401edo

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← 400edo401edo402edo →
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

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.

Approximation of odd harmonics in 401edo
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

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator
(reduced)
Cents
(reduced)
Associated
ratio
Temperaments
1 169\401 505.74 75/56 Diatessic

Scales

Music