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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>


'''37edo''' is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th [[prime_numbers|prime]] edo, following [[31edo|31edo]] and coming before [[41edo|41edo]].  
'''37edo''' is a scale derived from dividing the octave into 37 equal steps of approximately 32.43 cents each. It is the 12th [[prime_numbers|prime]] edo, following [[31edo]] and coming before [[41edo]].  


== Theory ==
== Theory ==
Using its best (and sharp) fifth, 37edo tempers out 250/243, making it a variant of [[Porcupine|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|gorgo]]/[[laconic|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]]).


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.


__FORCETOC__
=== Subgroups ===
=== Subgroups ===
37edo offers close approximations to [[OverToneSeries|harmonics]] 5, 7, 11, and 13 [and a usable approximation of 9 as well].
37edo offers close approximations to [[Overtone series|harmonics]] 5, 7, 11, and 13 [and a usable approximation of 9 as well].


12\37 = 389.2 cents
12\37 = 389.2 cents
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! Degrees
! Degrees
! Cents
! Cents
! Approximate Ratios
! Approximate Ratios<br>of 2.5.7.11.13.27 subgroup
 
of 2.5.7.11.13.27 subgroup
! Additional Ratios of 3<br>with a sharp 3/2
! Additional Ratios of 3<br>with a sharp 3/2
! Additional Ratios of 3<br>with a flat 3/2
! Additional Ratios of 3<br>with a flat 3/2
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| 97.30
| 97.30
|  
|  
| |
|
|  
|  
|  
|  
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| 551.35
| 551.35
| 11/8
| 11/8
| |
|
|  
|  
| 18/13
| 18/13
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|}
|}


==Scales==
== Scales ==


[[MOS_Scales_of_37edo|MOS Scales of 37edo]]
* [[MOS_Scales_of_37edo|MOS Scales of 37edo]]
* [[roulette6]]
* [[roulette7]]
* [[roulette13]]
* [[roulette19]]
* [[Chromatic_pairs#Shoe|Shoe]]
* [[37ED4]]
* [[square_root_of_13_over_10|The Square Root of 13/10]]


[[roulette6|roulette6]]
== Linear temperaments ==
 
* [[List of 37et rank two temperaments by badness]]
[[roulette7|roulette7]]
 
[[roulette13|roulette13]]
 
[[roulette19|roulette19]]
 
[[Chromatic_pairs#Shoe|Shoe]]
 
[[37ED4|37ED4]]
 
[[square_root_of_13_over_10|The Square Root of 13/10]]
 
==Linear temperaments==
[[List_of_37et_rank_two_temperaments_by_badness|List of 37et rank two temperaments by badness]]


{| class="wikitable"
{| class="wikitable"
|-
|-
! | Generator
! Generator
! | "Sharp 3/2" temperaments
! "Sharp 3/2" temperaments
! | "Flat 3/2" temperaments (37b val)
! "Flat 3/2" temperaments (37b val)
|-
|-
| | 1\37
| 1\37
| |  
|  
| |  
|  
|-
|-
| | 2\37
| 2\37
| | [[Sycamore_family|Sycamore]]
| [[Sycamore_family|Sycamore]]
| |  
|  
|-
|-
| | 3\37
| 3\37
| | [[Passion|Passion]]
| [[Passion]]
| |  
|  
|-
|-
| | 4\37
| 4\37
| | [[Twothirdtonic|Twothirdtonic]]
| [[Twothirdtonic]]
| | [[Negri|Negri]]
| [[Negri]]
|-
|-
| | 5\37
| 5\37
| | [[Porcupine|Porcupine]]/[[The_Biosphere#Oceanfront-Oceanfront Children-Porcupinefish|porcupinefish]]
| [[Porcupine]]/[[The_Biosphere#Oceanfront-Oceanfront Children-Porcupinefish|porcupinefish]]
| |  
|  
|-
|-
| | 6\37
| 6\37
| colspan="2" | [[Chromatic_pairs#Roulette|Roulette]]
| colspan="2" | [[Chromatic_pairs#Roulette|Roulette]]
|-
|-
| | 7\37
| 7\37
| | [[Semaja|Semaja]]
| [[Semaja]]
| | [[Gorgo|Gorgo]]/[[Laconic|Laconic]]
| [[Gorgo]]/[[Laconic]]
|-
|-
| | 8\37
| 8\37
| |  
|  
| | [[semiphore|Semiphore]]
| [[Semiphore]]
|-
|-
| | 9\37
| 9\37
| |  
|  
| |  
|  
|-
|-
| | 10\37
| 10\37
| |  
|  
| |  
|  
|-
|-
| | 11\37
| 11\37
| | [[Beatles|Beatles]]
| [[Beatles]]
| |  
|  
|-
|-
| | 12\37
| 12\37
| | [[Würschmidt|Würschmidt]] (out-of-tune)
| [[Würschmidt]] (out-of-tune)
| |  
|  
|-
|-
| | 13\37
| 13\37
| |  
|  
| |  
|  
|-
|-
| | 14\37
| 14\37
| | [[Ammonite|Ammonite]]
| [[Ammonite]]
| |  
|  
|-
|-
| | 15\37
| 15\37
| | [[The_Biosphere#Oceanfront-Oceanfront Children-Ultrapyth|Ultrapyth]], '''not''' [[Superpyth|superpyth]]
| [[The_Biosphere#Oceanfront-Oceanfront Children-Ultrapyth|Ultrapyth]], '''not''' [[superpyth]]
| |  
|  
|-
|-
| | 16\37
| 16\37
| |  
|  
| | '''Not''' [[Mavila|mavila]] (this is "undecimation")
| '''Not''' [[mavila]] (this is "undecimation")
|-
|-
| | 17\37
| 17\37
| | [[Emka|Emka]]
| [[Emka]]
| |  
|  
|-
|-
| | 18\37
| 18\37
| |  
|  
| |  
|  
|}
|}


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