285edo

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← 284edo285edo286edo →
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

285 equal divisions of the octave (285edo), or 285-tone equal temperament (285tet), 285 equal temperament (285et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 285 equal parts of about 4.21 ¢ each.

Theory

285edo has a sharp tendency. It 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 odd harmonics in 285edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +1.20 +1.05 -0.40 -1.80 +0.26 +1.58 -1.95 +0.31 +1.43 +0.80 -0.91
relative (%) +29 +25 -10 -43 +6 +37 -46 +7 +34 +19 -22
Steps
(reduced)
452
(167)
662
(92)
800
(230)
903
(48)
986
(131)
1055
(200)
1113
(258)
1165
(25)
1211
(71)
1252
(112)
1289
(149)

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
(Reduced)
Cents
(Reduced)
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)