Moonlight Serenade
From Memory Alpha, the free Star Trek reference
Moonlight Serenade was a popular musical recording by Glenn Miller, from North America on Earth in 1939. It has become his signature song.
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")
