How is The Art of Fugue organized around one main theme?

The Art of Fugue is a monothematic cycle composed by Johann Sebastian Bach that demonstrates his mastery of counterpoint. The work is organized around a single main theme introduced in the first movement, which serves as the foundation for the entire collection.1

Bach explores the potential of this subject through a series of approximately 20 fugues and canons, each increasing in complexity. To maintain unity while providing variety, he subjects the theme to various melodic and rhythmic transformations, including:21

• Augmentation and Diminution: Doubling or halving the rhythmic values of the notes.2
• Inversion: Reversing the upward and downward intervals of the melody.2
• Mirror Fugues: Creating movements where the second fugue is the exact mirror inversion of the first.2

By systematically applying these techniques, Bach illustrates the characteristic elements of the fugal form. The work culminates in a final, unfinished movement that incorporates a four-note motive based on his own name (B-A-C-H), serving as a signature for one of his final compositions.12