79edo: Difference between revisions
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79edo works well as a no-7 13- or 17-[[limit]] tuning. It is in fact [[consistent]] to the no-7 [[13-odd-limit]], even though it is a [[zeta valley edo]] (notably, it is the last one until [[5941edo]]). | 79edo works well as a no-7 13- or 17-[[limit]] tuning. It is in fact [[consistent]] to the no-7 [[13-odd-limit]], even though it is a [[zeta valley edo]] (notably, it is the last one until [[5941edo]]). | ||
=== | === Odd harmonics === | ||
Using the [[patent val]], | {{Harmonics in equal|79}} | ||
=== As a tuning of other temperaments === | |||
Using the [[patent val]], 79edo [[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 supports [[meantone]]. The 7-limit 79c val also supports [[superpine]], a [[weak extension]] of meantone that splits the perfect fourth into 3 [[35/32]]s. | 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 7-limit 79c val also supports [[superpine]], a [[weak extension]] of meantone that splits the perfect fourth into 3 [[35/32]]s. | ||
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79edo supports the [[bluebirds]] and [[sentinel]] temperaments. | 79edo supports the [[bluebirds]] and [[sentinel]] temperaments. | ||
=== Subsets and supersets === | === Subsets and supersets === | ||