61edo

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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
0 0
1 19.6721
2 39.3443
3 59.0164
4 78.6885
5 98.3607
6 118.0328
7 137.7049
8 157.377
9 177.0492
10 196.7213
11 216.3934
12 236.0656
13 255.7377
14 275.4098
15 295.082
16 314.7541
17 334.4262
18 354.0984
19 373.7705
20 393.4426
21 413.1148
22 432.7869
23 452.459
24 472.1311
25 491.8033
26 511.4754
27 531.1475
28 550.8197
29 570.4918
30 590.1639
31 609.8361
32 629.5082
33 649.1803
34 668.8525
35 688.5246
36 708.1967
37 727.8689
38 747.541
39 767.2131
40 786.8852
41 806.5574
42 826.2295
43 845.9016
44 865.5738
45 885.2459
46 904.918
47 924.5902
48 944.2623
49 963.9344
50 983.6066
51 1003.2787
52 1022.9508
53 1042.623
54 1062.2951
55 1081.9672
56 1101.6393
57 1121.3115
58 1140.9836
59 1160.6557
60 1180.3279