MILES DAVIS came as a shock.When he and I were in our Midwestern high schools 50 years ago, jazz had the grin of Louis Armstrong, the tousled hair of Gene Krupa, and the zoot suits with the draped shapes and reet pleats of musicians who looked as if they were having fun. When I finally got inside a New York jazz club in the next decade, Miles was on the bandstand, dark suit tailored for Wall Street, not a hair out of place, certainly no grin, and no hint of trying to please the crowd that was hanging on his every parsimonious note. At least he was holding his trumpet straight ahead, not pointing it at the floor as he often did in later years, avoiding eye contact entirely. "It was as if Einstein had been asked to lecture on the quantum theory to a class of backward teenagers," to quote British critic Kenneth Tynan on another Miles moment at the microphone. But here he was more like someone with a job to do who knew he was doing it well and would let it speak for itself - as it did, causing a future jazz chronicler to call his trumpet style the most widely, if vainly, imitated one in history. Just the music, please. No sales talk. No amiable bopping around like Dizzy Gillespie, whom Miles succeeded in superstar Charlie Parker's band. No show biz. Or was it show biz in spite of itself? This cat was cool. Soon cool was the thing to be, and on some bandstands cool was hard to distinguish from ordinary contempt. If cool conduct, why not cool music? Hot jazz was for the mouldy figs. Soon came Miles's short-lived Nonet, a nine-piece band whose smooth unhackneyed sound included a French horn and a tuba playing with the saxes instead of doing oom-pahs. The Nonet's recordings were gathered as "The Birth of the Cool." Their legacy was a whole West Coast school of cool jazz. "They called it cool, but we were just trying to do some new things," said pianist and composer John Lewis of the Modern Jazz Quartet when I asked him about his days with Miles and the Nonet. "We were all young and running around to Gil Evans's basement apartment." Evans was the innovative arranger who went on from the Nonet to such landmark Davis recordings as "Sketches of Spain" and "Porgy and Bess," virtually recomposing the source material from classical guitar music and George Gershwin's opera. Miles had called John Lewis back from a stay in Paris to join in the new musical explorations. Lewis recalled Miles as his oldest friend in New York. It was through Davis that Lewis got his first date playing with Charlie Parker. "Miles was a catalyst," said Lewis. "He made wonderful things come out of the people who worked with him." Among those people were saxophonists John Coltrane and Cannonball Adderley, drummer Philly Joe Jones, pianist Red Garland, bassist Paul Chambers, and the young virtuosos Miles had recruited by the next time I heard him live, now at a jazz club outside of Boston in the '60s. The sober suit had given way to more casual elegance, the existence of the audience was recognized, and the news was the title of a recording called "Miles Smiles a wry apology perhaps for the scowls and epithets and Prince of Darknes s image known around the world. The new team: Herbie Hancock, piano; Ron Carter, bass; Tony Williams, drums; Wayne Shorter, saxophone. Before long they all had their own bands, and it was time for Miles to make wonderful things come out of another crew. Not that everybody praised all of Miles's work It's mouse music, man," said Roy Eldridge, who played hot, high, and happy in the lineage of great trumpeters traced back from Davis to Gillespie to Eldridge to Armstrong to King Oliver to New Orleans's legendary Buddy Bolden whose horn could be heard across Lake Pontchartrain before there were microphones. A second trumpet line branches off from Bolden and Oliver and comes down through the Ellington trumpeters Bubber Miley and Rex Stewart in a family tree p repared by composer and musicologist Gunther Schuller - who happened to play French horn in Miles's Nonet. The other night I heard a bit of how Miles worked with people in tape made during a rehearsal. The sandpapery voice was quietly encouraging the drummer to do some little thing exactly right. I thought of all the stories about new musicians being summoned to a rehearsal or recording session and never quite being sure what they were supposed to do. Guitarist John McLaughlin recalled Miles's advice on "In a Silent Way": "Play it like you don't know how to play the guitar." Bassist Dave Holland recalled another nudge to creativity: "Don't play what's there. Play what's not there." Some said Miles conducted virtually by ESP (the title of one of his albums), letting people know by the merest musical hint or gesture which way to go. And he kept changing where he wanted to go, even as he spent some off hours at the boxing gym and some at the painter's easel. First it was reinterpreting the blues and familiar tunes in his eloquent middle register, often tightly muted into a shimmering filament of sound. Then it was constructing new pieces that began and ended where he felt like it, not necessarily after the standard 12 or 32 measures. Sometimes he reversed the jazz custom of setting a melodic pattern for the horns and letting the drums and bass improvise an accompaniment: Now he set a meticulous repeated pattern for the drums and bass and let the horns find t heir own melodies. THE next time I saw Miles was at a Boston Globe Jazz Festival, and he was beginning to go electric and free-form. Chick Corea was playing electric piano - another brilliant young musician who would soon be traveling the world with his own group. Instead of doing several - or even a few - tunes, Miles kept the musicians boiling in a single continuous improvisation of about 45 minutes. That's what he did a dozen years later, too, when he chose the Kix club in Boston to start a much-heralded return from a lengthy period of seclusion. But now an electric guitar and bass were adding to the post-jazz sound, which Miles had begun to create with an infusion of rock rhythms long before his temporary retirement. And now the Gentleman's Quarterly one-time "Fashion Personality for the Month of May" was wearing white coveralls; jabbing at a keyboard as well as playing an amplified trumpet in quick bursts and an occasional lingering and beautiful lament; clearing the room after a very short set; and leaving some of us feeling short-changed after all the anticipation of his return. If Count Basie was known as the Matisse of jazz, and Duke Ellington the Picasso, then on this occasion Miles was the Jackson Pollock. But he never stayed anything for too long. A while ago a musician friend told me how wonderful Miles was at Switzerland's Montreux Jazz Festival playing a tune of Cyndi Lauper's. Cyndi Lauper's! And just last year Miles filled the stage with amplification equipment and rock-show lighting at the Boston Symphony Orchestra's Tanglewood summer home in the Berkshires of Massachusetts. Previous jazz acts had been muddily amplified. But Miles's sound was perfect - loud but perfect. And the music was precisely performed even if not as marvelously subtle, textured, and swinging as the old "Milestones" or "Kind of Blue" albums. The latter is celebrated as a tour de force of "modal" improvising. It is based on scales instead of the usual chords, but, like so much of Miles, it stays in touch with the roots of jazz in the call-and-response feeling of Southern field hollers and gospel preaching. London biographer Ian Carr called it "perhaps the most influential single album in jazz history." Earlier a French critic, Andre Hodeir, had found in Miles's playing "a completely new swing phenomenon." It is what Hodeir called the "dancing note," when Miles - known for playing without vibrato - gained a dynamic "off center" rhythmic effect by playing certain notes with a touch of vibrato. I didn't know the orchestrated din at Tanglewood would be the last time I would hear Miles, who passed on recently, in person. I wish I'd remembered to listen for the dancing notes.