Maximal Translational Equivalence Classes of Musical Patterns in Point-Set Representations
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Representing musical notes as points in pitch-time space causes repeated motives and themes to appear as translationally related patterns that often correspond to maximal translatable patterns (MTPs) . However, an MTP is also often the union of a salient pattern with one or two temporally isolated notes. This has been called the problem of isolated membership . Examining the MTPs in musical works suggests that salient patterns may correspond more often to the intersections of MTPs than to the MTPs themselves. This paper makes a theoretical contribution, by exploring properties of patterns that are maximal with respect to their translational equivalence classes (MTEC). We prove that a pattern is MTEC if and only if it can be expressed as the intersection of MTPs. We also prove a relationship between MTECs and so-called conjugate patterns.
KeywordsPattern Discovery Motivic Analysis Repetition in Music Point-Set Patterns Music Analysis Geometric Music Representations
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