Matt Hooker wrote:

>Ad libitum - well indeed - a latin phrase, from where the English
>language takes ad lib, to do something 'off the cuff' - to 'make it up'
>- to perform without preperation .....

I would add only this to your definition as it would apply to music ...
to make the performance SEEM as if it is being made up spontaneously.
The key word is 'seem' if it appears in the printed score. It is not
entirely made up by the performer (unless there are no written notes,
in which case the passage is usually called a 'cadenza.')

Mimi Ezust