1889edo

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1889edo

1890edo →

Prime factorization	1889 (prime)
Step size	0.635257 ¢
Fifth	1105\1889 (701.959 ¢)
Semitones (A1:m2)	179:142 (113.7 ¢ : 90.21 ¢)
Consistency limit	27
Distinct consistency limit	27

1889edo is strong in the 23-limit, though 1578, which among other things has a lower 23-limit relative error, rather puts it in the shade. It is distinctly consistent through the 27-odd-limit, but not, unlike 1578, to the 29-odd-limit. Even so, it should be noted that it supplies the optimal patent val for the 7-limit monzismic temperament.

Prime harmonics

Approximation of prime harmonics in 1889edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.000	+0.004	-0.078	-0.059	+0.085	-0.083	-0.138	-0.213	-0.005	+0.174	-0.303
	Relative (%)	+0.0	+0.6	-12.2	-9.3	+13.4	-13.1	-21.7	-33.5	-0.9	+27.4	-47.7
Steps (reduced)		1889 (0)	2994 (1105)	4386 (608)	5303 (1525)	6535 (868)	6990 (1323)	7721 (165)	8024 (468)	8545 (989)	9177 (1621)	9358 (1802)

Subsets and supersets

1889edo is the 290th prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[2994 -1889⟩	[⟨1889 2994]]	-0.0012	0.0012	0.1889
2.3.5	[54 -37 2⟩, [-66 -36 53⟩	[⟨1889 2994 4386]]	+0.0104	0.0163	2.57
2.3.5.7	4375/4374, 3955078125/3954653486, [-57 16 10 3⟩	[⟨1889 2994 4386 5303]]	+0.0131	0.0149	2.35
2.3.5.7.11	4375/4374, 151263/151250, 820125/819896, 1879453125/1879048192	[⟨1889 2994 4386 5303 6535]]	+0.0055	0.0201	3.16
2.3.5.7.11.13	4375/4374, 4225/4224, 6656/6655, 4100625/4100096, 151263/151250	[⟨1889 2994 4386 5303 6535 6990]]	+0.0084	0.0194	3.05
2.3.5.7.11.13.17	4375/4374, 12376/12375, 4225/4224, 14400/14399, 14875/14872, 194481/194480	[⟨1889 2994 4386 5303 6535 6990 7721]]	+0.0120	0.0200	3.15
2.3.5.7.11.13.17.19	4375/4374, 12376/12375, 5985/5984, 4225/4224, 14400/14399, 6175/6174, 61965/61952	[⟨1889 2994 4386 5303 6535 6990 7721 8024]]	+0.0167	0.0226	3.56

Rank-2 temperaments

Table of rank-2 temperaments by generator

Periods per 8ve	Generator (reduced)*	Cents (reduced)*	Associated Ratio*	Temperaments
1	392\1889	249.021	[-26 18 1⟩	Monzismic
1	707\1889	449.127	35/27	Semidimi

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