53edo: Difference between revisions
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The famous ''53 equal division'' divides the octave into 53 equal comma-sized parts of 22.642 cents each. | The famous '''53 equal division''' divides the octave into 53 equal comma-sized parts of 22.642 cents each. | ||
== Theory == | == 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 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]]. | ||
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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. | 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. | ||
[ | ''See also: [[Wikipedia:53_equal_temperament|53 Equal Temperament - Wikipedia]]'' | ||
== Intervals == | == Intervals == | ||