181edo

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← 180edo181edo182edo →
Prime factorization 181 (prime)
Step size 6.62983¢
Fifth 106\181 (702.762¢)
Semitones (A1:m2) 18:13 (119.3¢ : 86.19¢)
Consistency limit 7
Distinct consistency limit 7

The 181 equal divisions of the octave (181edo), or the 181(-tone) equal temperament (181tet, 181et) when viewed from a regular temperament perspective, is the equal division of the octave into 181 parts of about 6.63 cents each.

Theory

181et tempers out 2109375/2097152 (semicomma) and [14 -22 9 in the 5-limit; 2401/2400, 5120/5103, and 390625/387072 in the 7-limit (supporting the hemififths and the cotritone). Using the patent val, it tempers out 385/384, 1375/1372, 2200/2187, and 4000/3993 in the 11-limit; 325/324, 352/351, 847/845, and 1575/1573 in the 13-limit.

181edo is the 42nd prime edo.

Prime harmonics

Approximation of prime harmonics in 181edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.00 +0.81 -1.78 -0.87 -1.04 +1.46 +1.12 +0.83 +1.56 -1.95 +1.93
relative (%) +0 +12 -27 -13 -16 +22 +17 +13 +24 -29 +29
Steps
(reduced)
181
(0)
287
(106)
420
(58)
508
(146)
626
(83)
670
(127)
740
(16)
769
(45)
819
(95)
879
(155)
897
(173)

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢)
Tuning error
Absolute (¢) Relative (%)
2.3 [287 -181 [181 287]] -0.255 0.255 3.84
2.3.5 2109375/2097152, [14 -22 9 [181 287 420]] +0.086 0.525 7.92
2.3.5.7 2401/2400, 5120/5103, 390625/387072 [181 287 420 508]] +0.142 0.465 7.01
2.3.5.7.11 385/384, 1375/1372, 2200/2187, 4000/3993 [181 287 420 508 626]] +0.174 0.421 6.35
2.3.5.7.11.13 325/324, 352/351, 385/384, 1375/1372, 1575/1573 [181 287 420 508 626 670]] +0.079 0.439 6.62
2.3.5.7.11.13.17 325/324, 352/351, 375/374, 385/384, 595/594, 1275/1274 [181 287 420 508 626 670 740]] +0.028 0.425 6.40
2.3.5.7.11.13.17.19 325/324, 352/351, 375/374, 385/384, 400/399, 595/594, 1275/1274 [181 287 420 508 626 670 740 769]] +0.000 0.404 6.09

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per octave
Generator
(reduced)
Cents
(reduced)
Associated
ratio
Temperaments
1 18\181 119.34 15/14 Septidiasemi
1 35\181 232.04 8/7 Quadrawell
1 39\181 258.56 [-32 13 5 Lafa
1 41\181 271.82 75/64 Orson
1 53\181 351.38 49/40 Hemififths (7-limit)
1 88\181 583.43 7/5 Cotritone (181f)

See Also