"Close Your Eyes" is a popular song and jazz-standard written by American composer Bernice Petkere. The song was published in 1933. The song is featured in the film The Abominable Dr. Phibes (1971), during a murder scene. The song was the end of transmission tune of Radio MonteCarlo in the '60's.
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http://en.wikipedia.org/wiki/Close_Your_Eyes_(1933_song)