79edo: Difference between revisions

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== Theory ==

79edo works well as a no-5 17-limit tuning~~, or as a dual~~-~~5 17~~-limit ~~tuning~~.

79edo works well as a no-7 13- or 17-limit tuning. It is in fact [[consistent]] in the no-7 [[15-odd-limit]].

~~As an equal temperament~~, 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.

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 slightly flat and very similar to the one of~~ [[~~12edo~~]] ~~– the major third is too sharp to be the closest approximation of~~ [[~~5/4~~]] ~~so 79edo actually does not qualify as~~ [[meantone]] ~~in the patent val~~.

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

=== Odd harmonics ===

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 == Theory ==
-edo works well as a no-5 17-limit tuning, or as a dual-5 17-limit tuning.
+edo works well as a no-7 13- or 17-limit tuning. It is in fact [[consistent]] in the no-7 [[15-odd-limit]].
-As an equal temperament, 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.
+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 slightly flat and very similar to the one of [[12edo]] – the major third is too sharp to be the closest approximation of [[5/4]] so 79edo actually does not qualify as [[meantone]] in the patent val.
+The 79c val [[support]]s [[meantone]] with a tuning very close to [[1/7-comma meantone|1/7-comma]].
 === Odd harmonics ===