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 | An '''extension''' of a [[temperament]] on a [[JI subgroup]] ''G'' to a larger subgroup ''G' '' is a new temperament that contains the same intervals as the original temperament, with the same JI interpretations in the subgroup ''G'', but adds JI interpretations not in the original subgroup (but are in the larger subgroup). | ||
For example | For example, [[septimal meantone]] and [[flattone]] are both extensions of [[5-limit]] (2.3.5) [[meantone]] to the [[7-limit]] (2.3.5.7). | ||
[[Category:Terms]] | [[Category:Terms]] | ||
Revision as of 12:10, 26 January 2021
An extension of a temperament on a JI subgroup G to a larger subgroup G' is a new temperament that contains the same intervals as the original temperament, with the same JI interpretations in the subgroup G, but adds JI interpretations not in the original subgroup (but are in the larger subgroup).
For example, septimal meantone and flattone are both extensions of 5-limit (2.3.5) meantone to the 7-limit (2.3.5.7).