469edo

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469edo

470edo →

Prime factorization	7 × 67
Step size	2.55864 ¢
Fifth	274\469 (701.066 ¢)
Semitones (A1:m2)	42:37 (107.5 ¢ : 94.67 ¢)
Dual sharp fifth	275\469 (703.625 ¢)
Dual flat fifth	274\469 (701.066 ¢)
Dual major 2nd	80\469 (204.691 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

469et is only consistent to the 5-odd-limit and the error of the harmonic 3 is quite large. It can be considered for the 2.9.5.7.13.17 subgroup, tempering out 2601/2600, 7616/7605, 5832/5831, 60112/60025 and 265625/264992. It supports gravity and french decimal.

Odd harmonics

Approximation of odd harmonics in 469edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-0.89	+0.04	+0.90	+0.78	-1.21	+1.26	-0.85	-0.05	-0.71	+0.01	+1.15
	Relative (%)	-34.7	+1.6	+35.1	+30.5	-47.3	+49.4	-33.2	-2.0	-27.8	+0.3	+44.9
Steps (reduced)		743 (274)	1089 (151)	1317 (379)	1487 (80)	1622 (215)	1736 (329)	1832 (425)	1917 (41)	1992 (116)	2060 (184)	2122 (246)

Subsets and supersets

Since 469 factors into 7 × 67, 469edo has 7edo and 67edo as its subset edos. 938edo, which doubles it, gives a good correction to the harmonics 3 and 5.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[1487 -469⟩	[⟨469 1487]]	-0.1232	0.1232	4.82
2.9.5	[38 -1 -15⟩, [13 -29 34⟩	[⟨469 1487 1089]]	-0.0879	0.1122	4.39