It is not true, as Collier claims in his preface, that there has been ""no full-dress history"" of jazz, the most recent contender being Frank Tirro's rather stuffy Jazz: A History (1977). However, if Collier is not alone, he is way out ahead, since he has covered all of jazz's major sounds and personalities while avoiding nearly every misstep made by jazz-book writers: he is niether jivey nor academic, neither afraid to get technical nor prone to overanalyze, neither obsessed nor uncomfortable with the black/white tension in jazz's cultural history. Confidently, he begins with African music--the off-pitch notes and cross-rhythms that will be crucial forces--but he refuses to minimize the input of European forms. He examines the myths and the counter-theories, often finding that the myth is closest to the truth. (Jazz really did start in New Orlenas and float up the Mississippi.) His balance and precision--especially in such touchy areas as Creole vs. black New Orleans influences--rarely flag as his subject branches out and around, and his serviceable style rises to perceptive eloquence when faced with a Benny Goodman in need of defending, an Ellington (""character. . . counted for more than talent""), or jazz's two ""authentic geniuses""--Louis Armstrong and ""a sociopath named Charlie Parker"" (""How can the art be so gracious, the artist so crabbed?""). Tasteful use is made of a cautious psychological approach to mini-biography, and the attentive layman will get the best possible explanation of such technicalities as Coleman Hawkins' ""playing against the chords."" Some may argue with Collier's refusal to discuss more than a few vocalists in detail (Ella Fitzgerald and her ilk are literally too square) or with his conservatism (""Jazz needs a respite from experiments""), but by thoroughly absorbing what everyone else has written and then listening freshly with his own ears, he has come up with the best comprehensive and detailed study on the charts.