Thomas Collins, David Meredith,
"Maximal Translational Equivalence Classes of Musical Patterns in Point-Set Representations"
: Proceedings of Mathematics and Computation in Music (MCM 2013), 2013
Original Titel:
Maximal Translational Equivalence Classes of Musical Patterns in Point-Set Representations
Sprache des Titels:
Englisch
Original Buchtitel:
Proceedings of Mathematics and Computation in Music (MCM 2013)
Original Kurzfassung:
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.
Forschungs-