53edo: Difference between revisions

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== Theory ==

53edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the [[schisma]], 32805/32768, the [[kleisma]], 15625/15552, the [[amity comma]], 1600000/1594323 and the [[semicomma]], 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[optimal patent val]] for [[Nuwell_family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma_family #Orwell|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 ~~and~~ 275/273, and gives the optimal patent val for [[Marvel_family #Athene|athene temperament]]. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] and the 16th [[prime_numbers|prime]] edo, following [[47edo]] and coming before [[59edo]].

53edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the [[schisma]], 32805/32768, the [[kleisma]], 15625/15552, the [[amity comma]], 1600000/1594323 and the [[semicomma]], 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[optimal patent val]] for [[Nuwell_family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma_family #Orwell|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168, 275/273 and 676/675, and gives the optimal patent val for [[Marvel_family #Athene|athene temperament]]. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] and the 16th [[prime_numbers|prime]] edo, following [[47edo]] and coming before [[59edo]].

~~53EDO~~ has also found a certain dissemination as an EDO tuning for [[Arabic,_Turkish,_Persian|Arabic/Turkish/Persian music]].

53edo has also found a certain dissemination as an EDO tuning for [[Arabic,_Turkish,_Persian|Arabic/Turkish/Persian music]].

It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 23-limit.

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[[Category:Edo]]

[[Category:Hanson]]

[[Category:Island]]

[[Category:Kleismic]]

[[Category:Listen]]

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 == Theory ==
-edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the [[schisma]], 32805/32768, the [[kleisma]], 15625/15552, the [[amity comma]], 1600000/1594323 and the [[semicomma]], 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[optimal patent val]] for [[Nuwell_family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma_family #Orwell|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 275/273, and gives the optimal patent val for [[Marvel_family #Athene|athene temperament]]. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] and the 16th [[prime_numbers|prime]] edo, following [[47edo]] and coming before [[59edo]].
+edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the [[schisma]], 32805/32768, the [[kleisma]], 15625/15552, the [[amity comma]], 1600000/1594323 and the [[semicomma]], 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[optimal patent val]] for [[Nuwell_family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma_family #Orwell|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168, 275/273 and 676/675, and gives the optimal patent val for [[Marvel_family #Athene|athene temperament]]. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] and the 16th [[prime_numbers|prime]] edo, following [[47edo]] and coming before [[59edo]].
-EDO has also found a certain dissemination as an EDO tuning for [[Arabic,_Turkish,_Persian|Arabic/Turkish/Persian music]].
+edo has also found a certain dissemination as an EDO tuning for [[Arabic,_Turkish,_Persian|Arabic/Turkish/Persian music]].
 It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 23-limit.
@@ Line 864: / Line 864: @@
 [[Category:Edo]]
 [[Category:Hanson]]
+[[Category:Island]]
 [[Category:Kleismic]]
 [[Category:Listen]]