401edo
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Prime factorization
401 (prime)
Step size
2.99252¢
Fifth
235\401 (703.242¢)
Semitones (A1:m2)
41:28 (122.7¢ : 83.79¢)
Dual sharp fifth
235\401 (703.242¢)
Dual flat fifth
234\401 (700.249¢)
Dual major 2nd
68\401 (203.491¢)
Consistency limit
3
Distinct consistency limit
3
| ← 400edo | 401edo | 402edo → |
401 equal divisions of the octave (401edo), or 401-tone equal temperament (401tet), 401 equal temperament (401et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 401 equal parts of about 2.99 ¢ each. It is the 79th prime edo
Theory
401et tempers out 283115520/282475249 and 703125/702464 in the 7-limit; 35156250/35153041, 2097152/2096325, 117649/117612, 226492416/226474325, 9765625/9732096, 42875/42768, 1375/1372, 5632/5625, 15488/15435, 202397184/201768035, 102487/102400 and 805255/802816 in the 11-limit. It provides the optimal patent val for diatessic temperament.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +1.29 | -0.28 | +0.75 | -0.42 | -0.69 | +0.37 | +1.01 | -0.22 | -1.25 | -0.96 | +0.15 |
| relative (%) | +43 | -9 | +25 | -14 | -23 | +12 | +34 | -7 | -42 | -32 | +5 | |
| Steps (reduced) |
636 (235) |
931 (129) |
1126 (324) |
1271 (68) |
1387 (184) |
1484 (281) |
1567 (364) |
1639 (35) |
1703 (99) |
1761 (157) |
1814 (210) | |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [636 -401⟩ | [⟨401 636]] | -0.4060 | 0.4058 | 13.56 |
| 2.3.5 | 15625/15552, [107 -66 -1⟩ | [⟨401 636 931]] | -0.2307 | 0.4139 | 13.83 |
| 2.3.5.7 | 10976/10935, 15625/15552, 67108864/66706983 | [⟨401 636 931 1126]] | -0.2400 | 0.3588 | 11.99 |
| 2.3.5.7.11 | 2200/2187, 1375/1372, 5632/5625, 102487/102400 | [⟨401 636 931 1126 1387]] | -0.1518 | 0.3661 | 12.23 |
| 2.3.5.7.11.13 | 325/324, 352/351, 625/624, 1375/1372, 3276800/3270267 | [⟨401 636 931 1126 1387 1484]] | -0.1431 | 0.3348 | 11.19 |
Rank-2 temperaments
| Periods per 8ve |
Generator (reduced) |
Cents (reduced) |
Associated ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 169\401 | 505.74 | 75/56 | Diatessic |
Scales
Music
- Diana Tessa by Francium