What is the term for a musical idea that undergoes transformation through repetition or variation?

The term that describes a musical idea that undergoes transformation through repetition or variation is variation. Variations can take many forms, such as changing the melody, harmony, rhythm, or instrumentation, allowing the same musical idea to evolve and develop. This technique is often employed in compositions to maintain interest while providing a cohesive connection to the original theme.

While a theme serves as the foundational melodic or harmonic idea in a composition, it does not inherently imply the process of transformation. A motive refers to a short musical idea or fragment, which can also be varied, but the term itself specifically defines a smaller unit than a theme. A phrase represents a musical thought or statement, typically made up of several measures, and is not focused on the transformative process implied in the question. Thus, variation is the most accurate answer in the context provided.