It’s fitting that the immaculate new restoration of Sergio Leone’s 1968 magnum opus “Once Upon a Time in the West,” which made its debut at the Tribeca Film Festival, will be on display in screenings at the Museum of Modern Art for the next five days. Leone’s film is perhaps the single most shameless modernist movie collage of tropes, scenes, themes, shots, and plot points from other films that was not intended to be satire.

The director’s previous Westerns had all borrowed heavily from their American progenitors, but the story that Leone and co-scenarists Bernardo Bertolucci and Dario Argento created out of the pieces of Nicholas Ray’s “Johnny Guitar,” John Ford’s “The Iron Horse,” Robert Aldrich’s “The Last Sunset,” and a dozen other American oaters of various vintages is a narrative Frankenstein. In making “Once Upon a Time in the West,” however, Leone brought his movie monster to life by creating something remarkably fresh and timeless out of the conceptual scraps of the pictures he loved.

The story — in which a nameless, harmonica-playing gunslinger (Charles Bronson), a widowed New Orleans prostitute (Claudia Cardinale), a world-weary outlaw (Jason Robards), a terminally ill railroad baron (Gabriele Ferzetti), and his ruthless regulator (Henry Fonda, cast deliriously against type) mingle destinies — is doled out so gradually that it borders on the irrelevant. Late in the film, Robards’s character, Cheyenne, describes himself and others who live by the pistol as being motivated by “something to do with death,” and for much of its running time, that’s about as specific as the film gets. And yet there is nothing vague or generalized about the emotions on display or the changing distances the characters keep from one another and from the inevitable oblivion of frontier history made at gunpoint.

“Once Upon a Time in the West” was brutally recut by Paramount Pictures, which shortened the film by some 20 minutes prior to its American release. Though shunned by stateside critics and audiences alike for decades, an unofficial restoration in the 1970s, undertaken by the 16 mm educational movie rental company, Films Incorporated, helped to begin a slow march to cult-film supremacy. That goal was finally achieved via a 35 mm release in 1984 of Leone’s original 165-minute international cut and subsequent home-video editions.

The architects of the current restoration have taken particular care with the soundtrack of “Once Upon a Time in the West.” This is only fitting, as the film’s musical score, by Ennio Morricone, is arguably even more revered than the movie itself. Mr. Morricone’s musical cues (the first of which doesn’t arrive until well into the second reel of the movie) were written in advance of the film’s script, and his music’s extravagantly emotional surges and brittle, anxious punctuations account for much of the power and gravity that “Once Upon a Time in the West” sustains.

The film’s symphonic tempo, in turn, gave Leone’s actors an opportunity to stretch out. Italian films of that era required their multinational casts to do post-recorded dialogue after their scenes were shot. But this potential hindrance proved to be an unusual opportunity for Robards, in particular, who attacked what few lines he has in the film with epicurean relish.

As in the rest of Leone’s 1960s work, the use of the bargain-price wide-screen format, Techniscope, adds much. Conventional wide-screen optics would never tolerate the luxurious depth of field and tight close-ups through which Leone told his stories. The Techniscope process — in which conventional lenses are used to create two wide-screen images per frame of film, rather than using a Cinemascope lens to squeeze a single distorted image onto the camera negative — allowed Leone to indulge himself to his heart’s content. The camera work and composition on display in “Once Upon a Time in the West” is poetic, baroque, and stunning from start to finish.

Like the old saw about how, from an engineering standpoint, a bumble bee shouldn’t be able to fly, in some ways “Once Upon a Time in the West,” a horse opera in which characters stare at one another far more than they shoot, shouldn’t work at all. Long and slow, narratively obtuse and oblique, the film can seem to the uninitiated like a compendium of its director’s stylistic obsessions run in slow motion. Its silences and spaces are vast enough to strand an impatient viewer in a three-hour movie purgatory. But Leone’s tectonically paced lullaby to the Western is a result of an immense, brooding romanticism unequaled in any of the director’s other films. It stands alongside Stanley Kubrick’s “2001: A Space Odyssey,” a movie that also turns 40 this year, as a pinnacle of ’60s auteurism run magnificently amuck, and genre filmmaking redefined, re-invigorated, and forever changed thereafter.

Through May 5 (11 W. 53rd St., between Fifth and Sixth avenues, 212-708-9400).