433edo
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Prime factorization
433 (prime)
Step size
2.77136¢
Fifth
253\433 (701.155¢)
Semitones (A1:m2)
39:34 (108.1¢ : 94.23¢)
Consistency limit
5
Distinct consistency limit
5
| ← 432edo | 433edo | 434edo → |
433 equal divisions of the octave (433edo), or 433-tone equal temperament (433tet), 433 equal temperament (433et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 433 equal parts of about 2.77 ¢ each.
Theory
433et tempers out 4096000/4084101, 95703125/95551488 and 1640558367/1638400000 in the 7-limit; 161280/161051, 25165824/25109315, 1019215872/1019046875, 4000/3993, 2359296/2358125, 6250/6237, 180224/180075, 17537553/17500000, 3025/3024 and 1362944/1361367 in the 11-limit.
Subsets and supersets
433edo is the 84th prime edo.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.80 | -1.09 | +1.15 | +1.17 | +0.18 | -0.80 | +0.88 | +0.36 | -0.98 | +0.35 | +0.82 |
| relative (%) | -29 | -39 | +42 | +42 | +7 | -29 | +32 | +13 | -35 | +13 | +30 | |
| Steps (reduced) |
686 (253) |
1005 (139) |
1216 (350) |
1373 (74) |
1498 (199) |
1602 (303) |
1692 (393) |
1770 (38) |
1839 (107) |
1902 (170) |
1959 (227) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-686 433⟩ | ⟨433 686] | 0.2525 | 0.2525 | 9.11 |
| 2.3.5 | [-21 3 7⟩, [-29 52 -23⟩ | ⟨433 686 1005] | 0.3254 | 0.2306 | 8.32 |
| 2.3.5.7 | 19683/19600, 4096000/4084101, 2109375/2097152 | ⟨433 686 1005 1216] | 0.1414 | 0.3759 | 13.56 |
| 2.3.5.7.11 | 3025/3024, 6250/6237, 30375/30184, 180224/180075 | ⟨433 686 1005 1216 1498] | 0.1026 | 0.3451 | 12.45 |
| 2.3.5.7.11.13 | 2080/2079, 625/624, 3025/3024, 18954/18865, 41472/41405 | ⟨433 686 1005 1216 1498 1602] | 0.1217 | 0.3179 | 11.47 |
| 2.3.5.7.11.13.17 | 2080/2079, 375/374, 715/714, 936/935, 1377/1372, 76032/75803 | ⟨433 686 1005 1216 1498 1602 1770] | 0.0919 | 0.3033 | 10.94 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 98\433 | 271.594 | 75/64 | Orson |
Music
- sleeping as we don't know by Francium