403edo
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Prime factorization
13 × 31
Step size
2.97767¢
Fifth
236\403 (702.73¢)
Semitones (A1:m2)
40:29 (119.1¢ : 86.35¢)
Consistency limit
5
Distinct consistency limit
5
| ← 402edo | 403edo | 404edo → |
403 equal divisions of the octave (403edo), or 403-tone equal temperament (403tet), 403 equal temperament (403et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 403 equal parts of about 2.98 ¢ each.
Theory
403et tempers out 134217728/133984375, 78125000/78121827 and 2100875/2097152 in the 7-limit; 100663296/100656875, 806736/805255, 2097152/2096325, 12005/11979, 7168000/7144929, 131072/130977, 107495424/107421875, 42875/42768, 1684375/1679616, 3025/3024, 766656/765625, 4108797/4096000 and 644204/643125 in the 11-limit.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.77 | +0.78 | -1.08 | -1.43 | -0.45 | -0.83 | -1.42 | -0.74 | +0.25 | -0.31 | +0.01 |
| relative (%) | +26 | +26 | -36 | -48 | -15 | -28 | -48 | -25 | +9 | -10 | +0 | |
| Steps (reduced) |
639 (236) |
936 (130) |
1131 (325) |
1277 (68) |
1394 (185) |
1491 (282) |
1574 (365) |
1647 (35) |
1712 (100) |
1770 (158) |
1823 (211) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [639 -403⟩ | ⟨403 639] | -0.2443 | 0.2443 | 8.20 |
| 2.3.5 | [9 -13 5⟩, [81 -13 -26⟩ | ⟨403 639 936] | -0.2753 | 0.2042 | 6.86 |
| 2.3.5.7 | 3136/3125, 1600000/1594323, 2100875/2097152 | ⟨403 639 936 1131] | -0.3751 | 0.2473 | 8.31 |
| 2.3.5.7.11 | 3025/3024, 3388/3375, 42875/42768, 131072/130977 | ⟨403 639 936 1131 1394] | -0.0621 | 0.3160 | 10.61 |
| 2.3.5.7.11.13 | 2080/2079, 3025/3024, 3388/3375, 4096/4095, 42875/42768 | ⟨403 639 936 1131 1394 1491] | -0.0146 | 0.3074 | 10.32 |
| 2.3.5.7.11.13.17 | 2080/2079, 595/594, 1225/1224, 3025/3024, 4096/4095, 3388/3375 | ⟨403 639 936 1131 1394 1491 1647] | +0.0133 | 0.2927 | 9.83 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 53\403 | 157.82 | 36756909/33554432 | Hemiegads |
| 1 | 106\403 | 315.63 | 6/5 | Egads |
| 1 | 114\403 | 339.45 | 243/200 | Amity |