383edo
| ← 382edo | 383edo | 384edo → |
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
| 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 | -4 | -30 | -22 | +4 | -27 | -50 | +4 | +48 | +39 | -46 | |
| 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
| 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