Extension and restriction: Difference between revisions
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Created page with "An '''extension''' of a temperament on a JI subgroup ''G'' to a larger subgroup ''G' '' is a new temperament that contains all the intervals of the original temperament, w..." |
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An '''extension''' of a temperament on a [[JI subgroup]] ''G'' to a larger subgroup ''G' '' is a new temperament that contains all the intervals of the original temperament, with the same JI interpretations in the subgroup ''G'', but adds JI interpretations (and possibly new intervals if necessary) not in the original subgroup (but are in the larger subgroup). | An '''extension''' of a [[temperament]] on a [[JI subgroup]] ''G'' to a larger subgroup ''G' '' is a new temperament that contains all the intervals of the original temperament, with the same JI interpretations in the subgroup ''G'', but adds JI interpretations (and possibly new intervals if necessary) not in the original subgroup (but are in the larger subgroup). | ||
For example [[septimal meantone]] and [[flattone]] are both extensions of [[5-limit]] [[meantone]] to the [[7-limit]]. | |||
[[Category:Terms]] | [[Category:Terms]] | ||
Revision as of 12:05, 26 January 2021
An extension of a temperament on a JI subgroup G to a larger subgroup G' is a new temperament that contains all the intervals of the original temperament, with the same JI interpretations in the subgroup G, but adds JI interpretations (and possibly new intervals if necessary) not in the original subgroup (but are in the larger subgroup).
For example septimal meantone and flattone are both extensions of 5-limit meantone to the 7-limit.