Whitney Balliett, jazz critic for The New Yorker for more than 30 years, is one of America's foremost jazz writers. "The most literate and knowledgeable living writer on jazz," Alistair Cooke called him, and Robert Dawidoff has written, "few people write as well about anything as Balliett writes about jazz." Two previous collections, American Musicians and American Singers, which gathered, respectively, Balliett's New Yorker profiles of jazz instrumentalists,...