407edo

← 406edo

407edo

408edo →

Prime factorization	11 × 37
Step size	2.9484 ¢
Fifth	238\407 (701.72 ¢)
Semitones (A1:m2)	38:31 (112 ¢ : 91.4 ¢)
Consistency limit	7
Distinct consistency limit	7

Theory

407et tempers out 32805/32768 in the 5-limit; 4096000/4084101, 134217728/133984375, 26873856/26796875, 78125000/78121827 and 48828125/48771072 in the 7-limit. It supports the pinkanberry chords and the temperament subsemifourth.

Prime harmonics

Approximation of prime harmonics in 407edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	-0.24	-0.07	+1.20	+0.03	-0.23	+1.19	+0.28	-0.26	-0.58	-1.06
	Relative (%)	+0.0	-8.0	-2.5	+40.7	+1.1	-7.9	+40.3	+9.4	-9.0	-19.8	-35.8
Steps (reduced)		407 (0)	645 (238)	945 (131)	1143 (329)	1408 (187)	1506 (285)	1664 (36)	1729 (101)	1841 (213)	1977 (349)	2016 (388)

Subsets and supersets

407 factors into 11 × 37, with 11edo and 37edo as its subset edos.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[-645 407⟩	[⟨407 645]]	0.0742	0.0742	2.52
2.3.5	32805/32768, [30 47 -45⟩	[⟨407 645 945]]	0.0599	0.0638	2.16

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)*	Cents (reduced)*	Associated Ratio*	Temperaments
1	63\407	185.75	[24 4 -13⟩	Pirate
1	169\407	498.28	4/3	Helmholtz

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