383edo

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← 382edo383edo384edo →
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