In the 1870s, Arthur Sullivan was a rising young composer whose reputation was growing steadily. At the same time, William S. Gilbert was a rising young dramatist whose plays were attracting an increasingly wider audience. They lived in the same city, they had friends in common, and each probably knew of the other’s work—we know Gilbert had heard Sullivan’s music, because he had reviewed Sullivan and Burnand’s operetta, Cox and Box, as the theater critic for Fun magazine. They had even collaborated on a Christmas entertainment, Thespis, or The Gods Grown Old. It was a successful venture in its limited way, but both men evidently considered the project a one-off.…