The rise of 'Satchmo': no one else's art echoed more widely; Louis Armstrong: An American Genius, by James Lincoln Collier. New York: Oxford University Press. 383 pp. $19.95.

It was an extraordinary half dozen years for the arts. T.S. Eliot's ''The Waste Land.'' James Joyce's ''Ulysses.'' Arnold Schoenberg's 12-tone method of musical composition. George Gershwin's ''Rhapsody in Blue.'' Thomas Mann's ''The Magic Mountain.'' Franz Kafka's ''The Trial.'' F. Scott Fitzgerald's ''The Great Gatsby.'' The first talking movies. Ernest Hemingway's ''The Sun Also Rises.''

And Louis Armstrong's move up the Mississippi.

Chicago and a wider world began to hear the young man who had learned music at the Colored Waifs' Home in New Orleans. He played with King Oliver's Creole Jazz Band, swung in and out of New York, and went back to Chicago for those first great flurries of innovative recordings that remain landmarks in 20 th-century music.

No one would try to rank the apples and oranges of literary and artistic achievement in those rich few years from 1922 to 1927. But, as James Lincoln Collier traces the influence of Armstrong's eloquent horn on later music of various kinds, it seems clear that no one else's art of the time has echoed more widely to more people.

Yet to Armstrong, Collier argues, his mastery of melody and improvisation was not art but entertainment, one of the few accepted options for black Americans in those days. And this explains why Armstrong did not ''sell out,'' as some jazz devotees lamented, when he left those peak recordings behind and became a well-paid commercial performer full of grins and showboating high notes. He was simply trying to entertain as always, even when the result of his enormous talent was sublime.

Unalloyed jazz was not the object, as the purists demanded. Armstrong rarely used the jazz label. The goal was music to please the people. Thus Armstrong's celebrated fondness for Guy Lombardo's ''sweetest music this side of heaven'' was not the mockery that jazz fans supposed. Nor were his own audiences at home and abroad limited to jazz fans.

It is too bad that Collier does not always display the ear for prose that he does for the nuances of Armstrong's playing and singing. His earlier book, ''The Making of Jazz,'' covered much historical ground quite efficiently. ''Louis Armstrong'' is often loose and repetitious, with even the misspelled ''vocal chords'' slipping through in discussion of Armstrong's marvelous gravelly voice. The book's admitted speculation on some matters is not very helpful.

Yet Collier avoids typical jazz-bio romanticization. He finds evidence to doubt previously published data such as Armstrong's birth on the Fourth of July in 1900. Indeed, he revises some Armstrong information in ''The Making of Jazz.'' The musician's hard early years in the midst of New Orleans's low life and his later successes and setbacks are placed in a broadly tempering perspective. And some lingering myths about jazz are sharply challenged:

* That jazz, scorned in its native land, was first appreciated in Europe. Some American musicians still say the quality of appreciation is higher abroad. But Collier shows that American critics and public were well ahead of Europe in recognizing their own music.

* That jazz musicians are most inspired at four in the morning in smoky nightclubs. Collier finds that few ''live'' recordings have proved better than the players' best work in recording studios.

* That jazz was originated by black people for black audiences in the ghetto. Collier finds that black as well as white jazz had a substantial white audience right from the beginning. Some black stars played mainly for white audiences during their whole careers.

To look at the deprivation of Armstrong's youth is to marvel at how a career like his could rise out of it, how he had so much joy left to share.

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