What is the musical term for a statement of a motive in another voice or hand?

The term that refers to a statement of a motive in another voice or hand is known as imitation. This concept is fundamental in various musical forms, particularly in counterpoint and polyphonic music, where a theme or motif introduced by one voice is subsequently repeated by another voice, often with some variation in pitch or rhythm.

Imitation helps create texture and complexity in music, allowing for the development of polyphonic structures where multiple independent voices interact harmoniously. Recognizing imitation is essential for understanding compositional techniques across different styles and periods in music.

In contrast, other terms like countermelody refer to an additional melody played alongside the main melody, which enhances rather than echoes it. Repetition, while it refers to the exact restatement of a motif, does not involve a different voice or part taking it up. Theme generally describes the main melodic idea of a piece, not specifically its re-presentation in another voice.