Abstract
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) [1]. 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 [2]. 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.
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Collins, T., Meredith, D. (2013). Maximal Translational Equivalence Classes of Musical Patterns in Point-Set Representations. In: Yust, J., Wild, J., Burgoyne, J.A. (eds) Mathematics and Computation in Music. MCM 2013. Lecture Notes in Computer Science(), vol 7937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39357-0_7
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DOI: https://doi.org/10.1007/978-3-642-39357-0_7
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