Coherence and sameness in well-formed and pairwise well-formed scales
| Autor: | Norman Carey |
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| Rok vydání: | 2007 |
| Předmět: |
Discrete mathematics
Class (set theory) Applied Mathematics media_common.quotation_subject Scalar (physics) Scale (descriptive set theory) Ambiguity Coherence (statistics) Combinatorics Pitch class Computational Mathematics Cardinality Modeling and Simulation Pairwise comparison Music media_common Mathematics |
| Zdroj: | Journal of Mathematics and Music. 1:79-98 |
| ISSN: | 1745-9745 1745-9737 |
| DOI: | 10.1080/17459730701376743 |
| Popis: | A common theme running through many of the scale studies in recent years is a concern for the distribution of intervals and pitch classes. The question of good distribution becomes increasingly complex with the increase in parameters. Complexity increases when the cardinality, N, increases, and when the number of step sizes increases relative to cardinality. Complexity is also shown to be dependent upon the relative sizes of the step intervals. Two measures of scalar complexity are the properties known as difference and coherence. Difference rates a scale according to the number of distinct specific intervals it contains, whereas coherence concerns conflicts between generic and specific intervallic measures. There are two types of conflicts, ‘ambiguity’ and ‘contradiction’. This paper demonstrates that well-formed scales have, as a class, the highest coherence rank—fewest numbers of ambiguities or contradictions—for scales of a given cardinality. They are, then, in this sense, ‘minimally complex’... |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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