The famous Hammerstein story is the one where Mrs. Jerome Kern and Mrs. Oscar Hammerstein are attending a luncheon party. Making the introductions, the hostess says, “Mrs. Kern’s husband wrote ‘Ol’ Man River,’” at which point Mrs. Hammerstein interjects: “My husband wrote ‘Ol’ Man River.’ Mrs. Kern’s husband wrote ‘Da-da dee-da.’”

Technically correct. But, in fairness to Jerome Kern, he wrote the tune first. In that sense, at least, he enabled the text of “Ol’ Man River”—for without those four notes the phrase would not exist. Mrs. Hammerstein’s somewhat touchy correction of her hostess applies more to his later work with Richard Rodgers. For score after score after score, Oscar Hammerstein sat down at his desk and produced some of the most effervescent song ideas in the American language without a bar of music to...