmaker David Lynch turned to his haunting work again and again, for “Blue Velvet,” “Mulholland Drive” and other neo-noir films.Angelo Badalamenti, an internationally sought-after composer who wrote the hypnotic theme to “Twin Peaks,” David Lynch’s 1990s television drama series, and the music for five Lynch films, including “Blue Velvet” (1986), died on Sunday at his home in Lincoln Park, N.J. He was 85.His niece Frances Badalamenti confirmed the death. She said she did not know the cause.Mr. Badalamenti was at the piano behind Isabella Rossellini when she sang “Blue Velvet” at the Slow Club in Lumberton, N.C., a flower-filled, picket-fence kind of town with a very dark side. Aside from the title song, a Bobby Vinton hit from 1963, he had composed much of the film’s music.He also wrote the music for Mr. Lynch’s 2001 neo-noir mystery “Mulholland Drive” and had a small role in the film as one of two mobster brothers who spits out his espresso in a conference-room scene.His best-known work was the “Twin Peaks” theme, recognizable from its first three ominous, otherworldly notes. He won the 1990 Grammy for best instrumental pop performance for the number, which was, according to the Allmusic website, “dark, cloying and obsessive — and one of the best scores ever written for television.”In 2015, a Billboard writer described the theme as “gorgeous and gentle one second, eerie and unsettling the next.” It was, according to Rolling Stone, the “most influential soundtrack in TV history.”Mr. Badalamenti didn’t really disagree.“Music and composing — I almost feel a little guilty about it — come so easily for me,” he told the north New Jersey newspaper The Record in 2004. “It’s like the well doesn’t seem to run dry.”Angelo Daniel Badalamenti was born on March 22, 1937, in Brooklyn. A second-generation Italian-American, he was the second of four children of John Badalamenti, a fish market owner, and Leonora (Ferrari) Badalamenti, a seamstress.Growing up in the Bensonhurst section, he started piano lessons at 8 but quit because he preferred playing stickball outdoors with his friends. He took it up again at his older brother’s insistence and came to appreciate the piano when girls admired his playing. He was soon accompanying vocalists and other acts at Catskills resorts during summers off from high school and college.Mr. Badalamenti attended the Eastman School of Music in Rochester, N.Y., and earned a master’s degree at the Manhattan School of Music in 1960.His first job was teaching the seventh grade in a public school, but when he wrote a musical Christmas program for his students, members of the Board of Education saw the production and told the local public TV station Channel 13 about it. The station videotaped and broadcast the show, and the Monday after Christmas, Mr. Badalamenti got a call from a Manhattan music publisher with a job offer.Nina Simone recorded some of his first songs, including “I Hold No Grudge,” in 1965. Nancy Wilson sang “Face It, Girl, It’s Over” (1968).Mr. Badalamenti got started in films by writing music for “Gordon’s War,” a 1973 blaxploitation film. Ossie Davis, the director, wanted an all-black crew, all “brothers,” he said. Mr. Badalamenti pointed to Sicily on a world map. “You do seven strokes from Sicily, and you’re in Africa,” he said he told Mr. Davis. “I may not be your brother, but I’m certainly your cousin!”Mr. Badalamenti was at the piano when Isabella Rossellini sang “Blue Velvet” in the 1986 David Lynch movie of the same title. De Laurentis Group/Courtesy Everett CollectionHe and Mr. Lynch met when Mr. Badalamenti was called in as a vocal coach for Ms. Rossellini on the set of “Blue Velvet.”Jamie Stewart, whose band Xiu Xiu did an album of “Twin Peaks” music, saw Mr. Badalamenti’s Lynchian work in a historical midcentury context: a postwar world where everything appeared to be sunshine and pastels but where the evil unleashed by World War II still lurked.“It’s very romantic but can be terrifying,” Mr. Stewart said of the music, speaking to The Guardian in 2017. “It has a violence and a sincere sentimentality — sadness but not despair.”Mr. Lynch, who described Mr. Badalamenti’s work as having “a deep and powerful beauty,” said that he and the composer would be entirely in sync in expressing Mr. Lynch’s vision for a film. “I sit next to him and I talk to him, and he plays what I say,” he said in an interview with the American Film Institute.As Mr. Badalamenti explained on NPR’s “All Things Considered,” that’s how he wrote “Laura Palmer’s Theme” for “Twin Peaks.” Sitting beside him at his Fender Rhodes keyboard, Mr. Lynch began talking.“It’s the dead of night,” Mr. Badalamenti said. “We’re in a dark wood. There’s a full moon out. There are sycamore trees that are gently swaying in the wind. There’s an owl.”The words became notes that evoked the story of a murdered homecoming queen in the Pacific Northwest.They collaborated again and again, on the films “Wild at Heart” (1990), “Lost Highway” (1997) and “The Straight Story” (1999), in addition to “Mulholland Drive.” There were five iterations of “Twin Peaks,” including the film “Twin Peaks: Fire Walk With Me” (1992) and an 18-episode sequel series (2017).In between, Mr. Badalamenti wrote for a wide variety of movies, among them “Nightmare on Elm Street 3: Dream Warriors” (1987), “The Comfort of Strangers” (1990), “Naked in New York” (1993), “The City of Lost Children” (1995), “A Very Long Engagement” (2004) and “The Wicker Man” (2006).He used what he called his “classical chops” to score “Stalingrad” (2013), a wartime love story set against that pivotal 1942 battle. It was an enormous box office success in Russia, where it was produced.One of his longest-running projects was the music for the PBS program “Inside the Actors Studio,” which was on the air from 1994 through 2019, hosted by James Lipton.Writer’s block was rarely a problem for Mr. Badalamenti, but composing a torch-lighting theme for the 1992 Summer Olympics in Barcelona had him stumped. The notes finally came to him in the shower, he recalled, and he hurried downstairs to his piano. “I wrote it in half an hour,” he said.He received the Henry Mancini Award from Ascap, the American Society of Composers, Authors and Publishers, and a Lifetime Achievement honor from the World Soundtrack Awards.Mr. Badalamenti is survived by his wife, Lonny; his daughter, Danielle; and four grandchildren. His son, André, died in 2012.His niece Frances interviewed him for a magazine, The Believer, in 2019. He remembered being drawn to film noir in his youth, telling her, “The haunting sounds have been there, the off-center instrumentals, ever since I was a child.”Alex Traub More