53edo: Difference between revisions

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~~The famous '''~~53 equal divisions of the octave''' ('''53edo'''), or '''53(-tone) equal temperament''' ('''53tet''', '''53et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 53 [[equal]] comma-sized parts of around 22.6 [[cent]]s each.

== Theory ==

53edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, notably tempering out the [[schisma]] (32805/32768) and the [[kleisma]] (15625/15552). More complex 5-limit commas tempered out include the [[amity comma]] (1600000/1594323), the [[semicomma]] (2109375/2097152), and the [[vulture comma]] ({{monzo| 24 -21 4 }}). 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]] 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.

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 {{Wikipedia| 53 equal temperament }}
-The famous '''53 equal divisions of the octave''' ('''53edo'''), or '''53(-tone) equal temperament''' ('''53tet''', '''53et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 53 [[equal]] comma-sized parts of around 22.6 [[cent]]s each.
+{{EDO intro|53}}
 == Theory ==
 edo is notable as a [[5-limit]] system, a fact apparently first noted by Isaac Newton, notably tempering out the [[schisma]] (32805/32768) and the [[kleisma]] (15625/15552). More complex 5-limit commas tempered out include the [[amity comma]] (1600000/1594323), the [[semicomma]] (2109375/2097152), and the [[vulture comma]] ({{monzo| 24 -21 4 }}). 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]] 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.