# 383edo

 ← 382edo 383edo 384edo →
Prime factorization 383 (prime)
Step size 3.13316¢
Fifth 224\383 (701.828¢)
Semitones (A1:m2) 36:29 (112.8¢ : 90.86¢)
Consistency limit 15
Distinct consistency limit 15

383 equal divisions of the octave (abbreviated 383edo or 383ed2), also called 383-tone equal temperament (383tet) or 383 equal temperament (383et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 383 equal parts of about 3.13 ¢ each. Each step represents a frequency ratio of 21/383, or the 383rd root of 2.

## Theory

383edo is distinctly consistent through the 15-odd-limit with a flat tendency. The equal temperament tempers out 32805/32768 (schisma) in the 5-limit; 2401/2400 in the 7-limit; 3025/3024, 4000/3993 and 6250/6237 in the 11-limit; and 625/624, 1575/1573 and 2080/2079 in the 13-limit. It provides the optimal patent val for the countertertiaschis temperament, and a good tuning for sesquiquartififths in the higher limit.

### Prime harmonics

Approximation of prime harmonics in 383edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.13 -0.94 -0.68 +0.12 -0.84 -1.56 +0.14 +1.49 +1.23 -1.43
Relative (%) +0.0 -4.1 -29.8 -21.7 +3.8 -26.8 -49.8 +4.4 +47.6 +39.3 -45.7
Steps
(reduced)
383
(0)
607
(224)
889
(123)
1075
(309)
1325
(176)
1417
(268)
1565
(33)
1627
(95)
1733
(201)
1861
(329)
1897
(365)

### Subsets and supersets

383edo is the 76th prime edo.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-607 383 [383 607]] +0.0402 0.0402 1.28
2.3.5 32805/32768, [-8 -55 41 [383 607 889]] +0.1610 0.1741 5.55
2.3.5.7 2401/2400, 32805/32768, 68359375/68024448 [383 607 889 1075]] +0.1813 0.1548 4.94
2.3.5.7.11 2401/2400, 3025/3024, 4000/3993, 32805/32768 [383 607 889 1075 1325]] +0.1382 0.1631 5.20
2.3.5.7.11.13 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976 [383 607 889 1075 1325 1417]] +0.1531 0.1525 4.87

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 53\383 166.06 11/10 Countertertiaschis
1 56\383 175.46 448/405 Sesquiquartififths
1 133\383 416.71 14/11 Unthirds
1 159\383 498.17 4/3 Helmholtz

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