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"That Old Black Magic" was a song published in 1942 on Earth.

In 2285, an instrumental version of the song was played in the San Francisco bar Doctor Leonard McCoy visited to charter a ship for a journey to the Genesis Planet. (Star Trek III: The Search for Spock)

In 2374, Seven of Nine sang the song during a holographic simulation of World War II in which her mind was altered by a hostile alien species, the Hirogen, to believe she was a French night club singer in 1944 occupied France. She was nearly through the third line when the mind control was broken, at which point she no longer remembered what she had been doing or the words to the song and was forced to abruptly halt her performance. (VOY: "The Killing Game")

In 2376, it was performed by The Doctor and Harry Kim and his jazz band called Harry Kim and the Kimtones. The band began by performing the song instrumentally during a recital for the Qomar, but the Qomar in the audience booed them because they only wished to hear The Doctor perform. Concerned because his friends were being ridiculed, Tom Paris asked The Doctor to help them. He did so by jumping on stage and instructing the band to pick up the pace, at which point he began singing the lyrics to the song, helping Kim and the band save face. The Qomar enjoyed this greatly and the performance still became a success. (VOY: "Virtuoso")

Lyrics (excerpt)

That old black magic has me in its spell, that old black magic that you weave so well.
Those icy fingers up and down my spine
That same old witchcraft when your eyes meet mine.
The same old tingle that I feel inside, and then that elevator starts its ride
And down and down I go, round and round I go, like a leaf that's caught in the tide.

"That Old Black Magic" was composed by Harold Arlen with lyrics by Johnny Mercer.
It was about humanoid love defying logical analysis. (Star Trek Encyclopedia (4th ed., vol. 2, p. 389))

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