editing disabled

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