Which term refers to performing at the liberty of the performer?

The term "ad libitum" is derived from Latin, meaning "at one's pleasure." In music, it indicates that the performer has the freedom to adjust the tempo, dynamics, or even omit certain parts of the score as they see fit. This permission allows for personal expression and creativity, enabling musicians to interpret the piece in a way that feels more authentic to them.

In contrast, other terms in the options have specific meanings related to tempo or style but do not convey the same sense of liberty. "Ritardando" directs the musician to gradually slow down the tempo, indicating a specific instruction rather than the freedom to choose. "Alla" is often used in phrases like "alla marcia," referring to a style or manner of playing, not individual interpretation. "Animato," which means animated or lively, instructs the performer to play with enthusiasm but does not provide the same level of flexibility as ad libitum.

Thus, ad libitum appropriately encapsulates the idea of performing at the liberty of the performer, allowing for personal expression within the performance.