79edo: Difference between revisions

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== Theory ==

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 is only [[consistent]] to the [[5-odd-limit]], but it works well as a no-7 [[13-limit|13-]] or [[17-limit]] tuning with a strong flat tuning tendency. 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]]).

~~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.

=== Odd harmonics ===

~~The 79c~~ val [[~~support~~]]s [[~~meantone~~]] ~~with a tuning very close to~~ [[1/7-~~comma meantone|1~~/7-~~comma~~]].

=== 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 supports the [[sentinel]] temperament and the 2.11.13-subgroup [[bluebirds]] temperament, and provides the [[optimal patent val]] for both.

~~=== Odd harmonics ===~~

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 closest approximation. The closest 5/4 is actually reached by stacking a whopping 16 fifths up (a double-augmented second), which corresponds to the [[python]] temperament. On the other hand, the 79c val uses the second-closest 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 three [[35/32]]'s.

~~{{Harmonics in equal|79}}~~

79edo also has an alternative fifth (albeit much less accurate) of 713.9 cents, which is quite similar to [[37edo]]'s fifth. This fifth allows for [[archy]] and [[oceanfront]] temperaments.

=== Subsets and supersets ===

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 == Theory ==
-edo 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]]).
+edo is only [[consistent]] to the [[5-odd-limit]], but it works well as a no-7 [[13-limit|13-]] or [[17-limit]] tuning with a strong flat tuning tendency. 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]]).
-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.
+=== Odd harmonics ===
+{{Harmonics in equal|79}}
-The 79c val [[support]]s [[meantone]] with a tuning very close to [[1/7-comma meantone|1/7-comma]].
+=== 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 supports the [[sentinel]] temperament and the 2.11.13-subgroup [[bluebirds]] temperament, and provides the [[optimal patent val]] for both.
-=== Odd harmonics ===
+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 closest approximation. The closest 5/4 is actually reached by stacking a whopping 16 fifths up (a double-augmented second), which corresponds to the [[python]] temperament. On the other hand, the 79c val uses the second-closest 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 three [[35/32]]'s.
-{{Harmonics in equal|79}}
+edo also has an alternative fifth (albeit much less accurate) of 713.9 cents, which is quite similar to [[37edo]]'s fifth. This fifth allows for [[archy]] and [[oceanfront]] temperaments.
 === Subsets and supersets ===

79edo: Difference between revisions

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