37edf: Difference between revisions

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Line 10: Line 10:
|-
|-
| | 0
| | 0
| | 0.0000
| | 0
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
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|-
|-
| | 4
| | 4
| | 75.8870
| | 75.887
| |  
| |25/24
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| |  
|-
|-
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| | 10
| | 10
| | 189.7176
| | 189.7176
| |  
| |10/9
| |  
| |  
|-
|-
| | 11
| | 11
| | 208.6893
| | 208.6893
| |  
| |9/8
| |  
| |  
|-
|-
| | 12
| | 12
| | 227.6611
| | 227.6611
| |  
| |8/7
| |  
| |  
|-
|-
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| | 16
| | 16
| | 303.5481
| | 303.5481
| | 81/68
| |25/21
| |  
| |  
|-
|-
| | 17
| | 17
| | 322.5199
| | 322.5199
| |  
| |6/5
| |  
| |  
|-
|-
| | 18
| | 18
| | 341.4916
| | 341.4916
| |  
| |11/9
| |  
| |  
|-
|-
| | 19
| | 19
| | 360.4634
| | 360.4634
| |  
| |27/22
| |  
| |  
|-
|-
| | 20
| | 20
| | 379.4351
| | 379.4351
| |  
| |5/4
| |  
| |  
|-
|-
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| | 26
| | 26
| | 493.2657
| | 493.2657
| |  
| |4/3
| |  
| |  
|-
|-
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| | 28
| | 28
| | 531.2092
| | 531.2092
| |  
| |15/11
| |  
| |  
|-
|-
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| | 550.1809
| | 550.1809
| | [[11/8]]
| | [[11/8]]
| |  
| |pseudo-25/18
|-
|-
| | 30
| | 30
| | 569.1527
| | 569.1527
| |  
| |
| |  
| | real 25/18
|-
|-
| | 31
| | 31
| | 588.1245
| | 588.1245
| | [[45/32]]
| | [[45/32]], 7/5
| |  
| |  
|-
|-
| | 32
| | 32
| | 607.0962
| | 607.0962
| |  
| |64/45, 10/7
| |  
| |  
|-
|-
| | 33
| | 33
| | 626.0680
| | 626.068
| |
| |  
| |  
| |real 36/25
|-
|-
| | 34
| | 34
| | 645.0397
| | 645.0397
| |  
| |16/11
| |  
| |pseudo-36/25
|-
|-
| | 35
| | 35
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| | 36
| | 36
| | 682.9832
| | 682.9832
| |  
| |40/27
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| |  
|-
|-
| | 37
| | 37
| | 701.9550
| | 701.955
| | '''exact [[3/2]]'''
| | '''exact [[3/2]]'''
| | just perfect fifth
| | just perfect fifth
|-
|38
|720.9268
|
|
|-
|39
|739.8985
|135/88
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|-
|40
|758.8703
|
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|-
|41
|777.842
|25/16
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|-
|42
|796.8138
|
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|-
|43
|815.7855
|8/5
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|-
|44
|834.7573
|
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|-
|45
|853.7291
|18/11
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|-
|46
|872.7008
|
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|-
|47
|891.6726
|5/3
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|-
|48
|910.6443
|27/16
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|-
|49
|929.6161
|12/7
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|-
|50
|948.5978
|45/26
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|-
|51
|967.5596
|7/4
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|-
|52
|986.5314
|99/56
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|-
|53
|1005.5031
|25/14
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|-
|54
|1024.4749
|9/5
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|-
|55
|1043.4466
|
|
|-
|56
|1062.4184
|
|
|-
|57
|1081.3901
|15/8
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|-
|58
|1100.3619
|17/9
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|-
|59
|1119.3336
|21/11
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|-
|60
|1138.3054
|27/14
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|-
|61
|1157.2772
|39/20
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|-
|62
|1176.2489
|
|
|-
|63
|1195.2007
|2/1
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|-
|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
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|-
|70
|1328.023
|
|real 54/25
|-
|71
|1347.9947
|24/11
|pseudo-54/25
|-
|72
|1365.9668
|11/5
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|-
|73
|1385.9382
|20/9
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|-
|74
|1403.91
|'''exact''' 9/4
|
|}
|}


Revision as of 02:13, 10 March 2019

37EDF is the equal division of the just perfect fifth into 37 parts of 18.9718 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.

Intervals

degree cents value corresponding
JI intervals 		comments
0 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&190

Commas: 2460375/2458624, 514714375/509607936

POTE generator: ~1728/1715 = 18.957

Map: [<1 1 3 2|, <0 37 -43 51|]

EDOs: 63, 190, 253

11-limit 63&190

Commas: 385/384, 12005/11979, 820125/819896

POTE generator: ~99/98 = 18.957

Map: [<1 1 3 2 3|, <0 37 -43 51 29|]

EDOs: 63, 190, 253

13-limit 63&190

Commas: 385/384, 1575/1573, 2200/2197, 4459/4455

POTE generator: ~99/98 = 18.959

Map: [<1 1 3 2 3 4|, <0 37 -43 51 29 -19|]

EDOs: 63, 190, 253

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