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	7mus
0	0.0000	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)