Extension and restriction: Difference between revisions

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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).

A '''strong extension''' is an extension in which the generators are not split compared to the original temperament. The structure of a strong extension is not changed, and no new intervals are introduced. A '''weak extension''' is one in which the generators are split.

A '''strong extension''' is an extension in which the generators are not split compared to the original temperament. The structure of a strong extension is not changed, and no new intervals are introduced. A '''weak extension''' is one in which the generators are split. Thus an extension is strong if and only if its [[pergen]] is the same as the original temperament's pergen.

For example, both septimal meantone and flattone are strong extensions of 5-limit meantone since they all share the same period and generator. [[Godzilla]] is a weak extension of meantone but a strong extension of [[semaphore]].

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 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).
-A '''strong extension''' is an extension in which the generators are not split compared to the original temperament. The structure of a strong extension is not changed, and no new intervals are introduced. A '''weak extension''' is one in which the generators are split.
+A '''strong extension''' is an extension in which the generators are not split compared to the original temperament. The structure of a strong extension is not changed, and no new intervals are introduced. A '''weak extension''' is one in which the generators are split. Thus an extension is strong if and only if its [[pergen]] is the same as the original temperament's pergen.
 For example, both septimal meantone and flattone are strong extensions of 5-limit meantone since they all share the same period and generator. [[Godzilla]] is a weak extension of meantone but a strong extension of [[semaphore]].