I grew up watching the imported science fiction show, Doctor Who. The Doctor is a time-traveling alien who has an affinity for Earth, and a penchant for running into trouble and setting things right in every episode.
Part of what set the tone and character of the show was its eerie theme song, and it is something that vies for “that song that runs through your head all the time”.
The process spearheaded by Delia Derbyshire in recording this theme song was a long and groundbreaking one. Considering the sort of equipment they were working with, the result sounds utterly unlike anything that can be done with a regular or synthesized instrument. The work that went into even one second worth of the recording and the conscious attention to every detail makes it a masterpiece.
[edit: changed video to one that works]