# 182edo

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 ← 181edo 182edo 183edo →
Prime factorization 2 × 7 × 13
Step size 6.59341¢
Fifth 106\182 (698.901¢) (→53\91)
Semitones (A1:m2) 14:16 (92.31¢ : 105.5¢)
Dual sharp fifth 107\182 (705.495¢)
Dual flat fifth 106\182 (698.901¢) (→53\91)
Dual major 2nd 31\182 (204.396¢)
Consistency limit 3
Distinct consistency limit 3

182 equal divisions of the octave (abbreviated 182edo or 182ed2), also called 182-tone equal temperament (182tet) or 182 equal temperament (182et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 182 equal parts of about 6.59 ¢ each. Each step represents a frequency ratio of 21/182, or the 182nd root of 2.

182edo is inconsistent to the 5-odd-limit and higher limits, with three mappings suitable for the 11-limit: 182 288 423 511 630] (patent val), 182 289 423 511 630] (182b), and 182 288 422 511 629] (182ce). It does have a potential as a 2.9.15.7.17.19 subgroup temperament.

Using the patent val, it tempers out the mynic comma, 10077696/9765625 and [-27 20 -2 in the 5-limit; 126/125, 1728/1715, and [-28 18 1 -1 in the 7-limit; 2187/2156, 2835/2816, 5632/5625, and 14700/14641 in the 11-limit; 364/363, 676/675, 1287/1280, and 1701/1690 in the 13-limit. Using the 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.

Using the 182ce val, it tempers out the kleisma, 15625/15552 and the python comma, 43046721/41943040 in the 5-limit; 2430/2401, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, 2420/2401, and 6250/6237 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1575/1573, and 1625/1617 in the 13-limit.

Using the 182b val, it tempers out the diaschisma, 2048/2025 and [-4 -37 27; in the 5-limit; 245/243, 6144/6125, and 9882516/9765625 in the 7-limit; 3025/3024, 3773/3750, and 4000/3993 in the 11-limit. Using the 182bf val, 196/195, 325/324, 364/363, and 1001/1000 are tempered out in the 13-limit. The 182bef val supports the shrutar temperament in the 19-limit and petrtri in the 2.11/5.13/5 subgroup.

### Odd harmonics

Approximation of odd harmonics in 182edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -3.05 +2.70 +0.40 +0.49 +2.53 -3.17 -0.36 +0.54 -0.81 -2.65 -1.90
Relative (%) -46.3 +40.9 +6.1 +7.4 +38.3 -48.0 -5.4 +8.2 -12.3 -40.2 -28.8
Steps
(reduced)
288
(106)
423
(59)
511
(147)
577
(31)
630
(84)
673
(127)
711
(165)
744
(16)
773
(45)
799
(71)
823
(95)

### Subsets and supersets

Since 182 factors into 2 × 7 × 13, 182edo has subset edos 2, 7, 13, 14, 26, and 91.