Extension and restriction: Difference between revisions
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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]], [[flattone]] and [[godzilla]] are all extensions of [[5-limit]] (2.3.5) [[meantone]] to the [[7-limit]] (2.3.5.7). | For example [[septimal meantone]], [[flattone]] and [[godzilla]] are all extensions of [[5-limit]] (2.3.5) [[meantone]] to the [[7-limit]] (2.3.5.7). [[Mohajira]] is naturally viewed as an 2.3.5.11 extension of 5-limit meantone. | ||
[[Category:Terms]] | [[Category:Terms]] | ||
Revision as of 12:08, 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, flattone and godzilla are all extensions of 5-limit (2.3.5) meantone to the 7-limit (2.3.5.7). Mohajira is naturally viewed as an 2.3.5.11 extension of 5-limit meantone.