The discovery of patterns in a point-set representation of music consists in identifying repeating subsets of points. In this task, musical symbolic data is modeled as a discrete set of points, usually in  \(\mathbb {R}^n\) , where each point represents a musical note and its coordinates represent the characteristics of the note, such as its onset or its pitch value. While numerous algorithms have been developed to discover all exact repetitions and extract musically relevant patterns, recent research has turned toward the discovery of patterns that repeat with some variations. Because the morphological erosion of a pattern provides its occurrences, we propose an adaptation of this operation to also obtain its variations with respect to a given approximation. This approach not only reveals certain variations of the pattern, but also enables to associate specific points to the pattern despite the fact that they were not initially present due to the constraints of strict repetition. We demonstrate that the proposed formalism satisfies certain fundamental properties for the musical pattern discovery task, such as the fact that iterating erosion produces cycles of patterns and its translation values. Finally, we apply these operations to the corpus of fugues from Bach’s Well-Tempered Clavier, highlighting the usefulness of the proposed approach.