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'''53EDT''' is the [[Edt|equal division of the third harmonic]] into 53 parts of 35.8859 [[cent|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).
{{Infobox ET}}
{{ED intro}}


==Intervals==
== Theory ==
53edt corresponds 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).


{| class="wikitable"
=== Harmonics ===
{{Harmonics in equal|53|3|1|columns=11}}
{{Harmonics in equal|53|3|1|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 53edt (continued)}}
 
== Intervals ==
{| class="wikitable center-1 right-2 right-3"
|-
|-
! | degree
! #
! | cents value
! Cents
! | corresponding <br>JI intervals
! Hekts
! | comments
! Approximate ratios
|-
|-
| | 0
| 0
| | 0.0000
| 0.0000
| | '''exact [[1/1]]'''
| 0.0000
| |
| [[1/1]]
|-
|-
| | 1
| 1
| | 35.8859
| 35.8859
| | [[50/49]], [[49/48]]
| 24.5283
| |
| [[50/49]], [[49/48]]
|-
|-
| | 2
| 2
| | 71.7719
| 71.7719
| | [[25/24]]
| 49.0566
| |
| [[25/24]]
|-
|-
| | 3
| 3
| | 107.6578
| 107.6578
| |
| 73.5849
| |
| [[17/16]], [[16/15]]
|-
|-
| | 4
| 4
| | 143.5438
| 143.5438
| | 38/35
| 98.1132
| |
| 38/35
|-
|-
| | 5
| 5
| | 179.4297
| 179.4297
| | 51/46, 132/119
| 122.6415
| |
| 51/46, 132/119
|-
|-
| | 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
| | [[16/13]]
| 245.283
| |
| [[16/13]]
|-
|-
| | 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
| | [[15/11]]
| 367.9245
| |
| [[15/11]]
|-
|-
| | 16
| 16
| | 574.1751
| 574.1751
| | 39/28
| 392.4528
| |
| 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
| |  
|  
|-
|-
| | 21
| 21
| | 753.6048
| 753.6048
| | [[17/11]]
| 515.0943
| |
| [[17/11]]
|-
|-
| | 22
| 22
| | 789.4908
| 789.4908
| | [[30/19]]
| 539.6226
| |
| [[30/19]]
|-
|-
| | 23
| 23
| | 825.3767
| 825.3767
| |
| 564.1509
| |
| [[13/8]]
|-
|-
| | 24
| 24
| | 861.2626
| 861.2626
| |
| 588.67945
| |  
|  
|-
|-
| | 25
| 25
| | 897.1486
| 897.1486
| |
| 613.20755
| |
| 42/25, 32/19
|-
|-
| | 26
| 26
| | 933.0345
| 933.0345
| | [[12/7]]
| 637.73585
| |
| [[12/7]]
|-
|-
| | 27
| 27
| | 968.9205
| 968.9205
| | [[7/4]]
| 662.26415
| |
| [[7/4]]
|-
|-
| | 28
| 28
| | 1004.8064
| 1004.8064
| |
| 686.79245
| |
| 25/14, 57/32
|-
|-
| | 29
| 29
| | 1040.6924
| 1040.6924
| |
| 711.32075
| |  
|  
|-
|-
| | 30
| 30
| | 1076.5783
| 1076.5783
| |
| 735.8491
| |
| 24/13
|-
|-
| | 31
| 31
| | 1112.4642
| 1112.4642
| | [[19/10]]
| 760.3774
| |
| [[19/10]]
|-
|-
| | 32
| 32
| | 1148.3502
| 1148.3502
| | 33/17
| 784.9057
| |
| 33/17
|-
|-
| | 33
| 33
| | 1184.2361
| 1184.2361
| |
| 809.434
| |  
|  
|-
|-
| | 34
| 34
| | 1220.1221
| 1220.1221
| | 85/42
| 833.9623
| |
| 85/42, 81/40
|-
|-
| | 35
| 35
| | 1256.0080
| 1256.008
| | 95/46
| 858.4906
| |
| 95/46
|-
|-
| | 36
| 36
| | 1291.8940
| 1291.894
| |
| 883.0189
| |
| 21/10
|-
|-
| | 37
| 37
| | 1327.7799
| 1327.7799
| | [[14/13|28/13]]
| 907.5472
| |
| [[14/13|28/13]]
|-
|-
| | 38
| 38
| | 1363.6658
| 1363.6658
| | [[11/5]]
| 932.0755
| |
| [[11/5]]
|-
|-
| | 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
| | [[39/32|39/16]]
| 1054.717
| |
| [[39/32|39/16]]
|-
|-
| | 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
| | 119/44
| 1177.3585
| |
| 119/44
|-
|-
| | 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
| | [[36/25|72/25]]
| 1250.9434
| |
| [[36/25|72/25]]
|-
|-
| | 52
| 52
| | 1866.0691
| 1866.0691
| |
| 1275.4717
| |
| 147/50, 144/49
|-
|-
| | 53
| 53
| | 1901.9550
| 1901.955
| | '''exact [[3/1]]'''
| 1300.0000
| |
| [[3/1]]
|}
|}


[[Category:Edt]]
{{Todo|unify precision|review}}
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/53edt"