Running to Catch the A-Train : DUKE ELLINGTON<i> by James Lincoln Collier (Oxford: $19.95; illustrated, 384 pp.) </i>

Edward Kennedy Ellington was arguably the most important composer-orchestra leader in the history of American jazz. His most ardent admirers would disagree and claim, with some justification, that Duke Ellington was the most important composer-orchestra leader in the history of American music.

Musical arguments may be resolved. Because recording was refined to an art form during his lifetime, Ellington compositions and orchestra--from the 1920s up to his death at age 75 in 1974--are preserved for future pleasure and dispute.

While the monumental body of work is with us, the life of the man is less easily resolved, left mostly to other people’s testimony.

The elusive Ellington was party to an autobiography, “Music Is My Mistress,” published by Doubleday & Co. in 1973, but the collaboration with writer Stanley Dance seems as much self-revising as self-revealing. A biography by Barry Ulanov in 1946 (“Duke Ellington,” Creative Age Press) and another collaboration involving Stanley Dance, this time with Ellington’s son Mercer in 1978 (“Duke Ellington in Person,” Houghton Mifflin), were also more comfortable when trying to translate the character of the music rather than the man.

Biographer James Lincoln Collier addresses his problem at the outset, using the usual words, “paradox,” “contradictions” and “mystery” to admit that the affable, urbane, apparently unruffled Ellington was essentially unknown to intimates and employees. The man is dead, and he did not leave behind the kind of words biographers like to analyze and interpret; he did not even leave a will that would have suggested the people he most treasured.

So Collier does the best he can, by surrounding the dead man with memories from other men and women. Those recollections reflect the complexities of character and the peculiar public characteristics of a private person: the easy-going man who managed to manipulate people without appearing to control them. The indifferent music student who devised his own methods of composing. The one-time arts student who turned away from the drawing board because making money and meeting women seemed simpler from the bandstand. The sophisticate who suffered such simple fears as drafts of outside air; the apparently outgoing Duke lived with his windows closed. The gourmand who had a silver serving spoon reserved for ice cream and sometimes liked it served ahead of steak. The gourmand who then grew vain enough and fat enough to switch to grapefruit and black coffee.

Such small matters hardly matter. To Collier’s credit, the biography deals more with real gifts rather than with perceived idiosyncrasies. And it dwells on the early years, through the ‘40s, at greatest length because those were the decades when Ellington emerged as a major force in American culture.

Unlike Louis Armstrong, who made his mark with his mouth attached to a trumpet, or Count Basie, whose legacy is an ensemble sound that “swung,” Ellington was writer, arranger, pianist and leader--all things musical to all listeners or what Collier calls “a master chef” who manages the entire creative operation. The orchestra was full of superior talents who made whole careers out of playing the Ellington library: Johnny Hodges, of the sour disposition but the most melodic alto saxophone; Harry Carney, of the dignified disposition and the heavy baritone sax; Cootie Williams, whose trumpet growled and whose personality sometimes also growled; Sonny Greer, a playful drummer on and off the stand; Ben Webster, a sweet and breathy-toned tenor saxophonist who turned mean when drunk; Billy Strayhorn, the classically trained composer-arranger who managed to teach Ellington some new elegance.

These musicians not only played the Ellington book, they helped create it, with greater or lesser credit coming from the leader at different times. Ellington wrote for them and to their strengths; most of them were never so famous as when they worked for Duke. Their stories are part of the biography and part of the chronology that started when a combo called the Washingtonians came to New York in the early 1920s. Ellington emerged as the leader in 1926 before the group was booked into Harlem’s famous Cotton Club. Collier writes about one major shift in priorities: In the early years Ellington’s composing was merely a means of giving the band something to play, with no notions of profundity or posterity. Only later, when he had played at Carnegie Hall and had played for royalty did Ellington claim that he kept his orchestra in order to hear his compositions played.

The context of the ‘20s and ‘30s is included, the gangsters who ran the nightclubs, the whites in the music business who both helped black musicians and exploited them, the way European music critics recognized jazz before American critics took it seriously.

Collier is a careful tracker and a controlled writer. This is not a biography by a fan. Collier can read scores as well as clippings, and there are fairly technical interpretations of what Ellington was doing--or trying to do--in the short jazz pieces and the extended concert works. He is not afraid to make value judgments: to suggest that Armstrong and Charlie Parker were greater influences on how instruments might be played; to insist that for all the pretensions of Ellington’s concert pieces--16 hours of recorded music plus serious compositions for film and theater--Ellington never did learn the techniques of constructing longer works nor did he like serious music as much as he liked the idea of being taken seriously; to evaluate the jazz pieces of the ‘40s--”Ko-Ko,” “Main Stem,” “Concerto for Cootie”--as superior to such earlier work as “Mood Indigo,” “Sophisticated Lady” and “Creole Love Call.”

The reader need not agree since the evidence is better heard than read. The reader conversant with the music may decide that the imperturbable leader was most deeply involved with submerging the person in favor of the personality. The public Ellington was what mattered--to him and to the audiences. The public Ellington wrote and performed his own American music, taught respect for the people who played it with him and gave jazz a dignity to accompany its drive. He was not always a good man, but he turned out to be a great one, this once-middle class, sometimes-lazy, partially educated black man who only wanted to enjoy a high life at the beginning but wound up leading a historic life instead.