The first four of J. S. Bach’s Fourteen Canons on the Goldberg Ground are more mathematical than musical. Rather than being developed pieces, they are written in the form of puzzles that instruct the reader in basic techniques used to form canons. I propose mathematical notation for representing two-part canons and use this notation to explore the first four Goldberg ground canons. My methods are independent of European common-practice music theory and can be used to create new canons of melodies, rhythms, or other features in different musical styles.