37edo: Difference between revisions
m State the primality in infobox |
ET parameter name, cleanup |
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| Prime factorization = 37 (prime) | | Prime factorization = 37 (prime) | ||
| Step size = 32.432¢ | | Step size = 32.432¢ | ||
| Fifth | | Fifth = 22\37 = 713.514¢ | ||
| Major 2nd = 7\37 = 227¢ | | Major 2nd = 7\37 = 227¢ | ||
| Minor 2nd = 1\37 = 32¢ | | Minor 2nd = 1\37 = 32¢ | ||
| Line 12: | Line 12: | ||
== 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 23: | Line 23: | ||
! prime 23 | ! prime 23 | ||
|- | |- | ||
! rowspan="2" |Error | ! rowspan="2" | Error | ||
! absolute (¢) | ! absolute (¢) | ||
| 0 | | 0.0 | ||
| | | +11.6 | ||
| | | +2.9 | ||
| | | +4.1 | ||
| | | +0.0 | ||
| | | +2.7 | ||
| | | -7.7 | ||
| | | -5.6 | ||
| | | -12.1 | ||
|- | |- | ||
![[Relative error|relative]] (%) | ! [[Relative error|relative]] (%) | ||
| 0 | | 0 | ||
| | | +36 | ||
| | | +9 | ||
| | | +13 | ||
| | | +0 | ||
| | | +8 | ||
| | | -24 | ||
| | | -17 | ||
| | | -37 | ||
|- | |- | ||
! colspan="2" |[[nearest edomapping]] | ! colspan="2" | [[nearest edomapping]] | ||
|37 | | 37 | ||
|22 | | 22 | ||
|12 | | 12 | ||
|30 | | 30 | ||
|17 | | 17 | ||
|26 | | 26 | ||
|3 | | 3 | ||
|9 | | 9 | ||
|19 | | 19 | ||
|} | |} | ||
Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[porcupine]] temperament. It is the optimal patent val for [[Porcupine_family#Porcupinefish|porcupinefish]], which is about as accurate as "13-limit porcupine" will be. Using its alternative flat fifth, it tempers out 16875/16384, making it a [[Negri|negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[gorgo]]/[[laconic]]). | Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[porcupine]] temperament. It is the optimal patent val for [[Porcupine_family#Porcupinefish|porcupinefish]], which is about as accurate as "13-limit porcupine" will be. Using its alternative flat fifth, it tempers out 16875/16384, making it a [[Negri|negri]] tuning. It also tempers out 2187/2000, resulting in a temperament where three minor whole tones make up a fifth ([[gorgo]]/[[laconic]]). | ||