82edo

82edo, or 82 equal temperament, divides the octave into 82 equal parts of 14.634 cents each. The patent val is contorted in the 11-limit, from 82 = 2*41, and in the 13-limit the patent val tempers out 169/168 and 676/675, and in the 17-limit tempers out 273/272. It provides the optimal patent val for soothsaying temperament and supports baladic temperament.

Approximation of prime harmonics in 82edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.48	-5.83	-2.97	+4.78	-6.38	-2.52	-4.83	+0.99	-5.19	-3.57
	Relative (%)	+0.0	+3.3	-39.8	-20.3	+32.7	-43.6	-17.2	-33.0	+6.8	-35.4	-24.4
Steps (reduced)		82 (0)	130 (48)	190 (26)	230 (66)	284 (38)	303 (57)	335 (7)	348 (20)	371 (43)	398 (70)	406 (78)

Interval table

Degree	Cents
0	0.000
1	14.634
2	29.268
3	43.902
4	58.537
5	73.171
6	87.805
7	102.439
8	117.073
9	131.707
10	146.341
11	160.976
12	175.610
13	190.244
14	204.878
15	219.512
16	234.146
17	248.780
18	263.415
19	278.049
20	292.683
21	307.317
22	321.951
23	336.585
24	351.220
25	365.854
26	380.488
27	395.122
28	409.756
29	424.390
30	439.024
31	453.659
32	468.293
33	482.927
34	497.561
35	512.195
36	526.829
37	541.463
38	556.098
39	570.732
40	585.366
41	600.000
...	...