quodlibet

noun

1. an academic debate or exercise in argument, esp. on a theological question
2. a humorously incongruous musical parody, esp. of well-known melodies or texts

Etymology: LME < ML quodlibeta, disputation < L quod libet, as you will < quod, neut. of qui, who + libet, 3d pers. sing., pres. of libere, to please