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). 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 reveals that salient patterns may correspond more often to the intersections of MTPs than to the MTPs themselves. We therefore explore 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. MTECs could therefore solve the problem of isolated membership. We also prove a relationship between MTECs and so-called conjugate patterns.
Originalsprog | Engelsk |
---|---|
Titel | Mathematics and Computation in Music : 4th International Conference, MCM 2013, Montreal, QC, Canada, June 12-14, 2013. Proceedings |
Antal sider | 12 |
Forlag | Springer Publishing Company |
Publikationsdato | 2013 |
Sider | 88-99 |
ISBN (Trykt) | 978-3-642-39356-3 |
ISBN (Elektronisk) | 978-3-642-39357-0 |
DOI | |
Status | Udgivet - 2013 |
Begivenhed | International Conference on Mathematics and Computation in Music - Schulich School of Music, McGill University, Montreal, Canada Varighed: 12 jun. 2013 → 14 jun. 2013 Konferencens nummer: 4 |
Konference
Konference | International Conference on Mathematics and Computation in Music |
---|---|
Nummer | 4 |
Lokation | Schulich School of Music, McGill University |
Land/Område | Canada |
By | Montreal |
Periode | 12/06/2013 → 14/06/2013 |
Navn | Lecture Notes in Computer Science |
---|---|
Vol/bind | 7937 |
ISSN | 0302-9743 |