It’s that time of year. Most holiday Muzak seems to do little more than contaminate the air, but Vince Guaraldi’s contribution remains comparatively fresh. The four best tracks from “A Charlie Brown Christmas” are in steady rotation. Guaraldi’s cover of “O Tannenbaum” is simple and “jazzy”; the slightly bland “Skating” offers rolling thirds in waltz time; “Christmas Time Is Here” is an excellent song given extra character by a children’s chorus. This is all good enough music, but there’s no doubt that the headliner is one of the most famous piano pieces of all time, “Linus and Lucy.”

The name isn’t as familiar as the sound. As any cocktail pianist can attest, drunken patrons fervently order “Peanuts!” or “Snoopy!” or “Charlie Brown!” instead of “Linus and Lucy.” (This is reminiscent of a time past when those who knew Paul Newman and Robert Redford better than Scott Joplin would demand “The Sting” instead of “The Entertainer.”)

Guaraldi was a proficient San Francisco jazz musician who worked with Cal Tjader and Stan Getz in the fifties. Though his bebop lines were enjoyable, he lacked the fire of Hampton Hawes or the mystery of Jimmy Rowles. Guaraldi probably would only have had a home-town career if it weren’t for an innovative composition that tuned into the early-sixties Zeitgeist. Disc jockeys picked up on Guaraldi’s “Cast Your Fate to the Wind” even though it was stuck at the back of a rather odd concept album, “Jazz Impressions of Black Orpheus,” which mostly offered straight-ahead jazz arrangements of Brazilian music from a hit movie. Until the album’s concluding track, the pianist is merely a light and competent mix of Red Garland and Bill Evans, but “Cast Your Fate to the Wind” feels like the start of an optimistic new era. In short order, the song won a Grammy for Best Original Jazz Composition and was covered by many non-jazz artists. Indeed, most easy-listening instrumental hits since then owe a debt to “Cast Your Fate to the Wind.”

When the budding producer Lee Mendelson searched for composer for a project about Charles Schulz and Charlie Brown, Guaraldi, a fellow Bay Area talent, seemed like an obvious choice. Mendelson later said, “I was driving over the Golden Gate Bridge, and I had the jazz station on—KSFO—and it was a show hosted by Al ‘Jazzbo’ Collins. He’d play Vince’s stuff a lot, and right then, he played ‘Cast Your Fate to the Wind.’ It was melodic and open, and came in like a breeze off the bay.”

It’s common for a producer to suggest to a composer, “I like this temp track—give me this but a little different.” Although Mendelson may not have said exactly those words to Guaraldi, there’s no doubt that the pianist went back to “Cast Your Fate to the Wind” when working out “Linus and Lucy.” Many details are imitated exactly. The main argument of “Fate” is a strong, syncopated, even eighth-note melody harmonized in diatonic triads floating over a left-hand bagpipe and bowed bass, followed by an answering call of gospel chords embellished by rumbles in the left hand borrowed from Horace Silver. This general scheme is followed for “Linus and Lucy,” even down to the same key, A-flat.

What is notably new in “Linus and Lucy” is the syncopated piano left-hand ostinato. (The bass still has that sustained bowed note, which is a genius bit of arranging.) Over the ostinato is a very old trick indeed: horn fifths, the same sequence of dyads used by European composers for hundreds of years to suggest hunting in the open air. In classic American fashion, Guaraldi steals that Old Country material and marries it to African-influenced rhythm in the bottom. Boom. You’ve got a hit.

The strong upbeat that begins the ostinato might be somewhat hard to hear correctly, at least for those unaccustomed to a syncopated style. I’ve played “Linus and Lucy” at least a hundred times at parties over the years, and somebody always claps along in a way that indicates he or she hears the upbeat as the downbeat. Few, if any, other pop piano works create this kind of rhythmic uncertainty within a significant portion of the intended audience. (It might be added that the delightful way the cartoon characters dance in the original program is completely unsynchronized to the music.)

Both “Cast Your Fate to the Wind” and “Linus and Lucy” also have a short central section of 4/4 swing; “Lucy” has a Latin section as well. Guaraldi’s jazz improvisations on “Linus and Lucy” are blocky and just barely acceptable. It is doubtful that the casual fan waits for those solo sections. The meat is the main tune. While the jazz is going on, you talk to your friend until the theme comes back. (After all these years, I still find the off-key D dominant stuck inside the end of the solo section of “Lucy” jarring and ugly.)

Guaraldi had trouble surmounting the tremendous success of “A Charlie Brown Christmas” and the corresponding best-selling soundtrack. His later output lacked the same fresh inspiration, and he didn’t grow as a serious jazz pianist or as a compelling tunesmith. Although the writer Derrick Bang gamely makes a case for depth and breadth in the valuable biography “Vince Guaraldi at the Piano,” most of us will remember Guaraldi for “Cast Your Fate to the Wind” and a few cartoon cues.

Still, this slender number of magical confluences are far more than most people get. It certainly would be wrong to omit Guaraldi from the jazz history books. The simple but effective techniques that Guaraldi pioneered, especially in “Cast Your Fate to the Wind,” were important to all the jazz that sported a folksy diatonic twang a few years later—by Gary Burton, Keith Jarrett, Pat Metheny, and so forth—and “A Charlie Brown Christmas” remains the ultimate gateway drug. Countless listeners have responded to Guaraldi’s optimistic swinging piano by searching for another hit of that tasty rhythmic realm.