56edo: Difference between revisions

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== Theory ==

It shares it's near perfect major third with [[28edo]], which it doubles, while also adding a superpythagorean 5th that is a convergent towards the [[Metallic harmonic series|bronze metallic mean]], following [[17edo]] and preceding [[185edo]]. Because it ~~ha a near perfect [[5/4]]~~ and a step size very close to the syntonic comma, 56edo contains very accurate approximations of both 5/4 and 81/64.

It shares it's near perfect major third with [[28edo]], which it doubles, while also adding a superpythagorean 5th that is a convergent towards the [[Metallic harmonic series|bronze metallic mean]], following [[17edo]] and preceding [[185edo]]. Because it contains 28edo's major third and also has a step size very close to the syntonic comma, 56edo contains very accurate approximations of both the classic major third [[5/4]] and the Pythagorean major third [[81/64]].

56edo can be used to tune [[hemithirds]], [[superkleismic]], [[sycamore]] and [[keen]] temperaments, and using {{val| 56 89 130 158 }} (56d) as the equal temperament val, for [[pajara]]. It provides the [[optimal patent val]] for 7-, 11- and 13-limit [[Sycamore family #Septimal sycamore|sycamore]], and the 11-limit 56d val is close to the [[POTE tuning]] for 11-limit pajara. 56edo can be used to tune [[Barium]] temperament which sets 56 syntonci commas to the octave.

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 == Theory ==
-It shares it's near perfect major third with [[28edo]], which it doubles, while also adding a superpythagorean 5th that is a convergent towards the [[Metallic harmonic series|bronze metallic mean]], following [[17edo]] and preceding [[185edo]]. Because it ha a near perfect [[5/4]] and a step size very close to the syntonic comma, 56edo contains very accurate approximations of both 5/4 and 81/64.
+It shares it's near perfect major third with [[28edo]], which it doubles, while also adding a superpythagorean 5th that is a convergent towards the [[Metallic harmonic series|bronze metallic mean]], following [[17edo]] and preceding [[185edo]]. Because it contains 28edo's major third and also has a step size very close to the syntonic comma, 56edo contains very accurate approximations of both the classic major third [[5/4]] and the Pythagorean major third [[81/64]].
 edo can be used to tune [[hemithirds]], [[superkleismic]], [[sycamore]] and [[keen]] temperaments, and using {{val| 56 89 130 158 }} (56d) as the equal temperament val, for [[pajara]]. It provides the [[optimal patent val]] for 7-, 11- and 13-limit [[Sycamore family #Septimal sycamore|sycamore]], and the 11-limit 56d val is close to the [[POTE tuning]] for 11-limit pajara. 56edo can be used to tune [[Barium]] temperament which sets 56 syntonci commas to the octave.