1381edo

← 1380edo

1381edo

1382edo →

Prime factorization	1381 (prime)
Step size	0.868936 ¢
Fifth	808\1381 (702.1 ¢)
Semitones (A1:m2)	132:103 (114.7 ¢ : 89.5 ¢)
Consistency limit	9
Distinct consistency limit	9

Theory

1381edo is consistent to the 9-odd-limit, tempering out 2401/2400, 29360128/29296875 and [33 -37 5 5⟩ in the 7-limit. It is strong in the 2.3.7.23.29 subgroup, tempering out 60817408/60761421, 5888/5887, 121025149/120932352 and 661153497088/660379746861. Using the 2.3.7.23.37 subgroup, it tempers out 1702/1701. The equal temperament supports quasiorwell.

Odd harmonics

Approximation of odd harmonics in 1381edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.145	+0.363	+0.037	+0.290	-0.413	-0.267	-0.361	+0.186	-0.337	+0.182	-0.034
	Relative (%)	+16.7	+41.7	+4.3	+33.4	-47.5	-30.7	-41.6	+21.4	-38.8	+21.0	-3.9
Steps (reduced)		2189 (808)	3207 (445)	3877 (1115)	4378 (235)	4777 (634)	5110 (967)	5395 (1252)	5645 (121)	5866 (342)	6066 (542)	6247 (723)

Subsets and supersets

1381edo is the 221st prime edo. 2762edo, which doubles it, gives a good correction to the harmonic 11.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[2189 -1381⟩	[⟨1381 2189]]	−0.0457	0.0457	5.26
2.3.5	[-16 35 -17⟩, [93 -3 -38⟩	[⟨1381 2189 3207]]	−0.0825	0.0641	7.38
2.3.5.7	2401/2400, 29360128/29296875, [33 -37 5 5⟩	[⟨1381 2189 3207 3877]]	−0.0652	0.0631	7.26

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	210\1381	182.476	10/9	Minortone
1	312\1381	271.108	1024/875	Quasiorwell

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct