470edo

← 469edo

470edo

471edo →

Prime factorization	2 × 5 × 47
Step size	2.55319 ¢
Fifth	275\470 (702.128 ¢) (→ 55\94)
Semitones (A1:m2)	45:35 (114.9 ¢ : 89.36 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

470 = 5 × 94, and 470edo shares the fifth with 94edo. Unlike 94edo, however, 470edo is only consistent to the 5-odd-limit. Using the patent val, the equal temperament tempers out 703125/702464, 823543/820125, and 1500625/1492992 in the 7-limit; 3025/3024, 4000/3993, 6250/6237, 19712/19683, and 117649/117128 in the 11-limit. It supports uniwiz and decimetra.

Prime harmonics

Approximation of prime harmonics in 470edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.00	+0.17	-0.78	-1.17	+0.17	-0.53	-0.27	+1.21	-0.19	-0.64	-1.21
	Relative (%)	+0.0	+6.8	-30.6	-45.7	+6.7	-20.7	-10.8	+47.4	-7.4	-25.1	-47.2
Steps (reduced)		470 (0)	745 (275)	1091 (151)	1319 (379)	1626 (216)	1739 (329)	1921 (41)	1997 (117)	2126 (246)	2283 (403)	2328 (448)

Subsets and supersets

Since 470 factors into 2 × 5 × 47, 470edo has subset edos 2, 5, 10, 47, 94, and 235.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3.5	1600000/1594323, [-77 -10 40⟩	[⟨470 745 1091]]	+0.0759	0.1897	7.43
2.3.5.7	703125/702464, 1500625/1492992, 1600000/1594323	[⟨470 745 1091 1319]]	+0.1608	0.2205	8.64
2.3.5.7.11	3025/3024, 4000/3993, 19712/19683, 117649/117128	[⟨470 745 1091 1319 1626]]	+0.1187	0.2144	8.40
2.3.5.7.11.13	625/624, 1575/1573, 2080/2079, 13720/13689, 15379/15360	[⟨470 745 1091 1319 1626 1739]]	+0.1227	0.1959	7.67
2.3.5.7.11.13.17	595/594, 625/624, 833/832, 1575/1573, 3185/3179, 8624/8619	[⟨470 745 1091 1319 1626 1739 1921]]	+0.1148	0.1824	7.14

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator*	Cents*	Associated Ratio*	Temperaments
1	133\470	339.57	243/200	Amity (5-limit)

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