"Moonlight Serenade" was a popular musical recording from North America on Earth in 1939.
In the 24th century the song was included as part of the programming for the Dixon Hill holonovels which were based on the novels of the same name and set in San Francisco during that time period. The song was played in Rex's Bar when Dixon Hill and Madeline entered the establishment. (TNG: "Manhunt")
The song was by Glenn Miller and became his signature song.