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.
| Original language | English |
|---|---|
| Title of host publication | Proceedings of Mathematics and Computation in Music (MCM 2013) |
| Number of pages | 12 |
| Publication status | Published - 2013 |
Fields of science
- 102 Computer Sciences
- 102001 Artificial intelligence
- 102003 Image processing
JKU Focus areas
- Computation in Informatics and Mathematics
- Engineering and Natural Sciences (in general)