# 389edo

 ← 388edo 389edo 390edo →
Prime factorization 389 (prime)
Step size 3.08483¢
Fifth 228\389 (703.342¢)
Semitones (A1:m2) 40:27 (123.4¢ : 83.29¢)
Dual sharp fifth 228\389 (703.342¢)
Dual flat fifth 227\389 (700.257¢)
Dual major 2nd 66\389 (203.599¢)
Consistency limit 3
Distinct consistency limit 3

389 equal divisions of the octave (abbreviated 389edo or 389ed2), also called 389-tone equal temperament (389tet) or 389 equal temperament (389et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 389 equal parts of about 3.08 ¢ each. Each step represents a frequency ratio of 21/389, or the 389th root of 2.

## Theory

389edo is inconsistent to the 5-odd-limit and harmonic 3 is about halfway between its steps, which makes it a dual-fifth system. Otherwise, it has a reasonable approximation to harmonics 7, 9, and 17, with optional additions of either 5 or 11 and 15, making it suitable for a 2.9.5.7.17 or 2.9.15.7.11.17 subgroup interpretation.

### Odd harmonics

Approximation of odd harmonics in 389edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +1.39 -0.71 -0.19 -0.31 +0.87 -1.45 +0.68 -0.07 -1.37 +1.20 +1.03
Relative (%) +45.0 -23.0 -6.1 -10.1 +28.1 -47.1 +22.0 -2.3 -44.4 +38.9 +33.4
Steps
(reduced)
617
(228)
903
(125)
1092
(314)
1233
(66)
1346
(179)
1439
(272)
1520
(353)
1590
(34)
1652
(96)
1709
(153)
1760
(204)

### Subsets and supersets

389edo is the 77th prime edo.

### Miscelleneous properties

389edo represents the north solstice (summer in the northern hemisphere) leap year cycle 69/389 as devised by Sym454 inventor Irvin Bromberg. The outcome scale uses 327\389, or 62\389 as its generator. The solstice leap day scale with 94 notes uses 269\389 as a generator. Since this is a maximal evenness scale, temperament can be generated by simply merging the numerator and the denominator.

#### Solstice leap day (94 & 295)

295 seems to precede 389.

Subgroup: 2.5.7.11.17

POTE generator: 370.1796c

Comma list: 250000/248897, 2100875/2097152, 4096000/4092529

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3.5 [20 -17 3, [-39 -12 25 [389 617 903]] -0.19 0.500 16.2
2.3.5 2109375/2097152, [-7 44 -27 [389 616 903]] (389b) 0.46 0.451 14.6
2.5.7 2100875/2097152, [0 52 -43 [389 903 1092]] 0.12 0.131 4.2
2.5.7.11.17 6664/6655, 156250/155771, 180625/180224, 184960/184877 [389 903 1092 1346 1590]] 0.03 0.177 5.7

## Scales

• Solstice[69]
• SolsticeDay[94]