Final answer:
A composition with strict imitation throughout is called a canon, a form of contrapuntal music known for its melody and imitations, which was particularly popular during the Renaissance within the madrigal genre.
Step-by-step explanation:
A composition with strict imitation throughout is called a canon. A canon is a piece of music where a melody is played and then imitated (repeated at a different pitch) by one or more parts after a short delay. It is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration. An example of a canon is the traditional song 'Frère Jacques'.
The mastery of the canon form can be observed during the Renaissance period, identified with the secular genre of the madrigal. Canons were often three-part secular pieces, prominently featuring the two higher voices in canon against a backdrop of instrumental accompaniment.