Awork in which a satirist creates new, humorous lyrics for a well-known song would be an example of reduction ad absurdum caricature sarcasm parody

This would be an example of a parody. According to the dictionary, a parody is "a work created to imitate, make fun of, or comment on an original work". This would include making humorous lyrics for a well-known original song. One example of a well-known artist who makes parody music is Weird Al Yankovich. 

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