53edt: Difference between revisions

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Created page with "'''53EDT''' is the equal division of the third harmonic into 53 parts of 35.8859 cents each, corresponding to 33.4393 edo. It has a generally sharp tenden..."
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Line 7: Line 7:
! | degree
! | degree
! | cents value
! | cents value
!hekts
! | corresponding <br>JI intervals
! | corresponding <br>JI intervals
! | comments
! | comments
|-
|-
| | 0
| | 0
| | 0.0000
| colspan="2"| 0
| | '''exact [[1/1]]'''
| | '''exact [[1/1]]'''
| |  
| |  
Line 17: Line 18:
| | 1
| | 1
| | 35.8859
| | 35.8859
|24.5283
| | [[50/49]], [[49/48]]
| | [[50/49]], [[49/48]]
| |  
| |  
Line 22: Line 24:
| | 2
| | 2
| | 71.7719
| | 71.7719
|49.0566
| | [[25/24]]
| | [[25/24]]
| |  
| |  
Line 27: Line 30:
| | 3
| | 3
| | 107.6578
| | 107.6578
| |  
|73.5849
| |[[17/16]], [[16/15]]
| |  
| |  
|-
|-
| | 4
| | 4
| | 143.5438
| | 143.5438
|98.1132
| | 38/35
| | 38/35
| |  
| |  
Line 37: Line 42:
| | 5
| | 5
| | 179.4297
| | 179.4297
|122.6415
| | 51/46, 132/119
| | 51/46, 132/119
| |  
| |  
Line 42: Line 48:
| | 6
| | 6
| | 215.3157
| | 215.3157
| |  
|147.1698
| |17/15
| |  
| |  
|-
|-
| | 7
| | 7
| | 251.2016
| | 251.2016
| |  
|171.6981
| | 15/13
| |  
| |  
|-
|-
| | 8
| | 8
| | 287.0875
| | 287.0875
| |  
|196.2264
| |33/28, 13/11
| |  
| |  
|-
|-
| | 9
| | 9
| | 322.9735
| | 322.9735
| |  
|220.7547
| | 6/5
| |  
| |  
|-
|-
| | 10
| | 10
| | 358.8594
| | 358.8594
|245.283
| | [[16/13]]
| | [[16/13]]
| |  
| |  
Line 67: Line 78:
| | 11
| | 11
| | 394.7454
| | 394.7454
| | 49/39
|269.8113
| | [[5/4]], 49/39
| |  
| |  
|-
|-
| | 12
| | 12
| | 430.6313
| | 430.6313
| | 50/39
|594.3396
| | [[9/7]], 50/39
| |  
| |  
|-
|-
| | 13
| | 13
| | 466.5173
| | 466.5173
| |  
|318.8679
| | 21/16
| |  
| |  
|-
|-
| | 14
| | 14
| | 502.4032
| | 502.4032
| |  
|343.3962
| | [[4/3]], 171/128
| |  
| |  
|-
|-
| | 15
| | 15
| | 538.2892
| | 538.2892
|367.9245
| | [[15/11]]
| | [[15/11]]
| |  
| |  
Line 92: Line 108:
| | 16
| | 16
| | 574.1751
| | 574.1751
|392.4528
| | 39/28
| | 39/28
| |  
| |  
|-
|-
| | 17
| | 17
| | 610.0610
| | 610.061
| |  
|416.9811
| | [[10/7]]
| |  
| |  
|-
|-
| | 18
| | 18
| | 645.9470
| | 645.947
| |  
|441.5094
| |35/24
| |  
| |  
|-
|-
| | 19
| | 19
| | 681.8329
| | 681.8329
| | 126/85
|466.0377
| | 126/85, 40/27
| |  
| |  
|-
|-
| | 20
| | 20
| | 717.7189
| | 717.7189
| |  
|490.566
| |  
| |
| |pseudo-3/2
|-
|-
| | 21
| | 21
| | 753.6048
| | 753.6048
|515.0943
| | [[17/11]]
| | [[17/11]]
| |  
| |  
Line 122: Line 144:
| | 22
| | 22
| | 789.4908
| | 789.4908
|539.6226
| | [[30/19]]
| | [[30/19]]
| |  
| |  
Line 127: Line 150:
| | 23
| | 23
| | 825.3767
| | 825.3767
| |  
|564.1509
| | [[13/8]]
| |  
| |  
|-
|-
| | 24
| | 24
| | 861.2626
| | 861.2626
|588.67945
| |  
| |  
| |  
| |  
Line 137: Line 162:
| | 25
| | 25
| | 897.1486
| | 897.1486
| |  
|613.20755
| | 42/25, 32/19
| |  
| |  
|-
|-
| | 26
| | 26
| | 933.0345
| | 933.0345
|637.73585
| | [[12/7]]
| | [[12/7]]
| |  
| |  
Line 147: Line 174:
| | 27
| | 27
| | 968.9205
| | 968.9205
|662.26415
| | [[7/4]]
| | [[7/4]]
| |  
| |  
Line 152: Line 180:
| | 28
| | 28
| | 1004.8064
| | 1004.8064
| |  
|686.79245
| | 25/14, 57/32
| |  
| |  
|-
|-
| | 29
| | 29
| | 1040.6924
| | 1040.6924
|711.32075
| |  
| |  
| |  
| |  
Line 162: Line 192:
| | 30
| | 30
| | 1076.5783
| | 1076.5783
| |  
|735.8491
| | 24/13
| |  
| |  
|-
|-
| | 31
| | 31
| | 1112.4642
| | 1112.4642
|760.3774
| | [[19/10]]
| | [[19/10]]
| |  
| |  
Line 172: Line 204:
| | 32
| | 32
| | 1148.3502
| | 1148.3502
|784.9057
| | 33/17
| | 33/17
| |  
| |  
Line 177: Line 210:
| | 33
| | 33
| | 1184.2361
| | 1184.2361
| |  
|809.434
| |  
| |
| |pseudooctave
|-
|-
| | 34
| | 34
| | 1220.1221
| | 1220.1221
| | 85/42
|833.9623
| | 85/42, 81/40
| |  
| |  
|-
|-
| | 35
| | 35
| | 1256.0080
| | 1256.008
|858.4906
| | 95/46
| | 95/46
| |  
| |  
|-
|-
| | 36
| | 36
| | 1291.8940
| | 1291.894
| |  
|883.0189
| | 21/10
| |  
| |  
|-
|-
| | 37
| | 37
| | 1327.7799
| | 1327.7799
|907.5472
| | [[14/13|28/13]]
| | [[14/13|28/13]]
| |  
| |  
Line 202: Line 240:
| | 38
| | 38
| | 1363.6658
| | 1363.6658
|932.0755
| | [[11/5]]
| | [[11/5]]
| |  
| |  
Line 207: Line 246:
| | 39
| | 39
| | 1399.5518
| | 1399.5518
| | [[64/57|128/57]]
|956.6038
| | 9/4, [[64/57|128/57]]
| |  
| |  
|-
|-
| | 40
| | 40
| | 1435.4377
| | 1435.4377
| |  
|981.1321
| | 16/7
| |  
| |  
|-
|-
| | 41
| | 41
| | 1471.3237
| | 1471.3237
| | 117/50
|1005.3304
| | 7/3, 117/50
| |  
| |  
|-
|-
| | 42
| | 42
| | 1507.2096
| | 1507.2096
| | 117/49
|1303.1887
| | 12/5, 117/49
| |  
| |  
|-
|-
| | 43
| | 43
| | 1543.0956
| | 1543.0956
|1054.717
| | [[39/32|39/16]]
| | [[39/32|39/16]]
| |  
| |  
Line 232: Line 276:
| | 44
| | 44
| | 1578.9815
| | 1578.9815
| |  
|1079.2453
| | 5/2
| |  
| |  
|-
|-
| | 45
| | 45
| | 1614.8675
| | 1614.8675
| |  
|1130.7736
| |28/11, 33/13
| |  
| |  
|-
|-
| | 46
| | 46
| | 1650.7534
| | 1650.7534
| |  
|1128.3019
| | 13/5
| |  
| |  
|-
|-
| | 47
| | 47
| | 1686.6393
| | 1686.6393
| |  
|1152.8302
| | 45/17
| |  
| |  
|-
|-
| | 48
| | 48
| | 1722.5253
| | 1722.5253
|1177.3585
| | 119/44
| | 119/44
| |  
| |  
Line 257: Line 306:
| | 49
| | 49
| | 1758.4112
| | 1758.4112
| |  
|1201.8868
| | 105/38
| |  
| |  
|-
|-
| | 50
| | 50
| | 1794.2972
| | 1794.2972
| |  
|1226.4151
| | 48/17, 45/16
| |  
| |  
|-
|-
| | 51
| | 51
| | 1830.1831
| | 1830.1831
|1250.9434
| | [[36/25|72/25]]
| | [[36/25|72/25]]
| |  
| |  
Line 272: Line 324:
| | 52
| | 52
| | 1866.0691
| | 1866.0691
| |  
|1275.4717
| | 147/50, 144/49
| |  
| |  
|-
|-
| | 53
| | 53
| | 1901.9550
| | 1901.955
|1300
| | '''exact [[3/1]]'''
| | '''exact [[3/1]]'''
| |  
| |  

Revision as of 22:08, 20 April 2019

53EDT is the equal division of the third harmonic into 53 parts of 35.8859 cents each, corresponding to 33.4393 edo. It has a generally sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, and 17 are all sharp. It tempers out 413343/390625 and 823543/820125 in the 7-limit; 891/875, 3087/3025, and 164025/161051 in the 11-limit; 637/625, 729/715, 847/845, and 1575/1573 in the 13-limit; 189/187, 429/425, 459/455, and 833/825 in the 17-limit; 171/169, 247/245, 361/357, and 855/847 in the 19-limit (no-twos subgroup).

Intervals

degree cents value hekts corresponding
JI intervals 		comments
0 0 exact 1/1
1 35.8859 24.5283 50/49, 49/48
2 71.7719 49.0566 25/24
3 107.6578 73.5849 17/16, 16/15
4 143.5438 98.1132 38/35
5 179.4297 122.6415 51/46, 132/119
6 215.3157 147.1698 17/15
7 251.2016 171.6981 15/13
8 287.0875 196.2264 33/28, 13/11
9 322.9735 220.7547 6/5
10 358.8594 245.283 16/13
11 394.7454 269.8113 5/4, 49/39
12 430.6313 594.3396 9/7, 50/39
13 466.5173 318.8679 21/16
14 502.4032 343.3962 4/3, 171/128
15 538.2892 367.9245 15/11
16 574.1751 392.4528 39/28
17 610.061 416.9811 10/7
18 645.947 441.5094 35/24
19 681.8329 466.0377 126/85, 40/27
20 717.7189 490.566 pseudo-3/2
21 753.6048 515.0943 17/11
22 789.4908 539.6226 30/19
23 825.3767 564.1509 13/8
24 861.2626 588.67945
25 897.1486 613.20755 42/25, 32/19
26 933.0345 637.73585 12/7
27 968.9205 662.26415 7/4
28 1004.8064 686.79245 25/14, 57/32
29 1040.6924 711.32075
30 1076.5783 735.8491 24/13
31 1112.4642 760.3774 19/10
32 1148.3502 784.9057 33/17
33 1184.2361 809.434 pseudooctave
34 1220.1221 833.9623 85/42, 81/40
35 1256.008 858.4906 95/46
36 1291.894 883.0189 21/10
37 1327.7799 907.5472 28/13
38 1363.6658 932.0755 11/5
39 1399.5518 956.6038 9/4, 128/57
40 1435.4377 981.1321 16/7
41 1471.3237 1005.3304 7/3, 117/50
42 1507.2096 1303.1887 12/5, 117/49
43 1543.0956 1054.717 39/16
44 1578.9815 1079.2453 5/2
45 1614.8675 1130.7736 28/11, 33/13
46 1650.7534 1128.3019 13/5
47 1686.6393 1152.8302 45/17
48 1722.5253 1177.3585 119/44
49 1758.4112 1201.8868 105/38
50 1794.2972 1226.4151 48/17, 45/16
51 1830.1831 1250.9434 72/25
52 1866.0691 1275.4717 147/50, 144/49
53 1901.955 1300 exact 3/1
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