285edo

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← 284edo 285edo 286edo →
Prime factorization 3 × 5 × 19
Step size 4.21053 ¢ 
Fifth 167\285 (703.158 ¢)
Semitones (A1:m2) 29:20 (122.1 ¢ : 84.21 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

Theory

285edo has a sharp tendency. The equal temperament tempers out the misty comma and the enneadeca in the 5-limit; 3136/3125 and 5120/5103 in the 7-limit; 3025/3024 and 3388/3375 in the 11-limit; 352/351, 676/675, 847/845, 1001/1000, and 2080/2079 in the 13-limit. It supports the 13-limit hemimist temperament.

Prime harmonics

Approximation of prime harmonics in 285edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +1.20 +1.05 -0.40 +0.26 +1.58 +0.31 +1.43 -0.91 +2.00 +0.23
Relative (%) +0.0 +28.6 +25.0 -9.6 +6.2 +37.5 +7.3 +34.1 -21.5 +47.5 +5.4
Steps
(reduced)
285
(0)
452
(167)
662
(92)
800
(230)
986
(131)
1055
(200)
1165
(25)
1211
(71)
1289
(149)
1385
(245)
1412
(272)

Subsets and supersets

Since 285 factors into 3 × 5 × 19, 285edo has subset edos 3, 5, 15, 19, 57, and 95.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢)
Tuning error
Absolute (¢) Relative (%)
2.3 [452 -285 [285 452]] −0.3795 0.3794 9.01
2.3.5 67108864/66430125, [-14 -19 19 [285 452 662]] −0.4043 0.3117 7.41
2.3.5.7 3136/3125, 5120/5103, 40353607/39858075 [285 452 662 800]] −0.2673 0.3596 8.54
2.3.5.7.11 3025/3024, 3136/3125, 5120/5103, 12005/11979 [285 452 662 800 986]] −0.2289 0.3307 7.85
2.3.5.7.11.13 352/351, 676/675, 847/845, 3025/3024, 12005/11979 [285 452 662 800 986 1055]] −0.2618 0.3107 7.38

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
ratio*
Temperaments
1 109\285 458.95 125/96 Majvam
3 59\285
(36\285)
248.42
(151.58)
15/13
(12/11)
Hemimist
3 59\285
(23\285)
496.84
(96.84)
4/3
(256/243)
Misty
19 118\285
(2\285)
496.84
(8.42)
4/3
(15625/15552)
Enneadecal (5-limit)

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct