Popular music sounds different today because of Ennio Morricone. The Italian composer’s ideas have thoroughly seeped into our collective cultural subconsciousness: the mental jukebox that seemingly spins of its own accord. That’s how the good stuff works. For decades now, ever since Mr. Morricone first broke out that signature jew’s-harp for “A Fistful of Dollars” (1964) and began his partnership with Sergio Leone (his primary-school classmate), we’ve been hearing his whispers in our inner ear.

Now, at 78, Mr. Morricone, who added six more film credits last year to his total of more than 500 in a 48-year career, will finally get the celebration he deserves on these shores. Beginning on Thursday, the Museum of Modern Art will honor the composer with a six-film tribute. Not to be outdone, the following day Film Forum will undertake a three-week, 26-film tribute, beginning with “Investigation of a Citizen Above Suspicion” and concluding with “Once Upon a Time in America.” To top it off, Mr. Morricone will conduct a 200-piece orchestra at Radio City Music Hall on February 3 in his first-ever North American concert.

Mr. Morricone’s work remains as vital as that of Clint Eastwood, who first made his mark as the nameless, cheroot-chewing antihero of Mr. Leone’s spaghetti Westerns.

“You play a few chords and it becomes axiomatic,” the senior curator in the film department at the Museum of Modern Art, Lawrence Kardish, said. MOMA’s six-film salute to Mr. Morricone includes his most operatic work for Leone (1984’s “Once Upon a Time in America”) but also some surprises. “Not many people realize he was responsible for Oliver Stone’s ‘UTurn.'” The 1997 film, a pulpy potboiler, caught Mr. Kardish’s attention for its eccentric “twanginess,” a quality that is one of the composer’s chief contributions to contemporary music.

But Mr. Morricone’s influence isn’t always so apparent. The biggest pop hit of 2006, Gnarls Barkley’s “Crazy,” builds its melody off a sample from a 1968 Italian horse opera, “Preparti la Bara,” whose score, by Gianfranco Reverbi, makes use of Mr. Morricone’s template. And sure, everyone can hum the key refrain from “The Good, the Bad, and the Ugly” (1967), but it’s not just that. Watch the shootout finale of “For a Few Dollars More” (1965) and listen as the individual elements build on the soundtrack. That springy jew’s harp, the ghostly whistler, the (yes) twangy guitar, the ominous chanting, and finally, the strings, swelling up above it all as a crane shot lifts higher and higher, and Mr. Eastwood and fellow gunslinger Lee Van Cleef ride into the solitary distance.

The pop producer Timbaland could do no better cooking up unusual sonic collisions for Justin Timberlake’s latest dance tracks. And even when Mr. Morricone’s work is more blatantly functional, like the predatory ostinato piano in “Peur Sur La Ville” (1975), it stays glued to your imagination.

“He’s one of the great orchestrators of the 20th century,” the WNYC radio host and composer, David Garland, said. “Because of the colors he chooses to use, the wonderful joy in hearing the crazy combinations of those sounds. I love how he uses music to tell a story, pushing the soundtrack way up front and in your face, as opposed to the subtle approach. There’s a wildness to his music.”

Mr. Garland, who often spins film music on his programs, cites a newly reissued soundtrack for Mr. Leone’s “Duck, You Sucker” (1971) as essential.

“You hear an ocarina with an oud [a pear-shaped, stringed instrument] with electronics with I don’t know what all,” he said. “It’s this grab bag of things, but it’s beautiful.”

Mr. Morricone’s background in electronic composition is a covert factor, like an unexpected plastic whistle in the bottom of a Cracker Jack box. During the 1960s, he belonged to the Roman collective Gruppo di Improvvisazione Nuovo Conso, which steeped itself in the avant-garde approaches of Italian visionaries such as Luigi Nono and Giacinto Scelsi. It’s part of what attracted a fresh generation of musicians to Mr. Morricone, first in the 1980s, when downtown jazz firebrand John Zorn recorded a memorable tribute album, “The Big Gundown,” on which a cadre of jazz and new-music improvisers tackled theme music from such films as “The Battle of Algiers” and “One Upon a Time in the West.”

Mr. Morricone was pleased enough with the project to pen some liner notes. “Work done by a maestro with great science-fantasy and creativity,” he said. The 1986 Nonesuch release, still among one of Mr. Zorn’s finest, brought Mr. Morricone to the attention of a new kind of listener: the art-wise hipster who also was busy rediscovering overlooked composers like Raymond Scott. A decade later, yet another circle of influential young musicians had their “eureka” moment with Mr. Morricone, whose ideas seeded exploratory new bands such as Tortoise, Stereolab, and the High Llamas.

David Grubbs, a co-founder with Jim O’Rourke of the experimental rock band Gastr Del Sol in the mid-1990s, and now a solo artist and Brooklyn college professor, remembers the strong impression Mr. Morricone’s music made at that pivotal time. “People started looking back to composers and arrangers of 1960s and ’70s soundtracks,” he said. “And the composers who were most important were Van Dyke Parks, Jack Nitzsche, and Ennio Morricone. And of them, Morricone had the strongest impact.”

That wasn’t due only to the unexpected juxtapositions of sounds the composer favored.

“You also had a sense of somehow he knew electronic music,” Mr. Grubbs said, noting how such a sensibility informs albums as seemingly unlikely as Smog’s “Red Apple Falls” (which Mr. O’Rourke produced).

Although fans such as Mr. Garland lament, with tongue somewhat in cheek, the way popular soundtrack composers such as John Williams have dominated the industry with their overblown, didactic scores, he knows that Mr. Morricone serves as a unique role model. Rather than tell audiences what to think and how to feel, his compositions assume a life of their own. At their best, they compel an otherwise passive moviegoer to puzzle over exactly what they should think.

“This guy’s made music like no one else’s,” Mr. Garland said. “He didn’t do it to be as weird as possible. He found a new language to say what needed to be said.”

Listen to a clip from The Good, the Bad and the Ugly.