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61edo: Difference between revisions

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=61 tone equal temperament=
'''61edo''' refers to the equal division of [[2/1]] ratio into 61 equal parts, of 19.6721 [[cent]]s each.  
'''61-EDO''' refers to the equal division of [[2/1|2/1]] ratio into 61 equal parts, of 19.6721 [[cent|cent]]s each. It is the 18th [[prime_numbers|prime]] EDO, after of [[59edo|59edo]] and before of [[67edo|67edo]]. It provides the optimal patent val for the 24&37 temperament in the 7-, 11- and 13-limit.


=Poem=
61edo is the 18th [[prime numbers|prime]] EDO, after of [[59edo]] and before of [[67edo]]. It provides the [[optimal patent val]] for the 24&37 temperament in the 7-, 11- and 13-limit.
 
== Poem ==
These 61 equal divisions of the octave,
These 61 equal divisions of the octave,


Line 23: Line 24:
and the 21st and 23rd are but a cent or two sharp!
and the 21st and 23rd are but a cent or two sharp!


==61-EDO Intervals==
== Intervals ==


{| class="wikitable"
{| class="wikitable center-1 right-2"
|-
|-
| | '''Degrees'''
! #
| | '''Cent Value'''
! Cents
|-
|-
| 0
| 0
|0.0000
| 0.000
|-
| 1
| 19.672
|-
|-
| | 1
| 2
| | 19.6721
| 39.344
|-
|-
| | 2
| 3
| | 39.3443
| 59.016
|-
|-
| | 3
| 4
| | 59.0164
| 78.689
|-
|-
| | 4
| 5
| | 78.6885
| 98.361
|-
|-
| | 5
| 6
| | 98.3607
| 118.033
|-
|-
| | 6
| 7
| | 118.0328
| 137.705
|-
|-
| | 7
| 8
| | 137.7049
| 157.377
|-
|-
| | 8
| 9
| | 157.37705
| 177.049
|-
|-
| | 9
| 10
| | 177.0492
| 196.721
|-
|-
| | 10
| 11
| | 196.7213
| 216.393
|-
|-
| | 11
| 12
| | 216.3934
| 236.066
|-
|-
| | 12
| 13
| | 236.0656
| 255.738
|-
|-
| | 13
| 14
| | 255.7377
| 275.410
|-
|-
| | 14
| 15
| | 275.4098
| 295.082
|-
|-
| | 15
| 16
| | 295.082
| 314.754
|-
|-
| | 16
| 17
| | 314.7541
| 334.426
|-
|-
| | 17
| 18
| | 334.4262
| 354.098
|-
|-
| | 18
| 19
| | 354.0984
| 373.770
|-
|-
| | 19
| 20
| | 373.7705
| 393.443
|-
|-
| | 20
| 21
| | 393.4426
| 413.115
|-
|-
| | 21
| 22
| | 413.11475
| 432.787
|-
|-
| | 22
| 23
| | 432.7869
| 452.459
|-
|-
| | 23
| 24
| | 452.459
| 472.131
|-
|-
| | 24
| 25
| | 472.13115
| 491.803
|-
|-
| | 25
| 26
| | 491.8033
| 511.475
|-
|-
| | 26
| 27
| | 511.4754
| 531.148
|-
|-
| | 27
| 28
| | 531.1475
| 550.820
|-
|-
| | 28
| 29
| | 550.8197
| 570.492
|-
|-
| | 29
| 30
| | 570.4918
| 590.164
|-
|-
| | 30
| 31
| | 590.1639
| 609.836
|-
|-
| | 31
| 32
| | 609.8361
| 629.508
|-
|-
| | 32
| 33
| | 629.5082
| 649.180
|-
|-
| | 33
| 34
| | 649.1803
| 668.852
|-
|-
| | 34
| 35
| | 668.8525
| 688.525
|-
|-
| | 35
| 36
| | 688.5246
| 708.197
|-
|-
| | 36
| 37
| | 708.1967
| 727.869
|-
|-
| | 37
| 38
| | 727.86885
| 747.541
|-
|-
| | 38
| 39
| | 747.541
| 767.213
|-
|-
| | 39
| 40
| | 767.2131
| 786.885
|-
|-
| | 40
| 41
| | 786.88525
| 806.557
|-
|-
| | 41
| 42
| | 806.5574
| 826.230
|-
|-
| | 42
| 43
| | 826.2295
| 845.902
|-
|-
| | 43
| 44
| | 845.9016
| 865.574
|-
|-
| | 44
| 45
| | 865.5738
| 885.246
|-
|-
| | 45
| 46
| | 885.2459
| 904.918
|-
|-
| | 46
| 47
| | 904.918
| 924.590
|-
|-
| | 47
| 48
| | 924.5902
| 944.262
|-
|-
| | 48
| 49
| | 944.2623
| 963.934
|-
|-
| | 49
| 50
| | 963.9344
| 983.607
|-
|-
| | 50
| 51
| | 983.6066
| 1003.279
|-
|-
| | 51
| 52
| | 1003.2787
| 1022.951
|-
|-
| | 52
| 53
| | 1022.9508
| 1042.623
|-
|-
| | 53
| 54
| | 1042.62295
| 1062.295
|-
|-
| | 54
| 55
| | 1062.2951
| 1081.967
|-
|-
| | 55
| 56
| | 1081.9672
| 1101.639
|-
|-
| | 56
| 57
| | 1101.6393
| 1121.311
|-
|-
| | 57
| 58
| | 1121.3115
| 1140.984
|-
|-
| | 58
| 59
| | 1140.9836
| 1160.656
|-
|-
| | 59
| 60
| | 1160.6557
| 1180.328
|-
|-
| | 60
| 61
| | 1180.3279
| 1200.000
|}
|}


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