53edo: Difference between revisions

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== Theory ==

53edo is notable as an excellent [[5-limit]] ~~system~~, a fact apparently first noted by Isaac Newton, notably tempering out [[Mercator's comma]] (353/284), the [[schisma|schisma (32805/32768)]], and the [[15625/15552|kleisma (15625/15552)]]. In the 7-limit it tempers out the [[225/224|marvel comma (225/224)]], [[1728/1715|orwellisma (1728/1715)]], and [[3125/3087|gariboh comma (3125/3087)]]. 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]] 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]], [[2080/2079]], and [[4096/4095]], 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 an excellent [[5-limit]], a fact apparently first noted by Isaac Newton, notably tempering out [[Mercator's comma]] (353/284), the [[schisma|schisma (32805/32768)]], the [[amity comma|amity comma (1600000/1594323)]] and the [[15625/15552|kleisma (15625/15552)]]. In the 7-limit it tempers out the [[225/224|marvel comma (225/224)]], [[1728/1715|orwellisma (1728/1715)]], [[4375/4374|ragisma (4375/4374)]] and [[3125/3087|gariboh comma (3125/3087)]]. 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]] 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]], [[2080/2079]], and [[4096/4095]], 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|Arabic, Turkish, and Persian music]]. It can also be used as an extended [[3-limit|Pythagorean tuning]], since its fifths are almost indistinguishable from just.

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 == Theory ==
-edo is notable as an excellent [[5-limit]] system, a fact apparently first noted by Isaac Newton, notably tempering out [[Mercator's comma]] (3<sup>53</sup>/2<sup>84</sup>), the [[schisma|schisma (32805/32768)]], and the [[15625/15552|kleisma (15625/15552)]]. In the 7-limit it tempers out the [[225/224|marvel comma (225/224)]], [[1728/1715|orwellisma (1728/1715)]], and [[3125/3087|gariboh comma (3125/3087)]]. 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]] 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]], [[2080/2079]], and [[4096/4095]], 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 is notable as an excellent [[5-limit]], a fact apparently first noted by Isaac Newton, notably tempering out [[Mercator's comma]] (3<sup>53</sup>/2<sup>84</sup>), the [[schisma|schisma (32805/32768)]], the [[amity comma|amity comma (1600000/1594323)]] and the [[15625/15552|kleisma (15625/15552)]]. In the 7-limit it tempers out the [[225/224|marvel comma (225/224)]], [[1728/1715|orwellisma (1728/1715)]], [[4375/4374|ragisma (4375/4374)]] and [[3125/3087|gariboh comma (3125/3087)]]. 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]] 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]], [[2080/2079]], and [[4096/4095]], 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|Arabic, Turkish, and Persian music]]. It can also be used as an extended [[3-limit|Pythagorean tuning]], since its fifths are almost indistinguishable from just.