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== Theory ==
== Theory ==
{| class="wikitable center-all"
{{Odd harmonics in edo|edo=53}}
! colspan="2" | <!-- empty cell -->
! prime 2
! prime 3
! prime 5
! prime 7
! prime 11
! prime 13
! prime 17
! prime 19
! prime 23
|-
! rowspan="2" | Error
! absolute (¢)
| 0.00
| -0.07
| -1.41
| +4.76
| -7.92
| -2.79
| +8.26
| -3.17
| +5.69
|-
! relative (%)
| 0
| -0
| -6
| +21
| -35
| -12
| +36
| -14
| +25
|-
! colspan="2" | Nearest edomapping
| 53
| 31
| 17
| 43
| 24
| 37
| 5
| 13
| 28
|-
! colspan="2" | [[Fifthspan]]
| 0
| +1
| -8
| -14
| +23
| +20
| +7
| -3
| +18
|}


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, 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]].  
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