61edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Jkarimak (talk | contribs)
191 edits
→61-EDO Intervals: Removed pions column
Line 29: Line 29:
| | '''Degrees'''
| | '''Degrees'''
| | '''Cent Value'''
| | '''Cent Value'''
|Pions
|7mus
|7mus
|-
|-
| colspan="4"| 0
| colspan="3" | 0
|-
|-
| | 1
| | 1
| | 19.6721
| | 19.6721
|20.8525
|25.1803 (19.2E2A<sub>16</sub>)
|25.1803 (19.2E2A<sub>16</sub>)
|-
|-
| | 2
| | 2
| | 39.3443
| | 39.3443
|41.7049
|50.3607 (32.5C54<sub>16</sub>)
|50.3607 (32.5C54<sub>16</sub>)
|-
|-
| | 3
| | 3
| | 59.0164
| | 59.0164
|62.5574
|75.541 (4B.8A7E<sub>16</sub>)
|75.541 (4B.8A7E<sub>16</sub>)
|-
|-
| | 4
| | 4
| | 78.6885
| | 78.6885
|83.4098
|100.7213 (64.B8A8<sub>16</sub>)
|100.7213 (64.B8A8<sub>16</sub>)
|-
|-
| | 5
| | 5
| | 98.3607
| | 98.3607
|104.2623
|125.9016 (7D.E6D2<sub>16</sub>)
|125.9016 (7D.E6D2<sub>16</sub>)
|-
|-
| | 6
| | 6
| | 118.0328
| | 118.0328
|125.11475
|151.082 (97.14FC<sub>16</sub>)
|151.082 (97.14FC<sub>16</sub>)
|-
|-
| | 7
| | 7
| | 137.7049
| | 137.7049
|145.9672
|176.2623 (B0.4326<sub>16</sub>)
|176.2623 (B0.4326<sub>16</sub>)
|-
|-
| | 8
| | 8
| | 157.37705
| | 157.37705
|166.8197
|201.4426 (C9.715<sub>16</sub>)
|201.4426 (C9.715<sub>16</sub>)
|-
|-
| | 9
| | 9
| | 177.0492
| | 177.0492
|187.6721
|226.62295 (E2.9F7A<sub>16</sub>)
|226.62295 (E2.9F7A<sub>16</sub>)
|-
|-
| | 10
| | 10
| | 196.7213
| | 196.7213
|208.5246
|251.8033 (FB.CDA4<sub>16</sub>)
|251.8033 (FB.CDA4<sub>16</sub>)
|-
|-
| | 11
| | 11
| | 216.3934
| | 216.3934
|229.37705
|276.9836 (114.FBCE<sub>16</sub>)
|276.9836 (114.FBCE<sub>16</sub>)
|-
|-
| | 12
| | 12
| | 236.0656
| | 236.0656
|250.2295
|302.1639 (12E.29F8<sub>16</sub>)
|302.1639 (12E.29F8<sub>16</sub>)
|-
|-
| | 13
| | 13
| | 255.7377
| | 255.7377
|271.082
|327.3443 (147.5822<sub>16</sub>)
|327.3443 (147.5822<sub>16</sub>)
|-
|-
| | 14
| | 14
| | 275.4098
| | 275.4098
|291.9344
|352.5246 (160.864B8<sub>16</sub>)
|352.5246 (160.864B8<sub>16</sub>)
|-
|-
| | 15
| | 15
| | 295.082
| | 295.082
|312.7869
|377.7049 (179.B4758<sub>16</sub>)
|377.7049 (179.B4758<sub>16</sub>)
|-
|-
| | 16
| | 16
| | 314.7541
| | 314.7541
|333.6393
|402.88525 (192.E29F8<sub>16</sub>)
|402.88525 (192.E29F8<sub>16</sub>)
|-
|-
| | 17
| | 17
| | 334.4262
| | 334.4262
|354.4918
|428.0656 (1AC.10BC<sub>16</sub>)
|428.0656 (1AC.10BC<sub>16</sub>)
|-
|-
| | 18
| | 18
| | 354.0984
| | 354.0984
|375.3443
|453.2459 (1C5.3EF3<sub>16</sub>)
|453.2459 (1C5.3EF3<sub>16</sub>)
|-
|-
| | 19
| | 19
| | 373.7705
| | 373.7705
|396.1967
|478.4262 (1DE.6D1E<sub>16</sub>)
|478.4262 (1DE.6D1E<sub>16</sub>)
|-
|-
| | 20
| | 20
| | 393.4426
| | 393.4426
|417.0492
|503.6066 (1F7.9B47<sub>16</sub>)
|503.6066 (1F7.9B47<sub>16</sub>)
|-
|-
| | 21
| | 21
| | 413.11475
| | 413.11475
|437.9016
|528.7869 (210.C971<sub>16</sub>)
|528.7869 (210.C971<sub>16</sub>)
|-
|-
| | 22
| | 22
| | 432.7869
| | 432.7869
|458.7541
|553.9672 (229.F79B<sub>16</sub>)
|553.9672 (229.F79B<sub>16</sub>)
|-
|-
| | 23
| | 23
| | 452.459
| | 452.459
|479.6066
|579.1475 (243.25C5<sub>16</sub>)
|579.1475 (243.25C5<sub>16</sub>)
|-
|-
| | 24
| | 24
| | 472.13115
| | 472.13115
|500.459
|604.3279 (25C.53EF<sub>16</sub>)
|604.3279 (25C.53EF<sub>16</sub>)
|-
|-
| | 25
| | 25
| | 491.8033
| | 491.8033
|521.3115
|629.5082 (275.8219<sub>16</sub>)
|629.5082 (275.8219<sub>16</sub>)
|-
|-
| | 26
| | 26
| | 511.4754
| | 511.4754
|542.1639
|654.6885 (28E.B043<sub>16)</sub>
|654.6885 (28E.B043<sub>16)</sub>
|-
|-
| | 27
| | 27
| | 531.1475
| | 531.1475
|563.0164
|679.86885 (2A7.DE6D<sub>16</sub>)
|679.86885 (2A7.DE6D<sub>16</sub>)
|-
|-
| | 28
| | 28
| | 550.8197
| | 550.8197
|583.86885
|705.0492 (2C1.0C97<sub>16</sub>)
|705.0492 (2C1.0C97<sub>16</sub>)
|-
|-
| | 29
| | 29
| | 570.4918
| | 570.4918
|604.7213
|730.2295 (2DA.3AC1<sub>16</sub>)
|730.2295 (2DA.3AC1<sub>16</sub>)
|-
|-
| | 30
| | 30
| | 590.1639
| | 590.1639
|625.5738
|755.4098 (2F3.68EB<sub>16</sub>)
|755.4098 (2F3.68EB<sub>16</sub>)
|-
|-
| | 31
| | 31
| | 609.8361
| | 609.8361
|646.4262
|780.5902 (30C.9715<sub>16</sub>)
|780.5902 (30C.9715<sub>16</sub>)
|-
|-
| | 32
| | 32
| | 629.5082
| | 629.5082
|667.2787
|805.7705 (325.C53F<sub>16</sub>)
|805.7705 (325.C53F<sub>16</sub>)
|-
|-
| | 33
| | 33
| | 649.1803
| | 649.1803
|688.13115
|830.9508 (33E.F359<sub>16</sub>)
|830.9508 (33E.F359<sub>16</sub>)
|-
|-
| | 34
| | 34
| | 668.8525
| | 668.8525
|708.9836
|856.13115 (358.2183<sub>16</sub>)
|856.13115 (358.2183<sub>16</sub>)
|-
|-
| | 35
| | 35
| | 688.5246
| | 688.5246
|729.8361
|881.3115 (371.4FAD<sub>16</sub>)
|881.3115 (371.4FAD<sub>16</sub>)
|-
|-
| | 36
| | 36
| | 708.1967
| | 708.1967
|750.6885
|906.4918 (38A.7DD7<sub>16</sub>)
|906.4918 (38A.7DD7<sub>16</sub>)
|-
|-
| | 37
| | 37
| | 727.86885
| | 727.86885
|771.541
|931.6721 (3A3.AC11<sub>16</sub>)
|931.6721 (3A3.AC11<sub>16</sub>)
|-
|-
| | 38
| | 38
| | 747.541
| | 747.541
|792.3934
|956.8525 (3BC.DA3B<sub>16</sub>)
|956.8525 (3BC.DA3B<sub>16</sub>)
|-
|-
| | 39
| | 39
| | 767.2131
| | 767.2131
|813.2459
|982.0328 (3D6.0865<sub>16</sub>)
|982.0328 (3D6.0865<sub>16</sub>)
|-
|-
| | 40
| | 40
| | 786.88525
| | 786.88525
|834.0984
|1007.2169 (3EF.268F<sub>16</sub>
|1007.2169 (3EF.268F<sub>16</sub>
|-
|-
| | 41
| | 41
| | 806.5574
| | 806.5574
|854.9508
|1032.3934 (408.62B9<sub>16</sub>)
|1032.3934 (408.62B9<sub>16</sub>)
|-
|-
| | 42
| | 42
| | 826.2295
| | 826.2295
|875.8033
|1057.5738 (421.90E3<sub>16</sub>)
|1057.5738 (421.90E3<sub>16</sub>)
|-
|-
| | 43
| | 43
| | 845.9016
| | 845.9016
|896.6557
|1082.7541 (43A.BEFD<sub>16</sub>)
|1082.7541 (43A.BEFD<sub>16</sub>)
|-
|-
| | 44
| | 44
| | 865.5738
| | 865.5738
|917.5082
|1107.9344 (453.EF44<sub>16</sub>)
|1107.9344 (453.EF44<sub>16</sub>)
|-
|-
| | 45
| | 45
| | 885.2459
| | 885.2459
|938.3607
|1133.11475 (46D.1D608<sub>16</sub>)
|1133.11475 (46D.1D608<sub>16</sub>)
|-
|-
| | 46
| | 46
| | 904.918
| | 904.918
|959.2131
|1158.2951 (486.4B8A8<sub>16</sub>)
|1158.2951 (486.4B8A8<sub>16</sub>)
|-
|-
| | 47
| | 47
| | 924.5902
| | 924.5902
|980.0656
|1183.4754 (49F.79B48<sub>16</sub>)
|1183.4754 (49F.79B48<sub>16</sub>)
|-
|-
| | 48
| | 48
| | 944.2623
| | 944.2623
|1000.918
|1208.6557 (4B8.A7DE<sub>16</sub>)
|1208.6557 (4B8.A7DE<sub>16</sub>)
|-
|-
| | 49
| | 49
| | 963.9344
| | 963.9344
|1021.7705
|1233.8361 (4D1.D708<sub>16</sub>)
|1233.8361 (4D1.D708<sub>16</sub>)
|-
|-
| | 50
| | 50
| | 983.6066
| | 983.6066
|1042.62295
|1259.0164 (4EA.0431<sub>16</sub>)
|1259.0164 (4EA.0431<sub>16</sub>)
|-
|-
| | 51
| | 51
| | 1003.2787
| | 1003.2787
|1063.4754
|1284.1967 (504.325C<sub>16</sub>)
|1284.1967 (504.325C<sub>16</sub>)
|-
|-
| | 52
| | 52
| | 1022.9508
| | 1022.9508
|1084.3279
|1309.37705 (51D.6085<sub>16</sub>)
|1309.37705 (51D.6085<sub>16</sub>)
|-
|-
| | 53
| | 53
| | 1042.62295
| | 1042.62295
|1105.1803
|1334.5574 (536.8EB<sub>16</sub>)
|1334.5574 (536.8EB<sub>16</sub>)
|-
|-
| | 54
| | 54
| | 1062.2951
| | 1062.2951
|1126.0328
|1359.7377 (54F.BCDA<sub>16</sub>)
|1359.7377 (54F.BCDA<sub>16</sub>)
|-
|-
| | 55
| | 55
| | 1081.9672
| | 1081.9672
|1146.88525
|1384.918 (568.EB04<sub>16</sub>)
|1384.918 (568.EB04<sub>16</sub>)
|-
|-
| | 56
| | 56
| | 1101.6393
| | 1101.6393
|1167.7377
|1410.0984 (582.192E<sub>16</sub>)
|1410.0984 (582.192E<sub>16</sub>)
|-
|-
| | 57
| | 57
| | 1121.3115
| | 1121.3115
|1188.5902
|1435.2787 (59B.4748<sub>16</sub>)
|1435.2787 (59B.4748<sub>16</sub>)
|-
|-
| | 58
| | 58
| | 1140.9836
| | 1140.9836
|1209.4426
|1460.459 (5B4.7581<sub>16</sub>)
|1460.459 (5B4.7581<sub>16</sub>)
|-
|-
| | 59
| | 59
| | 1160.6557
| | 1160.6557
|1230.2951
|1485.6393 (5CD.A3AB<sub>16</sub>)
|1485.6393 (5CD.A3AB<sub>16</sub>)
|-
|-
| | 60
| | 60
| | 1180.3279
| | 1180.3279
|1251.1475
|1510.8197 (5D7.D1D5<sub>16</sub>)
|1510.8197 (5D7.D1D5<sub>16</sub>)
|}
|}

Revision as of 13:15, 12 December 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 7mus
0
1 19.6721 25.1803 (19.2E2A16)
2 39.3443 50.3607 (32.5C5416)
3 59.0164 75.541 (4B.8A7E16)
4 78.6885 100.7213 (64.B8A816)
5 98.3607 125.9016 (7D.E6D216)
6 118.0328 151.082 (97.14FC16)
7 137.7049 176.2623 (B0.432616)
8 157.37705 201.4426 (C9.71516)
9 177.0492 226.62295 (E2.9F7A16)
10 196.7213 251.8033 (FB.CDA416)
11 216.3934 276.9836 (114.FBCE16)
12 236.0656 302.1639 (12E.29F816)
13 255.7377 327.3443 (147.582216)
14 275.4098 352.5246 (160.864B816)
15 295.082 377.7049 (179.B475816)
16 314.7541 402.88525 (192.E29F816)
17 334.4262 428.0656 (1AC.10BC16)
18 354.0984 453.2459 (1C5.3EF316)
19 373.7705 478.4262 (1DE.6D1E16)
20 393.4426 503.6066 (1F7.9B4716)
21 413.11475 528.7869 (210.C97116)
22 432.7869 553.9672 (229.F79B16)
23 452.459 579.1475 (243.25C516)
24 472.13115 604.3279 (25C.53EF16)
25 491.8033 629.5082 (275.821916)
26 511.4754 654.6885 (28E.B04316)
27 531.1475 679.86885 (2A7.DE6D16)
28 550.8197 705.0492 (2C1.0C9716)
29 570.4918 730.2295 (2DA.3AC116)
30 590.1639 755.4098 (2F3.68EB16)
31 609.8361 780.5902 (30C.971516)
32 629.5082 805.7705 (325.C53F16)
33 649.1803 830.9508 (33E.F35916)
34 668.8525 856.13115 (358.218316)
35 688.5246 881.3115 (371.4FAD16)
36 708.1967 906.4918 (38A.7DD716)
37 727.86885 931.6721 (3A3.AC1116)
38 747.541 956.8525 (3BC.DA3B16)
39 767.2131 982.0328 (3D6.086516)
40 786.88525 1007.2169 (3EF.268F16
41 806.5574 1032.3934 (408.62B916)
42 826.2295 1057.5738 (421.90E316)
43 845.9016 1082.7541 (43A.BEFD16)
44 865.5738 1107.9344 (453.EF4416)
45 885.2459 1133.11475 (46D.1D60816)
46 904.918 1158.2951 (486.4B8A816)
47 924.5902 1183.4754 (49F.79B4816)
48 944.2623 1208.6557 (4B8.A7DE16)
49 963.9344 1233.8361 (4D1.D70816)
50 983.6066 1259.0164 (4EA.043116)
51 1003.2787 1284.1967 (504.325C16)
52 1022.9508 1309.37705 (51D.608516)
53 1042.62295 1334.5574 (536.8EB16)
54 1062.2951 1359.7377 (54F.BCDA16)
55 1081.9672 1384.918 (568.EB0416)
56 1101.6393 1410.0984 (582.192E16)
57 1121.3115 1435.2787 (59B.474816)
58 1140.9836 1460.459 (5B4.758116)
59 1160.6557 1485.6393 (5CD.A3AB16)
60 1180.3279 1510.8197 (5D7.D1D516)
Retrieved from "https://en.xen.wiki/index.php?title=61edo&oldid=42612"