37edo: Difference between revisions
m Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot |
added the template, moved the primes-error table up to the top |
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<span style="display: block; text-align: right;">[[:de:37edo|Deutsch]]</span> | <span style="display: block; text-align: right;">[[:de:37edo|Deutsch]]</span> | ||
{{Infobox ET | |||
| Step size = 32.432¢ | |||
| Fifth type = 20\34 = 705.88¢ = [[17edo]] | |||
| Major 2nd = 7\37 = 227¢ | |||
| Minor 2nd = 1\37 = 32¢ | |||
| Augmented 1sn = 6\37 = 195¢ | |||
}} | |||
== Theory == | == Theory == | ||
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]]). | {| class="wikitable center-all" | ||
! colspan="2" | | |||
! prime 2 | |||
! prime 3 | |||
! prime 5 | |||
! prime 7 | |||
! prime 11 | |||
! prime 13 | |||
! prime 17 | |||
! prime 19 | |||
! prime 23 | |||
|- | |||
! rowspan="2" |Error | |||
! absolute (¢) | |||
| 0 | |||
| +11.56 | |||
| +2.9 | |||
| +4.1 | |||
| +0.03 | |||
| +2.7 | |||
| -7.7 | |||
| -5.6 | |||
| -12.1 | |||
|- | |||
![[Relative error|relative]] (%) | |||
| 0 | |||
| +36 | |||
| +9 | |||
| +13 | |||
| +0.1 | |||
| +8 | |||
| -24 | |||
| -17 | |||
| -37 | |||
|- | |||
! colspan="2" |[[nearest edomapping]] | |||
|37 | |||
|22 | |||
|12 | |||
|30 | |||
|17 | |||
|26 | |||
|3 | |||
|9 | |||
|19 | |||
|} | |||
'''37edo''' is a scale derived from dividing the octave into 37 equal steps. It is the 12th [[prime_numbers|prime]] edo, following [[31edo]] and coming before [[41edo]]. 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]]). | |||
37edo is also a very accurate equal tuning for [[undecimation]] temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS. | 37edo is also a very accurate equal tuning for [[undecimation]] temperament, which has a generator of about 519 cents; 2 generators lead to 29/16; 3 generators to 32/13; 6 generators to a 10 cent sharp 6/1; 8 generators to a very accurate 11/1 and 10 generators to 20/1. It has a 7L+2s nonatonic MOS, which in 37-edo scale degrees is 0, 1, 6, 11, 16, 17, 22, 27, 32, a scale structure reminiscent of mavila; as well as a 16 note MOS. | ||
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== Just approximation == | == Just approximation == | ||
=== Temperament measures === | === Temperament measures === | ||