Extension and restriction: Difference between revisions

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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'''.

An '''extension''' of a [[regular temperament]] of a [[JI subgroup]] to a larger subgroup 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 original subgroup, 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).

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	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'''.		An '''extension''' of a [[regular temperament]] of a [[JI subgroup]] to a larger subgroup 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 original subgroup, 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).