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'''37EDF''' is the [[EDF|equal division of the just perfect fifth]] into 37 parts of 18.9718 [[cent|cents]] each, corresponding to 63.2519 [[edo]] (similar to every fourth step of [[253edo]]). It is related to the regular temperament which tempers out 385/384, 12005/11979, and 820125/819896 in the 11-limit, which is supported by [[63edo]], [[190edo]], and [[253edo]] among others.
{{Infobox ET}}
{{ED intro}}


[[Category:Edf]]
== Theory ==
[[Category:Edonoi]]
37edf corresponds to 63.2519[[edo]], similar to every fourth step of [[253edo]]. It is related to the [[regular temperament]] which [[tempering out|tempers out]] 385/384, 12005/11979, and 820125/819896 in the [[11-limit]], which is supported by [[63edo]], [[190edo]], and [[253edo]] among others.
 
=== Harmonics ===
{{Harmonics in equal|37|3|2}}
{{Harmonics in equal|37|3|2|start=12|collapsed=1}}
 
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 37edf
|-
! | degree
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
|  colspan="2"| 0
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 18.9718
| |
| |
|-
| | 2
| | 37.9435
| | [[45/44]]
| |
|-
| | 3
| | 56.9153
| |
| |
|-
| | 4
| | 75.887
| |25/24
| |
|-
| | 5
| | 94.8588
| |
| |
|-
| | 6
| | 113.8305
| | [[16/15]]
| |
|-
| | 7
| | 132.8023
| |
| |
|-
| | 8
| | 151.7741
| | [[12/11]]
| |
|-
| | 9
| | 170.7458
| |
| |
|-
| | 10
| | 189.7176
| |10/9
| |
|-
| | 11
| | 208.6893
| |9/8
| |
|-
| | 12
| | 227.6611
| |8/7
| |
|-
| | 13
| | 246.6328
| | [[15/13]]
| |
|-
| | 14
| | 265.6046
| | [[7/6]]
| |
|-
| | 15
| | 284.5764
| | 33/28
| |
|-
| | 16
| | 303.5481
| |25/21
| |
|-
| | 17
| | 322.5199
| |6/5
| |
|-
| | 18
| | 341.4916
| |11/9
| |
|-
| | 19
| | 360.4634
| |27/22
| |
|-
| | 20
| | 379.4351
| |5/4
| |
|-
| | 21
| | 398.4069
| | 34/27
| |
|-
| | 22
| | 417.3786
| | [[14/11]]
| |
|-
| | 23
| | 436.3504
| | [[9/7]]
| |
|-
| | 24
| | 455.3222
| | [[13/10]]
| |
|-
| | 25
| | 474.2939
| |
| |
|-
| | 26
| | 493.2657
| |4/3
| |
|-
| | 27
| | 512.2374
| |
| |
|-
| | 28
| | 531.2092
| |15/11
| |
|-
| | 29
| | 550.1809
| | [[11/8]]
| |pseudo-25/18
|-
| | 30
| | 569.1527
| |
| | real 25/18
|-
| | 31
| | 588.1245
| | [[45/32]], 7/5
| |
|-
| | 32
| | 607.0962
| |64/45, 10/7
| |
|-
| | 33
| | 626.068
| |
| |real 36/25
|-
| | 34
| | 645.0397
| |16/11
| |pseudo-36/25
|-
| | 35
| | 664.0115
| | [[22/15]]
| |
|-
| | 36
| | 682.9832
| |40/27
| |
|-
| | 37
| | 701.955
| | '''exact [[3/2]]'''
| | just perfect fifth
|-
|38
|720.9268
|
|
|-
|39
|739.8985
|135/88
|
|-
|40
|758.8703
|
|
|-
|41
|777.842
|25/16
|
|-
|42
|796.8138
|
|
|-
|43
|815.7855
|8/5
|
|-
|44
|834.7573
|
|
|-
|45
|853.7291
|18/11
|
|-
|46
|872.7008
|
|
|-
|47
|891.6726
|5/3
|
|-
|48
|910.6443
|27/16
|
|-
|49
|929.6161
|12/7
|
|-
|50
|948.5978
|45/26
|
|-
|51
|967.5596
|7/4
|
|-
|52
|986.5314
|99/56
|
|-
|53
|1005.5031
|25/14
|
|-
|54
|1024.4749
|9/5
|
|-
|55
|1043.4466
|
|
|-
|56
|1062.4184
|
|
|-
|57
|1081.3901
|15/8
|
|-
|58
|1100.3619
|17/9
|
|-
|59
|1119.3336
|21/11
|
|-
|60
|1138.3054
|27/14
|
|-
|61
|1157.2772
|39/20
|
|-
|62
|1176.2489
|
|
|-
|63
|1195.2007
|2/1
|
|-
|64
|1214.1924
|
|
|-
|65
|1233.1642
|45/22
|
|-
|66
|1252.1359
|33/16
|pseudo-25/12
|-
|67
|1271.1077
|
|real 25/12
|-
|68
|1290.0795
|135/64, 21/10
|
|-
|69
|1309.0512
|32/15, 15/7
|
|-
|70
|1328.023
|
|real 54/25
|-
|71
|1347.9947
|24/11
|pseudo-54/25
|-
|72
|1365.9668
|11/5
|
|-
|73
|1385.9382
|20/9
|
|-
|74
|1403.91
|'''exact''' 9/4
|
|}
 
==Related regular temperaments==
===7-limit 63&amp;190===
Commas: 2460375/2458624, 514714375/509607936
 
POTE generator: ~1728/1715 = 18.957
 
Mapping: [&lt;1 1 3 2|, &lt;0 37 -43 51|]
 
EDOs: 63, 190, 253
 
===11-limit 63&amp;190===
Commas: 385/384, 12005/11979, 820125/819896
 
POTE generator: ~99/98 = 18.957
 
Mapping: [&lt;1 1 3 2 3|, &lt;0 37 -43 51 29|]
 
EDOs: 63, 190, 253
 
===13-limit 63&amp;190===
Commas: 385/384, 1575/1573, 2200/2197, 4459/4455
 
POTE generator: ~99/98 = 18.959
 
Mapping: [&lt;1 1 3 2 3 4|, &lt;0 37 -43 51 29 -19|]
 
EDOs: 63, 190, 253
 
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