Jazz-critic Collier's (Louis Armstrong: An American Genius; The Making of Jazz) sharp, expert analysis of Ellington's music and character achieves a balance as elegant as that musician's finest work. As a boy, Ellington stood on the steps of his middle-class home and told his cousins, ""I am the grand, noble Duke. Crowds will be running to me."" According to Collier, Ellington, who at his death in 1974 left behind ""possibly the most significant body of work in jazz,"" succeeded ""not so much by raw talent"" as by ""the sheer force of his character."" He points out that many of the trademark songs (""Sophisticated Lady,"" ""Mood Indigo,"" ""Take the A-Train"") were written by band members, that Ellington was a technically poor pianist and an essentially lazy composer. Ellington used to say that he took up the piano to meet girls, and while the remark was usually perceived as ironic, Collier contends it was not. His great gift, Collier concludes, was that of a master chef: ""The chef does not chop all the vegetables himself. . .but he tastes everything, adjusts the spices, and in the end we credit him with the results."" Collier excels in bar-by-bar breakdowns of the major works, alternately praising and damning (the later, artsy ""extended pieces"" he dismisses as hopeless ""mishmash""). and energetically traces Ellington's colorful career. A colleague describes Ellington as the kind of man who ""built a wall around himself,"" and his autobiography, Music is My Mistress, is generally regarded as less than candid. His story, however, is rendered unflinchingly here.