Final answer:
The cerebellum coordinates the hand movements needed to play the piano, controlling balance and movement precision.
Step-by-step explanation:
The hand movements that musicians use when playing the piano are most likely coordinated by the cerebellum. The cerebellum is a part of the brain situated at the base, just below the cerebrum and behind the brainstem. It is responsible for coordinating body movements and is particularly involved in movements that are learned through repeated practice, such as playing a musical instrument. While the peripheral nervous system also plays a role in coordinating finger movements and synchronizing them, especially in complex activities like two people playing the same piano, it is the cerebellum that controls balance and aids in coordinating precise movement and learning new motor tasks.