61edo

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	0.0000
1	19.6721
2	39.3443
3	59.0164
4	78.6885
5	98.3607
6	118.0328
7	137.7049
8	157.37705
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	413.11475
22	432.7869
23	452.459
24	472.13115
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	727.86885
38	747.541
39	767.2131
40	786.88525
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	1042.62295
54	1062.2951
55	1081.9672
56	1101.6393
57	1121.3115
58	1140.9836
59	1160.6557
60	1180.3279