What a shift of meaning this humble if slightly exotic term has undergone. It started life in the sense of a topic for philosophical or theological discussion. It has since transformed its meaning to refer to a light-hearted medley of well-known tunes.
Though the first sense has fallen out of day-to-day use, it is given in dictionaries because philosophers at times have cause to refer to some medieval quodlibet, as here in The Review of Metaphysics of June 2003: “In his Quodlibet III, disputed in 1288, Giles of Rome asked ex professo whether the will could move itself.”
These disputations, frequently on subtle points of logic or religious doctrine, were often exercises or improvised oral examinations for students, in the same spirit as moots (mock court cases) are for the legal fraternity. This may be why this Latin word was given to them, as it derives from quod, what, plus libet, it pleases, so roughly “what pleases you” or “as you like”. It seems to have had much the same idea behind it as the modern hand-waving whatever — argue away, the word seems to be saying, the result is of little consequence.
How it got from philosophy to music is intriguing, not least because it didn’t happen in English. In the late Middle Ages in Germany, quodlibet started to be applied to a type of humour that featured daft lists of items loosely combined under an absurd theme — one example was objects forgotten by women fleeing from a harem. Something similar happened in France, where a quodlibet became a witty riddle — even today, avoir de quolibet means to produce clever repartee on demand.
The German idea of the humorous conglomeration was first applied to a musical composition by Wolfgang Schmeltzl in 1544 and the name later became the usual term in that language for facetious combinations of tunes haphazardly combined. Famous examples exist in works by Bach and Mozart in the eighteenth century. In this connection it certainly lives up to the idea behind the Latin word, since the aim is to produce a humorous amalgam of tunes to please the audience.
While the disputational sense is recorded in English from the twelfth century, the musical one only appears in 1845 and was clearly borrowed from German.