How does a fugue develop one main musical subject across several voices?

A fugue develops a main musical theme, known as the subject, through a systematic process of imitation across multiple voices.12

The Exposition

The process begins with the exposition, where the subject is stated by one voice alone. As this voice continues, other voices enter successively, typically alternating between the main key and the dominant key (the fifth degree of the scale). When the subject is transposed to the dominant, it is called the answer.1

Development and Techniques

Following the exposition, the subject is restated throughout the piece, often separated by connective passages called episodes. Composers develop the subject using various techniques:1
* Countersubject: A recurring counterpoint that accompanies the subject.1
* Stretto: Overlapping statements of the subject, where a new entry begins before the previous one has finished.3
* Melodic Manipulation: The subject may be varied through inversion (reversing the intervals), augmentation (doubling note values), or diminution (halving note values).3

These procedures allow the composer to create complex, symmetrical musical textures while maintaining the integrity of the original subject.12