Saturation, torsion, and contorsion: Difference between revisions
Cmloegcmluin (talk | contribs) use "saturation" in visible text to user in the saturation section, but change the links under the hood to go to the pages which were written using the term "defactor"; no need for the redirect pages that were only used for this purpose |
Cmloegcmluin (talk | contribs) →Contorsion: contorted order |
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== Contorsion == | == Contorsion == | ||
'''Contorsion''' is used to refer to the opposite of saturation, but only regarding mappings; in other words, a mapping is either saturated, or it ''has contorsion'' (or we can say that it ''is contorted''). | '''Contorsion''' is used to refer to the opposite of saturation, but only regarding mappings; in other words, a mapping is either saturated, or it ''has contorsion'' (or we can say that it ''is contorted''). The greatest factor of a mapping has been called its '''contorted order'''. | ||
Contorted mappings represent a different sort of pathology from comma bases with torsion: they involve tuning systems for which some pitches are unmapped, i.e. no just intonation interval maps to them. Contorted mappings can be useful in a way that unsaturated comma bases can not: these matrices do at least represent temperament-like systems with sensible notions of pitch. When compared to the temperament that is represented by the saturated version of the same mapping, they simply have these extra unmapped pitches that no just ratio tempers to. | Contorted mappings represent a different sort of pathology from comma bases with torsion: they involve tuning systems for which some pitches are unmapped, i.e. no just intonation interval maps to them. Contorted mappings can be useful in a way that unsaturated comma bases can not: these matrices do at least represent temperament-like systems with sensible notions of pitch. When compared to the temperament that is represented by the saturated version of the same mapping, they simply have these extra unmapped pitches that no just ratio tempers to. | ||