Date of Award
5-2025
Document Type
Thesis
Degree Name
Master of Science (MS)
College/School
College of Science and Mathematics
Department/Program
Mathematics
Thesis Sponsor/Dissertation Chair/Project Chair
Bogdan G. Nita
Committee Member
Ashwin Vaidya
Committee Member
Deepak Bal
Abstract
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 [7] 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.
File Format
Recommended Citation
Cellar, Joshua, "Analysis and Mathematical Recomposition of The Art of the Fugue" (2025). Theses, Dissertations and Culminating Projects. 1574.
https://digitalcommons.montclair.edu/etd/1574