79edo: Difference between revisions

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Using the [[patent val]], it [[tempering out|tempers out]] [[3125/3072]] in the 5-limit, [[1728/1715]], [[4000/3969]] and [[4375/4374]] in the 7-limit, [[99/98]], [[243/242]], [[385/384]], 1331/1323, and [[4000/3993]] in the 11-limit, and [[169/168]], [[275/273]], [[325/324]], [[351/350]], [[640/637]], [[1188/1183]], [[1575/1573]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It provides the [[optimal patent val]] for the [[sentinel]] temperament.

79edo's fifth is very close to [[1/7-comma meantone]], but 79edo does not support [[meantone]] in its [[patent val]]. This is because 79edo's fifth is very close to [[12edo]] and stacking 4 fifths upwards results in a sharp approximation of 5/4 which is not the best approximation. The best 5/4 is actually reached by stacking a whopping 16 fifths up (a doubly-augmented second), which corresponds to the [[python]] temperament. On the other hand, the 79c val uses the second-best approximation of 5/4 and thus [[~~support~~]]s [[~~meantone~~]].

79edo's fifth is very close to [[1/7-comma meantone]], but 79edo does not [[support]] [[meantone]] in its [[patent val]]. This is because 79edo's fifth is very close to [[12edo]] and stacking 4 fifths upwards results in a sharp approximation of 5/4 which is not the best approximation. The best 5/4 is actually reached by stacking a whopping 16 fifths up (a doubly-augmented second), which corresponds to the [[python]] temperament. On the other hand, the 79c val uses the second-best approximation of 5/4 and thus supports [[meantone]]. The 79c val also supports [[superpine]], a weak extension of meantone.

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 Using the [[patent val]], it [[tempering out|tempers out]] [[3125/3072]] in the 5-limit, [[1728/1715]], [[4000/3969]] and [[4375/4374]] in the 7-limit, [[99/98]], [[243/242]], [[385/384]], 1331/1323, and [[4000/3993]] in the 11-limit, and [[169/168]], [[275/273]], [[325/324]], [[351/350]], [[640/637]], [[1188/1183]], [[1575/1573]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It provides the [[optimal patent val]] for the [[sentinel]] temperament.
-edo's fifth is very close to [[1/7-comma meantone]], but 79edo does not support [[meantone]] in its [[patent val]]. This is because 79edo's fifth is very close to [[12edo]] and stacking 4 fifths upwards results in a sharp approximation of 5/4 which is not the best approximation. The best 5/4 is actually reached by stacking a whopping 16 fifths up (a doubly-augmented second), which corresponds to the [[python]] temperament. On the other hand, the 79c val uses the second-best approximation of 5/4 and thus [[support]]s [[meantone]].
+edo's fifth is very close to [[1/7-comma meantone]], but 79edo does not [[support]] [[meantone]] in its [[patent val]]. This is because 79edo's fifth is very close to [[12edo]] and stacking 4 fifths upwards results in a sharp approximation of 5/4 which is not the best approximation. The best 5/4 is actually reached by stacking a whopping 16 fifths up (a doubly-augmented second), which corresponds to the [[python]] temperament. On the other hand, the 79c val uses the second-best approximation of 5/4 and thus supports [[meantone]]. The 79c val also supports [[superpine]], a weak extension of meantone.
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79edo: Difference between revisions

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