182edo

From Xenharmonic Wiki
Jump to navigation Jump to search
← 181edo182edo183edo →
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 6.593 ¢ each. Each step represents a frequency ratio of 21/182, or the 182nd root of 2.

Theory

182edo is inconsistent to the 5-limit and higher limit, 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 2.7.9.15.17.19 subgroup temperament.

182edo (182bef val) is a tuning for 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 +41 +6 +7 +38 -48 -5 +8 -12 -40 -29
Steps
(reduced)
288
(106)
423
(59)
511
(147)
577
(31)
630
(84)
673
(127)
711
(165)
744
(16)
773
(45)
799
(71)
823
(95)

Regular temperament properties

Commas

Using the patent val, it tempers out the quinbigu comma, 10077696/9765625 and 3486784401/3355443200 in the 5-limit; 126/125, 1728/1715, and 1937102445/1879048192 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 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. Using the 182ce val, it tempers out the kleisma, 15625/15552 and the lalagu 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 182f val, 144/143, 847/845, 1001/1000, and 1716/1715 are tempered out in the 13-limit.