401edo

← 400edo 401edo 402edo →
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

Template:EDO intro 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
Error	Relative (%)	+43.0	-9.3	+25.1	-14.0	-23.2	+12.4	+33.7	-7.3	-41.9	-31.9	+5.2
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
Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	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

Diana Tessa by Francium