Watching the vivid new restoration of Martin Scorsese’s Taxi Driver at Film Forum the other night—showing in limited theaters across the country now, and due out on Blu-ray on April 5—I was struck above all by the film’s score, which 35 years on sounds more radical, more brilliant, and crazier than ever. An original title card after the closing credits dedicates the film to the composer Bernard Herrmann, who died in 1975 only hours after the final recording session and months before the movie’s release. It was the last score he would compose in his career, and it may be one of his best.

That’s saying something when you consider that Herrmann, who would have celebrated his centennial birthday this year, wrote an astonishing percentage of the greatest movie scores, for the greatest movies, of all time. His first film was Citizen Kane , after a long stint as conductor for CBS radio that included scoring Orson Welles’ “War of the Worlds” broadcast. Of course Herrmann is most known for his collaboration with Alfred Hitchcock; he scored nearly every film the director made from 1955 through 1964, including Vertigo , with its famous ascending love theme echoing Wagner’s Liebestod from Tristan and Isolde, and Psycho, probably the most influential horror score ever, with its relentless shrieking strings. Herrmann was so prolific, and his work so wide-ranging, that the only natural response to his filmography is amazed laughter: Jason and the Argonauts. Jane Eyre. The Devil and Daniel Webster(which won him his only Oscar in 1941.) The Day the Earth Stood Still (a pioneer in electronic sound and the use of the theremin in science fiction.)

Herrmann and Hitchcock eventually broke over the score of Torn Curtain (1966). Herrmann’s classical style of orchestral scoring was going out of fashion (for reasons that were economical as well as aesthetic), but he refused to provide the jazz- and pop-inflected score that Universal demanded to capture younger audiences. The two men would never collaborate again. (Herrmann’s widow tells an affecting story of the two men’s “cool” encounter many years later.)

Herrmann, a famously temperamental and prickly man, insisted on the musical equivalent of final cut: “I have the final say, or I don’t do the music. … If I have to take what the director says, I’d rather not take the film. It’s just impossible to work that way.” When Scorsese contacted Herrmann about working on Taxi Driver, the 65-year-old composer was living in London. (Scorsese was 34.) Initially, Herrmann resisted the proposition with his customary brusqueness, scoffing, “I don’t know anything about cabdrivers.” But he was intrigued by a scene in which De Niro’s demented cabbie Travis Bickle pours peach Schnapps over torn-up white bread for his breakfast, and took the job on his usual terms of total musical control.

What resulted from their collaboration is an astonishing piece of film music that brings together old and new Hollywood, or rather, one that places old and new Hollywood side by side in an uneasy but productive tension. Here, finally, is the jazz that Hitchcock asked for and never got; the film’s familiar lyrical theme (identified on the soundtrack as “They Can’t Touch Her” or “Betsey’s theme”) is played by a mournful alto sax, giving the early scenes in which it appears a laconic neo-noir feel. Intertwined with that “new” jazz sound (no longer now a teenybopper novelty, of course, but still a new idiom for Herrmann) are passages in the lushly orchestrated classical style. “Getting Into Shape,” the music cue that plays under the still-frightening montage of Bickle pumping iron and holding his arm in an open flame to “train” for his killing spree, is a grim descending figure of blasting horns that could easily be imagined accompanying the rampage of some giant radioactive ant from a 1950s horror film.

As Taxi Driver goes on, that warm, jazzy sax theme—which still leaves some room for the viewer to construe Bickle’s loneliness as a burnished, romantic “alienation”—gives way to a darker, harsher, more unforgiving soundscape. When Betsey (Cybill Shepherd), the pretty campaign worker whom Bickle takes out on a date, rejects him in disgust—pseudo-scientific Swedish porn wasn’t her first entertainment choice, apparently—Betsey’s leitmotif begins to mutate in disturbing ways. By the time he has procured a suitcase full of guns from the rodent-like arms dealer Easy Andy (Steven Prince in a great cameo), Betsey’s theme has been reduced to a wonky little electric-piano part played (deliberately badly) over a martial-sounding snare that reminds us of Bickle’s service in Vietnam.

This music cue, titled “The .44 Magnum Is a Monster,” may represent the pinnacle of the Taxi Driver score’s lunacy, and its achievement. The swirling harps associated with Travis’ racing thoughts, and with his vigilante fantasies about Jodie Foster’s child-prostitute character, weave in and out of menacing bass chords, while that sadly diminished love theme wanders in and out. The film’s screenwriter Paul Schrader has spoken of his sense, during filming, that the movie was a three-way collaboration between writer, director, and star: “Scorsese and De Niro and I … we were in sync. We didn’t need to communicate with each other that much; we knew what this movie was about.” The profound understanding of the film present in Herrmann’s music—its characters, its themes, its place in film history—indicates that the collaboration actually went four ways.

This is a conversation for another day, but one of the very few parts of Taxi Driver that now seems imperfectly judged is the movie’s strange, almost sentimental coda, which—without giving too much plot away—sounds a heavily ironic note of redemption. But one musical choice near the end of the very last shot leaves us with something much more ambivalent, and richer. As Bickle sees his beloved Betsey disappearing in the rear-view mirror, that familiar golden alto sax theme kicks in, recalling the nostalgic Betsey reveries from earlier on. Then suddenly, for the briefest of seconds, we hear a high-pitched, nonmusical sound, almost like the squeal of a malfunctioning machine. It’s a little vibraphone chime known as a “sting,” often used to mark moments of surprise or shock in movies—but this sting is played backward, giving it a vaguely demonic sound. (As paranoid rock fans everywhere can attest, “backmasking” can make just about anything sound Satanic.)