53edo: Difference between revisions
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53edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, notably tempering out the [[schisma]] (32805/32768), the [[kleisma]] (15625/15552), the [[amity comma]] (1600000/1594323), the [[semicomma]] (2109375/2097152), and the [[vulture comma]] (10485760000/10460353203). 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]] (in addition to their difference, [[540/539]]), and is the [[optimal patent val]] for [[Big Brother]] temperament, which tempers out both, as well as 11-limit [[Orwell|orwell temperament]], which also tempers out the 11-limit commas [[176/175]] and [[385/384]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], and [[2080/2079]], and gives the optimal patent val for [[Marvel family #Athene|athene temperament]]. It is the seventh [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta edo]]. It can also be treated as a no-elevens, no-seventeens tuning, on which it is [[consistent]] all the way up to the 23-odd-limit. | 53edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, notably tempering out the [[schisma]] (32805/32768), the [[kleisma]] (15625/15552), the [[amity comma]] (1600000/1594323), the [[semicomma]] (2109375/2097152), and the [[vulture comma]] (10485760000/10460353203). 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]] (in addition to their difference, [[540/539]]), and is the [[optimal patent val]] for [[Big Brother]] temperament, which tempers out both, as well as 11-limit [[Orwell|orwell temperament]], which also tempers out the 11-limit commas [[176/175]] and [[385/384]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[625/624]], [[676/675]], [[1001/1000]], and [[2080/2079]], and gives the optimal patent val for [[Marvel family #Athene|athene temperament]]. It is the seventh [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta edo]]. It can also be treated as a no-elevens, no-seventeens tuning, on which it is [[consistent]] all the way up to the 23-odd-limit. | ||
53edo has also found a certain dissemination as an | 53edo has also found a certain dissemination as an edo tuning for [[Arabic, Turkish, Persian]] music. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|53}} | {{Harmonics in equal|53}} | ||
=== Divisors === | |||
53edo is the 16th [[prime edo]], following [[47edo]] and coming before [[59edo]]. | |||
== Intervals == | == Intervals == | ||
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* [[Lumatone mapping for 53edo]] | * [[Lumatone mapping for 53edo]] | ||
[[Category:Amity]] | [[Category:Amity]] | ||
[[Category:Athene]] | [[Category:Athene]] | ||
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[[Category:Schismic]] | [[Category:Schismic]] | ||
[[Category:3-limit]] | [[Category:3-limit]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||