When a piece changes key, it is called a(n)?

The correct term for when a piece changes key is "modulation." Modulation refers to the process of shifting from one tonal center or key to another within a musical composition. This can enhance the emotional impact of the music, create contrast, or provide a fresh perspective on the material as it develops.

In music, modulation can occur in various ways, such as through a direct modulation (jumping to a new key) or a more gradual approach that prepares the listener for the transition. It serves to maintain interest and keep the listener engaged by exploring new harmonic territories.

Transposition, while related to changing the key, typically involves shifting an entire piece of music to a different key without altering the relationships between the notes. Variation refers to altering a theme in different ways, while development usually pertains to expanding or transforming themes or motifs, often found in sonata form. These concepts are distinct from modulation, which specifically indicates a change in key during the piece.