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), 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]], and is the [[optimal patent val]] for [[Big Brother]] temperament, which tempers out both, as well as [[~~Semicomma family #~~Orwell|~~11-limit~~ orwell temperament]], which also tempers out the 11-limit ~~comma~~ [[176/175]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[~~540~~/~~539~~]], [[~~625~~/~~624~~]], [[~~676~~/~~675~~]], 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]] ~~and the 16th [[prime edo]]~~, ~~following~~ [[~~47edo]] and coming before [[59edo~~]].

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 EDO tuning for [[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-odd-limit~~.

53edo is the 16th [[prime edo]], following [[47edo]] and coming before [[59edo]].

=== Prime harmonics ===

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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), 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]], and is the [[optimal patent val]] for [[Big Brother]] temperament, which tempers out both, as well as [[Semicomma family #Orwell|11-limit orwell temperament]], which also tempers out the 11-limit comma [[176/175]]. In the 13-limit, it tempers out [[169/168]], [[275/273]], [[325/324]], [[540/539]], [[625/624]], [[676/675]], 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]] and the 16th [[prime edo]], following [[47edo]] and coming before [[59edo]].
+edo 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.
 edo has also found a certain dissemination as an EDO tuning for [[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-odd-limit.
+edo is the 16th [[prime edo]], following [[47edo]] and coming before [[59edo]].
 === Prime harmonics ===