82edo

← 81edo

82edo

83edo →

Prime factorization	2 × 41
Step size	14.6341 ¢
Fifth	48\82 (702.439 ¢) (→ 24\41)
Semitones (A1:m2)	8:6 (117.1 ¢ : 87.8 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

82edo's patent val is contorted in the 11-limit, from 82 = 2 × 41. 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.

Prime harmonics

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)

Subsets and supersets

82edo contains 2edo and 41edo as subsets. 164edo, which doubles it, is a notable tuning.

A step of 82edo is exactly 30 minas.

Intervals

#	Cents	21-odd-limit no-11 ratios	Additional Ratios with 11's (82e Val)	Additional Ratios with 11's (Patent Val)
0	0.000	1/1	1/1	1/1
1	14.634
2	29.268
3	43.902
4	58.537
5	73.171		22/21
6	87.805	21/20, 20/19, 19/18		22/21
7	102.439	18/17, 17/16
8	117.073	16/15, 15/14
9	131.707	14/13, 13/12
10	146.341			12/11
11	160.976		12/11, 11/10
12	175.610	10/9, 21/19		11/10
13	190.244	19/17
14	204.878	9/8
15	219.512	17/15
16	234.146	8/7
17	248.780	15/13	22/19
18	263.415	7/6		22/19
19	278.049	20/17		13/11
20	292.683	19/16	13/11
21	307.317
22	321.951	6/5
23	336.585	17/14	11/9
24	351.220			11/9
25	365.854	16/13, 21/17, 26/21
26	380.488	5/4
27	395.122
28	409.756	24/19, 19/15		14/11
29	424.390		14/11
30	439.024	9/7	22/17
31	453.659	13/10		22/17
32	468.293	17/13, 21/16
33	482.927
34	497.561	4/3
35	512.195
36	526.829	19/14		15/11
37	541.463	26/19	15/11, 11/8
38	556.098			11/8
39	570.732	18/13
40	585.366	7/5
41	600.000	24/17, 17/12
…	…