The 41 jazz pieces in this collection appeared in The New Yorker between 1957 and 1962. Some have been revised; none has been reprinted before. Balliett is a fine writer and an apt listener. But this consists for the most part of portraits and sound analyses which have been done ad nauseum. Balliett has said the definitive couple of words re Lester Young -- ""a perfect balance between tension and relaxation"" -- but one must wade first through paragraph upon paragraph on how Pres held his sax, what he did in the first chorus, how his vibrato was different from all other vibratos, and why his imitators have failed miserably. Other personality pieces parallel this one pretty closely. There is precious little left to say about Billie Holiday, Theolonious Monk, Django Reinhardt, Coleman Hawkins, Humphrey Lyttelton, or the new Sonny Rollins. Balliett's criticism -- however fine and mellow it may be -- will have meaning only to a select few.