53edo: Difference between revisions
template cleanup |
ET parameter name, cleanup |
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{{Infobox ET | {{Infobox ET | ||
| Step size = 22.642¢ | | Step size = 22.642¢ | ||
| Fifth | | Fifth = 31\53 = 701.886¢ | ||
| Major 2nd = 9\53 = 204¢ | | Major 2nd = 9\53 = 204¢ | ||
| Minor 2nd = 4\53 = 91¢ | | Minor 2nd = 4\53 = 91¢ | ||
| Line 17: | Line 17: | ||
== Theory == | == Theory == | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! colspan="2" | | ! colspan="2" | <!-- empty cell --> | ||
! prime 2 | ! prime 2 | ||
! prime 3 | ! prime 3 | ||
| Line 30: | Line 30: | ||
! rowspan="2" |Error | ! rowspan="2" |Error | ||
! absolute (¢) | ! absolute (¢) | ||
| 0 | | 0.00 | ||
| | | -0.07 | ||
| | | -1.41 | ||
| | | +4.76 | ||
| | | -7.92 | ||
| | | -2.79 | ||
| | | +8.26 | ||
| | | -3.17 | ||
| | | +5.69 | ||
|- | |- | ||
! relative (%) | ! relative (%) | ||
| 0 | | 0 | ||
| | | 0 | ||
| | | -6 | ||
| | | +21 | ||
| | | -35 | ||
| | | -12 | ||
| | | +36 | ||
| | | -14 | ||
| | | +25 | ||
|- | |- | ||
! colspan="2" |nearest edomapping | ! colspan="2" | nearest edomapping | ||
|53 | | 53 | ||
|31 | | 31 | ||
|17 | | 17 | ||
|43 | | 43 | ||
|24 | | 24 | ||
|37 | | 37 | ||
|5 | | 5 | ||
|13 | | 13 | ||
|28 | | 28 | ||
|- | |- | ||
! colspan="2" |[[fifthspan]] | ! colspan="2" | [[fifthspan]] | ||
| 0 | | 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 and the [[semicomma]], 2109375/2097152. 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]] and [[676/675]], and gives the optimal patent val for [[Marvel family #Athene|athene temperament]]. It is the eighth [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral 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 and the [[semicomma]], 2109375/2097152. 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]] and [[676/675]], and gives the optimal patent val for [[Marvel family #Athene|athene temperament]]. It is the eighth [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]] and the 16th [[prime edo]], following [[47edo]] and coming before [[59edo]]. | ||