There's a moment in "Thelonious," a composition from Thelonious Monk's first recording, in which just about everything shifts in jazz, and consequently in a good part of American music. It's 1947, and Monk, 30 years old, is improvising. What he's doing makes no sense within the context of what's come before him. Though there's an obvious stride section in his solo and hints of Earl Hines and boogie pianists, there's a strange feeling of stasis, as if in the middle of a river, a patch of water refuses to move. Lines crisscross, and abrupt left-hand explosions come from nowhere. Instead of jazz's linear movement, Monk stops time, offering a new logic. Forty-five years later, the music's newness still startles. Coming across Monk is like discovering a new continent, populated with new species and ideas, shaped by a new geology.

The radical nature of the pianist's inventions aren't questioned anymore, but for a long time they were. Monk, who would be celebrating his 75th birthday this Saturday, was called a fraud, and his personal eccentricities, along with his name -- Thelonious Sphere Monk -- were enough to suggest a lack of seriousness in an era when vanguard jazz was turning its back on entertainment and taking a public position of seriousness. He would dance at the piano, wear beautifully odd hats, and when he spoke to people he didn't much like, he tended to be evasive, or short, if he answered at all. None of this helped at first, and Monk spent the years 1947 through 1955 under a virtual blackout, rarely performing and recording, known unto only a few of New York's hardcore be-boppers.

But Monk in the late 40's and early 50's acted as a magnet to younger musicians. His apartment -- now buried somewhere under Lincoln Center -- was a classroom, where, from a piano lodged between the kitchen and living room, he would dispense information. And if not at the piano, then in bed: Monk spent a good deal of time revealing, from his bed, the correct harmony to compositions for the second generation of New York's jazz be-bop intellectuals, including Jackie McLean, Sonny Rollins and Art Taylor. Through Monk's tutelage a set of rules congealed, an approach to harmony that exists to this day.

Monk, who had been in on the famous early be-bop sessions at Minton's, a Harlem nightclub, was soon recognized as a genius by musicians (marketing hyperbole aside, his first albums were called "Genius of Modern Music"), and he was an able teacher.

His public obscurity lasted some eight years, until he recorded "Thelonious Monk Plays Duke Ellington" in 1955, and from then until his death, in 1982, he was one of jazz's biggest stars, someone who could tour virtually anywhere. He became a concert attraction. Club engagements were packed, and he produced, in the 50's, a series of brilliant albums with odd covers that confirmed his status as an iconoclast with a sense of humor. In 1964, Time magazine put him on the cover as the high priest of be-bop.

All of this built an unfortunate sort of deification that has obscured his real contributions. His late success encouraged the idea that publically unacceptable art needed only time until the unenlightened public came to its senses and accepted it. Monk became, in the traditional European critical perspective prevalent at the time, a rule-breaker, the avant-guardist in the garrett. Because of his eccentricities, he became the image of a bohemian.

It's a perception laden with irony. Of all the great American artists to have developed during the 20th century, Monk more than most took the best elements of homespun entertainment and esthetics to cobble together something distinct to its time and place. Monk played in a circus band, and if his experience was typical, he probably played for strippers, dancers, weddings, church services, bar mitzvahs and just about anything else that American society could offer. If a mighty part of the American experience is excess and humor, Monk's music reflects it. If the American artistic experience at its best combines the populism of entertainment and the intelligence of the self-aware, Monk's music has it. And if the American experience has been the shaping of personal expression to make sense of a new environment, then Monk's music, with all its different elements does that, too.

Given that he usually performed with either a trio or a quartet, his music ranged over a variety of emotions. The ballads -- "Ugly Beauty," "Ruby, My Dear" and his best-known composition, " 'Round Midnight" -- are affirmations of tenderness and vulnerability in a culture that didn't open up much space for that until Miles Davis arrived with full force nearly a decade later.

As for his other tunes, a short list -- "Straight, No Chaser," "Hackensack," "Trinkle Tinkle," "Four in One," "Criss Cross," "Evidence," "Blue Monk" -- communicates the durability of his work. Unlike most jazz compositions, his pieces were rarely riffs, nor did they come out of Tin Pan Alley standards -- though his songs often borrowed some basic harmonies from tunes he liked. His pieces weren't meant to compete with standards, or to bear lyrics. They were meant to be taken for what they were, thoroughly composed pieces. Monk was after a specific world view, and he got it.

And the music is deceptive. Though it often appears to be simply constructed, with a melody, then improvisations on the harmony, the pieces are much more difficult to interpret. Monk's tempos are exceedingly difficult to play: everything is between the cracks, a bit faster or slower than the obvious would suggest, and without his tempos the compositions don't work as well.

Rhythmically, Monk was a master as well, using silence and hammered repetitions, or melodies whose accents get displaced, bar by bar, to impose his way of thinking on the world. It's that precision, that sense of craft, that meticulous control and self-awareness of the things he needed to get the affect he wanted, that allowed him to be brilliant.

Genius is a matter of consensus: craft isn't. It is his attention to the small specifics of music making -- all quantifiable, all on record -- that has allowed the consensus to be reached about his greatness. Avoid the myth, hear the music.

Photo: Thelonious Monk, who would have been 75 years old on Saturday. ("Eclecticism in Jazz"/Oxford University Press)