457edo
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Prime factorization
457 (prime)
Step size
2.62582¢
Fifth
267\457 (701.094¢)
Semitones (A1:m2)
41:36 (107.7¢ : 94.53¢)
Consistency limit
7
Distinct consistency limit
7
| ← 456edo | 457edo | 458edo → |
457 equal divisions of the octave (457edo), or 457-tone equal temperament (457tet), 457 equal temperament (457et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 457 equal parts of about 2.63 ¢ each.
Theory
457et tempers out 283115520/282475249, 1220703125/1219784832, 26873856/26796875, 65625/65536 and 200120949/200000000 in the 7-limit; 95703125/95664294, 100663296/100656875, 161280/161051, 29296875/29218112, 166698/166375, 1953125/1951488, 151263/151250, 2359296/2358125, 540/539, 5767168/5764801, 825000/823543, 8019/8000, 160083/160000, 16808715/16777216, 539055/537824, 244515348/244140625, 67110351/67108864 and 43923/43904 in the 11-limit.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | -0.86 | -0.32 | +0.10 | +0.90 | +0.10 | -0.27 | -1.18 | +0.08 | -0.80 | -0.76 | -0.70 |
| relative (%) | -33 | -12 | +4 | +34 | +4 | -10 | -45 | +3 | -30 | -29 | -27 | |
| Steps (reduced) |
724 (267) |
1061 (147) |
1283 (369) |
1449 (78) |
1581 (210) |
1691 (320) |
1785 (414) |
1868 (40) |
1941 (113) |
2007 (179) |
2067 (239) | |
Subsets and supersets
457edo is the 88th prime edo.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-724 457⟩ | ⟨457 724] | 0.2716 | 0.2716 | 10.34 |
| 2.3.5 | [-36 11 8⟩, [-5 31 -19⟩ | ⟨457 724 1061] | 0.2267 | 0.2307 | 8.79 |
| 2.3.5.7 | 19683/19600, 65625/65536, 7381125/7340032 | ⟨457 724 1061 1283] | 0.1609 | 0.2300 | 8.76 |
| 2.3.5.7.11 | 540/539, 8019/8000, 19683/19600, 43923/43904 | ⟨457 724 1061 1283 1581] | 0.1227 | 0.2194 | 8.36 |
| 2.3.5.7.11.13 | 540/539, 1716/1715, 4225/4224, 41067/40960, 43940/43923 | ⟨457 724 1061 1283 1581 1691] | 0.1142 | 0.2012 | 7.66 |
| 2.3.5.7.11.13.17 | 936/935, 1089/1088, 1275/1274, 1575/1573, 2601/2600, 4225/4224 | ⟨457 724 1061 1283 1581 1691 1868] | 0.0952 | 0.1920 | 7.31 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 10\457 | 26.258 | 49/48 | Sfourth |
| 1 | 136\457 | 357.11 | 49/40 | Dodifo |
| 1 | 213\457 | 559.30 | 864/625 | Tritriple |