61edo: Difference between revisions

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| | '''Degrees'''
| | '''Degrees'''
| | '''Cent Value'''
| | '''Cent Value'''
|Pions
|7mus
|-
|-
| | 0
| | 0
| | 0
| colspan="3"| 0
|-
|-
| | 1
| | 1
| | 19.6721
| | 19.6721
|20.8525
|25.1803 (19.2E2A<sub>16</sub>)
|-
|-
| | 2
| | 2
| | 39.3443
| | 39.3443
|41.7049
|50.3607 (32.5C54<sub>16</sub>)
|-
|-
| | 3
| | 3
| | 59.0164
| | 59.0164
|62.5574
|75.541 (4B.8A7E<sub>16</sub>)
|-
|-
| | 4
| | 4
| | 78.6885
| | 78.6885
|83.4098
|100.7213 (64.B8A8<sub>16</sub>)
|-
|-
| | 5
| | 5
| | 98.3607
| | 98.3607
|104.2623
|125.9016 (7D.E6D2<sub>16</sub>)
|-
|-
| | 6
| | 6
| | 118.0328
| | 118.0328
|125.11475
|151.082 (97.14FC<sub>16</sub>)
|-
|-
| | 7
| | 7
| | 137.7049
| | 137.7049
|145.9672
|176.2623 (B0.4326<sub>16</sub>)
|-
|-
| | 8
| | 8
| | 157.377
| | 157.37705
|166.8197
|201.4426 (C9.715<sub>16</sub>)
|-
|-
| | 9
| | 9
| | 177.0492
| | 177.0492
|187.6721
|226.62295 (E2.9F7A<sub>16</sub>)
|-
|-
| | 10
| | 10
| | 196.7213
| | 196.7213
|208.5246
|251.8033 (FB.CDA4<sub>16</sub>)
|-
|-
| | 11
| | 11
| | 216.3934
| | 216.3934
|229.37705
|276.9836 (114.FBCE<sub>16</sub>)
|-
|-
| | 12
| | 12
| | 236.0656
| | 236.0656
|250.2295
|302.1639 (12E.29F8<sub>16</sub>)
|-
|-
| | 13
| | 13
| | 255.7377
| | 255.7377
|271.082
|327.3443 (147.5822<sub>16</sub>)
|-
|-
| | 14
| | 14
| | 275.4098
| | 275.4098
|291.9344
|352.5246 (160.864B8<sub>16</sub>)
|-
|-
| | 15
| | 15
| | 295.082
| | 295.082
|312.7869
|377.7049 (179.B4758<sub>16</sub>)
|-
|-
| | 16
| | 16
| | 314.7541
| | 314.7541
|333.6393
|402.88525 (192.E29F8<sub>16</sub>)
|-
|-
| | 17
| | 17
| | 334.4262
| | 334.4262
|354.4918
|428.0656 (1AC.10BC<sub>16</sub>)
|-
|-
| | 18
| | 18
| | 354.0984
| | 354.0984
|375.3443
|453.2459 (1C5.3EF3<sub>16</sub>)
|-
|-
| | 19
| | 19
| | 373.7705
| | 373.7705
|396.1967
|478.4262 (1DE.6D1E<sub>16</sub>)
|-
|-
| | 20
| | 20
| | 393.4426
| | 393.4426
|417.0492
|503.6066 (1F7.9B47<sub>16</sub>)
|-
|-
| | 21
| | 21
| | 413.1148
| | 413.11475
|437.9016
|528.7869 (210.C971<sub>16</sub>)
|-
|-
| | 22
| | 22
| | 432.7869
| | 432.7869
|458.7541
|553.9672 (229.F79B<sub>16</sub>)
|-
|-
| | 23
| | 23
| | 452.459
| | 452.459
|479.6066
|579.1475 (243.25C5<sub>16</sub>)
|-
|-
| | 24
| | 24
| | 472.1311
| | 472.13115
|500.459
|604.3279 (25C.53EF<sub>16</sub>)
|-
|-
| | 25
| | 25
| | 491.8033
| | 491.8033
|521.3115
|629.5082 (275.8219<sub>16</sub>)
|-
|-
| | 26
| | 26
| | 511.4754
| | 511.4754
|542.1639
|654.6885 (28E.B043<sub>16)</sub>
|-
|-
| | 27
| | 27
| | 531.1475
| | 531.1475
|563.0164
|679.86885 (2A7.DE6D<sub>16</sub>)
|-
|-
| | 28
| | 28
| | 550.8197
| | 550.8197
|583.86885
|705.0492 (2C1.0C97<sub>16</sub>)
|-
|-
| | 29
| | 29
| | 570.4918
| | 570.4918
|604.7213
|730.2295 (2DA.3AC1<sub>16</sub>)
|-
|-
| | 30
| | 30
| | 590.1639
| | 590.1639
|625.5738
|755.4098 (2F3.68EB<sub>16</sub>)
|-
|-
| | 31
| | 31
| | 609.8361
| | 609.8361
|646.4262
|780.5902 (30C.9715<sub>16</sub>)
|-
|-
| | 32
| | 32
| | 629.5082
| | 629.5082
|667.2787
|805.7705 (325.C53F<sub>16</sub>)
|-
|-
| | 33
| | 33
| | 649.1803
| | 649.1803
|688.13115
|830.9508 (33E.F359<sub>16</sub>)
|-
|-
| | 34
| | 34
| | 668.8525
| | 668.8525
|708.9836
|856.13115 (358.2183<sub>16</sub>)
|-
|-
| | 35
| | 35
| | 688.5246
| | 688.5246
|729.8361
|881.3115 (371.4FAD<sub>16</sub>)
|-
|-
| | 36
| | 36
| | 708.1967
| | 708.1967
|750.6885
|906.4918 (38A.7DD7<sub>16</sub>)
|-
|-
| | 37
| | 37
| | 727.8689
| | 727.86885
|771.541
|931.6721 (3A3.AC11<sub>16</sub>)
|-
|-
| | 38
| | 38
| | 747.541
| | 747.541
|792.3934
|956.8525 (3BC.DA3B<sub>16</sub>)
|-
|-
| | 39
| | 39
| | 767.2131
| | 767.2131
|813.2459
|982.0328 (3D6.0865<sub>16</sub>)
|-
|-
| | 40
| | 40
| | 786.8852
| | 786.88525
|834.0984
|1007.2169 (3EF.268F<sub>16</sub>
|-
|-
| | 41
| | 41
| | 806.5574
| | 806.5574
|854.9508
|1032.3934 (408.62B9<sub>16</sub>)
|-
|-
| | 42
| | 42
| | 826.2295
| | 826.2295
|875.8033
|1057.5738 (421.90E3<sub>16</sub>)
|-
|-
| | 43
| | 43
| | 845.9016
| | 845.9016
|896.6557
|1082.7541 (43A.BEFD<sub>16</sub>)
|-
|-
| | 44
| | 44
| | 865.5738
| | 865.5738
|917.5082
|1107.9344 (453.EF44<sub>16</sub>)
|-
|-
| | 45
| | 45
| | 885.2459
| | 885.2459
|938.3607
|1133.11475 (46D.1D608<sub>16</sub>)
|-
|-
| | 46
| | 46
| | 904.918
| | 904.918
|959.2131
|1158.2951 (486.4B8A8<sub>16</sub>)
|-
|-
| | 47
| | 47
| | 924.5902
| | 924.5902
|980.0656
|1183.4754 (49F.79B48<sub>16</sub>)
|-
|-
| | 48
| | 48
| | 944.2623
| | 944.2623
|1000.918
|1208.6557 (4B8.A7DE<sub>16</sub>)
|-
|-
| | 49
| | 49
| | 963.9344
| | 963.9344
|1021.7705
|1233.8361 (4D1.D708<sub>16</sub>)
|-
|-
| | 50
| | 50
| | 983.6066
| | 983.6066
|1042.62295
|1259.0164 (4EA.0431<sub>16</sub>)
|-
|-
| | 51
| | 51
| | 1003.2787
| | 1003.2787
|1063.4754
|1284.1967 (504.325C<sub>16</sub>)
|-
|-
| | 52
| | 52
| | 1022.9508
| | 1022.9508
|1084.3279
|1309.37705 (51D.6085<sub>16</sub>)
|-
|-
| | 53
| | 53
| | 1042.623
| | 1042.62295
|1105.1803
|1334.5574 (536.8EB<sub>16</sub>)
|-
|-
| | 54
| | 54
| | 1062.2951
| | 1062.2951
|1126.0328
|1359.7377 (54F.BCDA<sub>16</sub>)
|-
|-
| | 55
| | 55
| | 1081.9672
| | 1081.9672
|1146.88525
|1384.918 (568.EB04<sub>16</sub>)
|-
|-
| | 56
| | 56
| | 1101.6393
| | 1101.6393
|1167.7377
|1410.0984 (582.192E<sub>16</sub>)
|-
|-
| | 57
| | 57
| | 1121.3115
| | 1121.3115
|1188.5902
|1435.2787 (59B.4748<sub>16</sub>)
|-
|-
| | 58
| | 58
| | 1140.9836
| | 1140.9836
|1209.4426
|1460.459 (5B4.7581<sub>16</sub>)
|-
|-
| | 59
| | 59
| | 1160.6557
| | 1160.6557
|1230.2951
|1485.6393 (5CD.A3AB<sub>16</sub>)
|-
|-
| | 60
| | 60
| | 1180.3279
| | 1180.3279
|1251.1475
|1510.8197 (5D7.D1D5<sub>16</sub>)
|}
|}


Revision as of 21:42, 12 May 2019

61 tone equal temperament

61-EDO refers to the equal division of 2/1 ratio into 61 equal parts, of 19.6721 cents each. It is the 18th 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,

though rare are assuredly a ROCK-tave (har har),

while the 3rd and 5th harmonics are about six cents sharp,

(and the flattish 15th poised differently on the harp),

the 7th and 11th err by less, around three,

and thus mayhap, a good orgone tuning found to be;

slightly sharp as well, is the 13th harmonic's place,

but the 9th and 17th lack near so much grace,

interestingly the 19th is good but a couple cents flat,

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

61-EDO Intervals

Degrees Cent Value Pions 7mus
0 0
1 19.6721 20.8525 25.1803 (19.2E2A16)
2 39.3443 41.7049 50.3607 (32.5C5416)
3 59.0164 62.5574 75.541 (4B.8A7E16)
4 78.6885 83.4098 100.7213 (64.B8A816)
5 98.3607 104.2623 125.9016 (7D.E6D216)
6 118.0328 125.11475 151.082 (97.14FC16)
7 137.7049 145.9672 176.2623 (B0.432616)
8 157.37705 166.8197 201.4426 (C9.71516)
9 177.0492 187.6721 226.62295 (E2.9F7A16)
10 196.7213 208.5246 251.8033 (FB.CDA416)
11 216.3934 229.37705 276.9836 (114.FBCE16)
12 236.0656 250.2295 302.1639 (12E.29F816)
13 255.7377 271.082 327.3443 (147.582216)
14 275.4098 291.9344 352.5246 (160.864B816)
15 295.082 312.7869 377.7049 (179.B475816)
16 314.7541 333.6393 402.88525 (192.E29F816)
17 334.4262 354.4918 428.0656 (1AC.10BC16)
18 354.0984 375.3443 453.2459 (1C5.3EF316)
19 373.7705 396.1967 478.4262 (1DE.6D1E16)
20 393.4426 417.0492 503.6066 (1F7.9B4716)
21 413.11475 437.9016 528.7869 (210.C97116)
22 432.7869 458.7541 553.9672 (229.F79B16)
23 452.459 479.6066 579.1475 (243.25C516)
24 472.13115 500.459 604.3279 (25C.53EF16)
25 491.8033 521.3115 629.5082 (275.821916)
26 511.4754 542.1639 654.6885 (28E.B04316)
27 531.1475 563.0164 679.86885 (2A7.DE6D16)
28 550.8197 583.86885 705.0492 (2C1.0C9716)
29 570.4918 604.7213 730.2295 (2DA.3AC116)
30 590.1639 625.5738 755.4098 (2F3.68EB16)
31 609.8361 646.4262 780.5902 (30C.971516)
32 629.5082 667.2787 805.7705 (325.C53F16)
33 649.1803 688.13115 830.9508 (33E.F35916)
34 668.8525 708.9836 856.13115 (358.218316)
35 688.5246 729.8361 881.3115 (371.4FAD16)
36 708.1967 750.6885 906.4918 (38A.7DD716)
37 727.86885 771.541 931.6721 (3A3.AC1116)
38 747.541 792.3934 956.8525 (3BC.DA3B16)
39 767.2131 813.2459 982.0328 (3D6.086516)
40 786.88525 834.0984 1007.2169 (3EF.268F16
41 806.5574 854.9508 1032.3934 (408.62B916)
42 826.2295 875.8033 1057.5738 (421.90E316)
43 845.9016 896.6557 1082.7541 (43A.BEFD16)
44 865.5738 917.5082 1107.9344 (453.EF4416)
45 885.2459 938.3607 1133.11475 (46D.1D60816)
46 904.918 959.2131 1158.2951 (486.4B8A816)
47 924.5902 980.0656 1183.4754 (49F.79B4816)
48 944.2623 1000.918 1208.6557 (4B8.A7DE16)
49 963.9344 1021.7705 1233.8361 (4D1.D70816)
50 983.6066 1042.62295 1259.0164 (4EA.043116)
51 1003.2787 1063.4754 1284.1967 (504.325C16)
52 1022.9508 1084.3279 1309.37705 (51D.608516)
53 1042.62295 1105.1803 1334.5574 (536.8EB16)
54 1062.2951 1126.0328 1359.7377 (54F.BCDA16)
55 1081.9672 1146.88525 1384.918 (568.EB0416)
56 1101.6393 1167.7377 1410.0984 (582.192E16)
57 1121.3115 1188.5902 1435.2787 (59B.474816)
58 1140.9836 1209.4426 1460.459 (5B4.758116)
59 1160.6557 1230.2951 1485.6393 (5CD.A3AB16)
60 1180.3279 1251.1475 1510.8197 (5D7.D1D516)
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