Extension and restriction: Difference between revisions

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An '''extension''' of a [[regular temperament]] from a [[JI subgroup]] to an expanded 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'''.

An '''extension''' of a [[regular temperament]] from a [[JI subgroup]] to an expanded subgroup is a new temperament that contains the same intervals as the original temperament, and whose [[rank]] remains the same, with the same representations of JI intervals of the original subgroup, but adding new JI interpretations not in the original subgroup (but which 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 05:58, 15 May 2025 view source Lériendil (talk \| contribs) autopatrolled, Interface administrators, Sysops 7,596 edits added further discussion about what exactly strong and weak extensions entail and how to easily identify them ← Older edit		Revision as of 05:59, 15 May 2025 view source Lériendil (talk \| contribs) autopatrolled, Interface administrators, Sysops 7,596 edits mNo edit summary Newer edit →
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	An '''extension''' of a [[regular temperament]] from a [[JI subgroup]] to an expanded 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'''.		An '''extension''' of a [[regular temperament]] from a [[JI subgroup]] to an expanded subgroup is a new temperament that contains the same intervals as the original temperament, and whose [[rank]] remains the same, with the same representations of JI intervals of the original subgroup, but adding new JI interpretations not in the original subgroup (but which 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).