The Art of the Fugue is a collection of 18 fugues and cannons written by Johann Sebastian Bach in the 1700s. Each piece starts with a single theme which is transformed, developed, and mixed in fascinating mathematical combinations resulting in a distinctive musical style. In this paper, we use the method introduced in Nita et al. (UMAP J 45(1):41–56, 2024) to analyze 14 pieces from The Art of the Fugue. We focus on the variation of motifs from one piece to another as well as the complexities of mathematical transformations present throughout the entire collection. We also demonstrate how using maps of transformations and the rules of counterpoint could guide non-musicians to compose original pieces in the style of Bach’s fugues.