7L 4s: Difference between revisions

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7L 4s's generator range contains [[17/14]] and [[23/19]].

In the equal divisions which are in the size of hundreds, [[cohemimabila]] temperament is the first intepretation of 7L 4s of reasonable hardness (roughly semihard) through regular temperament theory. It is supported by [[43edo]], notable for being studied by [[Wikipedia:Joseph Sauveur|Joseph Sauveur]] due to harmonic strength, and [[111edo]], which is uniquely consistent in the 15-odd-limit. The generator is mapped to [[128/105]], and in higher limits it is tempered together with 17/14. ~~While not typical of regular temperament theory, the~~ scale can be made by using every other generator of the [[tertiaschis]] temperament, for example in [[159edo]].

In the equal divisions which are in the size of hundreds, [[cohemimabila]] temperament is the first intepretation of 7L 4s of reasonable hardness (roughly semihard) through regular temperament theory. It is supported by [[43edo]], notable for being studied by [[Wikipedia:Joseph Sauveur|Joseph Sauveur]] due to harmonic strength, and [[111edo]], which is uniquely consistent in the 15-odd-limit. The generator is mapped to [[128/105]], and in higher limits it is tempered together with 17/14.

The scale can be made by using every other generator of the [[tertiaschis]] temperament, for example in [[159edo]], which is realized as 2.9.5.7.33.13.17 subgroup 47 & 112 temperament, where it tempers out exactly the same commas as tertiaschis.

== Nomenclature ==

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 L 4s's generator range contains [[17/14]] and [[23/19]].
-In the equal divisions which are in the size of hundreds, [[cohemimabila]] temperament is the first intepretation of 7L 4s of reasonable hardness (roughly semihard) through regular temperament theory. It is supported by [[43edo]], notable for being studied by [[Wikipedia:Joseph Sauveur|Joseph Sauveur]] due to harmonic strength, and [[111edo]], which is uniquely consistent in the 15-odd-limit. The generator is mapped to [[128/105]], and in higher limits it is tempered together with 17/14. While not typical of regular temperament theory, the scale can be made by using every other generator of the [[tertiaschis]] temperament, for example in [[159edo]].
+In the equal divisions which are in the size of hundreds, [[cohemimabila]] temperament is the first intepretation of 7L 4s of reasonable hardness (roughly semihard) through regular temperament theory. It is supported by [[43edo]], notable for being studied by [[Wikipedia:Joseph Sauveur|Joseph Sauveur]] due to harmonic strength, and [[111edo]], which is uniquely consistent in the 15-odd-limit. The generator is mapped to [[128/105]], and in higher limits it is tempered together with 17/14.
+The scale can be made by using every other generator of the [[tertiaschis]] temperament, for example in [[159edo]], which is realized as 2.9.5.7.33.13.17 subgroup 47 & 112 temperament, where it tempers out exactly the same commas as tertiaschis.
 == Nomenclature ==