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At the conclusion of Kubrick's classic Dr. Strangelove there's a ballet of nuclear explosions set against a wistful "We'll Meet Again". The result was the quintessence of black comedy. More recently, the pairing of music and repetitive declassified atomic test footage has become a genre unto itself.
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Pure Armageddon abandonment Here
Same footage, different soundtrack Here
Mash-Up style Here
Holocost gone Classical Here
Extremely scary underground blast Here
...and more Here, Here, & Here
Below is my favorite (yet not entirely musical) clip which pits mannequins -"Mr. and Mrs. America"- against a very severe atomic heat rash.