82edo

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← 81edo82edo83edo →
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

82 equal divisions of the octave (abbreviated 82edo or 82ed2), also called 82-tone equal temperament (82tet) or 82 equal temperament (82et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 82 equal parts of about 14.6 ¢ each. Each step represents a frequency ratio of 21/82, or the 82nd root of 2.

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)

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