Discovering Repeated Patterns from the Onsets in a Multidimensional Representation of Music

This article deals with the discovery of repeated patterns in a multidimensional representation of music using the theory of mathematical morphology. The main idea proposed here is to use the onsets to discover musical patterns. By definition, the morphological erosion of musical data by a musical pattern corresponds to its onsets. However, the erosion of musical data by the onsets is not always equal to the musical pattern. We propose a theorem which guarantees the equality if the musical pattern satisfies a topological condition. This condition is met when the patterns do not intersect, or only slightly, which is coherent in a musical context. Due to the importance of repetition in music, this idea proves to be relevant for the musical pattern discovery task.