Extension and restriction: Difference between revisions

Line 1:

An '''extension''' of a [[regular temperament]] on a [[JI subgroup]] ''G'' to a larger subgroup ''G' '' is a new temperament that contains the same intervals as the original temperament, and ~~that the~~ [[rank]] remains the same, with the same JI interpretations in the subgroup ''G'', but gives them new JI interpretations not in the original subgroup (but are in the larger subgroup). The opposite of extension is '''restriction'''.

An '''extension''' of a [[regular temperament]] on a [[JI subgroup]] ''G'' to a larger subgroup ''G' '' is a new temperament that contains the same intervals as the original temperament, and whose [[rank]] remains the same, with the same JI interpretations in the subgroup ''G'', but gives them new JI interpretations not in the original subgroup (but are in the larger subgroup). The opposite of extension is '''restriction'''.

For example, [[septimal meantone]] and [[flattone]] are both extensions of [[5-limit]] (2.3.5) [[meantone]] to the [[7-limit]] (2.3.5.7), because C-E (4 fifths) represents [[5/4]] in both. They are different extensions, because in septimal meantone, 7/4 is C-A# (10 fifths), while in flattone, 7/4 is C-Bbb (-9 fifths).

Revision as of 11:21, 28 January 2023 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 18,317 edits m FloraC moved page Extension to Extension and restriction: The operation works both ways ← Older edit		Revision as of 18:29, 28 January 2023 view source Inthar (talk \| contribs) autopatrolled, emailconfirmed 15,004 edits grammar Newer edit →
Line 1:		Line 1:
	An '''extension''' of a [[regular temperament]] on a [[JI subgroup]] ''G'' to a larger subgroup ''G' '' is a new temperament that contains the same intervals as the original temperament, and ~~that the~~ [[rank]] remains the same, with the same JI interpretations in the subgroup ''G'', but gives them new JI interpretations not in the original subgroup (but are in the larger subgroup). The opposite of extension is '''restriction'''.		An '''extension''' of a [[regular temperament]] on a [[JI subgroup]] ''G'' to a larger subgroup ''G' '' is a new temperament that contains the same intervals as the original temperament, and whose [[rank]] remains the same, with the same JI interpretations in the subgroup ''G'', but gives them new JI interpretations not in the original subgroup (but are in the larger subgroup). The opposite of extension is '''restriction'''.

	For example, [[septimal meantone]] and [[flattone]] are both extensions of [[5-limit]] (2.3.5) [[meantone]] to the [[7-limit]] (2.3.5.7), because C-E (4 fifths) represents [[5/4]] in both. They are different extensions, because in septimal meantone, 7/4 is C-A# (10 fifths), while in flattone, 7/4 is C-Bbb (-9 fifths).		For example, [[septimal meantone]] and [[flattone]] are both extensions of [[5-limit]] (2.3.5) [[meantone]] to the [[7-limit]] (2.3.5.7), because C-E (4 fifths) represents [[5/4]] in both. They are different extensions, because in septimal meantone, 7/4 is C-A# (10 fifths), while in flattone, 7/4 is C-Bbb (-9 fifths).