How does a fugue use melodic imitation to develop a musical subject?

A fugue develops a musical subject—a principal theme—through the systematic use of imitation across multiple melodic lines, or counterpoint.1

The process typically unfolds as follows:

• Exposition: The subject is introduced by a single voice. As it continues, other voices enter successively, stating the subject (often transposed as an answer in the dominant key) while the previous voices continue with accompanying counterpoint.2
• Contrapuntal Interaction: If a specific counterpoint consistently accompanies the subject, it is called a countersubject. Composers often ensure this relationship is invertible, meaning the lines work effectively whether the subject is above or below the counterpoint.2
• Development: Following the exposition, the subject is restated periodically in different voices and keys. These statements are often separated by episodes, which are connective melodic passages.2
• Advanced Techniques: Composers may further develop the subject through various treatments, including:
  • Inversion: Moving the melody in the opposite direction.3
  • Augmentation: Lengthening the note values of the subject.3
  • Stretti: Overlapping entrances of the subject.3
  • Cancrizans: Presenting the subject backward, note for note.3