Generating Multiple Hierarchical Segmentations Of Music Sequences Using Adapted Correlative Matrices
Résumé
Segmentation is an important problem for music analysis, performance, perception, and retrieval. There is often more than one way to segment a piece of music, as reflected in the multiple interpretations of a piece of music. Here, we present an algorithm that can generate multiple hierarchical segmentations of a music sequence based on approximate repeated patterns. A relation between music objects defines this approximation to generate an adapted correlative matrix (ACM). Correlative matrices are data structures for representing repeated patterns that can overlap; ACMs constrain patterns to not overlap. We propose an algorithm that extracts meaningful information from ACMs to identify segmentations in a hierarchical way. Changing the relation produces alternate hierarchical segmentations of the same sequence. The algorithm iteratively selects patterns based on their distinctiveness, i.e. if other patterns begin with the same starting note or immediately after it. We apply this method to various musical objects: a sequence of notes, chords, or bars. In each case, we define different relations on these musical objects and test the method on musical examples to produce multiple hierarchical segmentations. Given a segmentation, the relation that produces that segmentation then gives a possible explanation for that segmentation.
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