1861edo

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1861edo

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Prime factorization	1861 (prime)
Step size	0.644815 ¢
Fifth	1089\1861 (702.203 ¢)
Semitones (A1:m2)	179:138 (115.4 ¢ : 88.98 ¢)
Dual sharp fifth	1089\1861 (702.203 ¢)
Dual flat fifth	1088\1861 (701.558 ¢)
Dual major 2nd	316\1861 (203.761 ¢)
Consistency limit	5
Distinct consistency limit	5

Theory

1861et tempers out 369140625/369098752, 537109375/536870912 and 3025/3024 in the 11-limit; 1181640625/1181599328, 225000/224939, 78125/78078, 1610510000/1610497161, 8859375/8859136, 4096/4095, 196625/196608, 405769/405504, 10549994/10546875 and 91182091/91125000 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 1861edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	+0.248	-0.070	-0.314	-0.149	-0.001	+0.311	+0.178	+0.149	-0.253	-0.066	-0.225
	Relative (%)	+38.5	-10.8	-48.8	-23.0	-0.2	+48.2	+27.7	+23.2	-39.3	-10.3	-34.9
Steps (reduced)		2950 (1089)	4321 (599)	5224 (1502)	5899 (316)	6438 (855)	6887 (1304)	7271 (1688)	7607 (163)	7905 (461)	8174 (730)	8418 (974)

Subsets and supersets

1861edo is the 284th prime edo.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.3	[2950 -1861⟩	⟨1861 2950]	-0.0783	0.0783	12.14
2.3.5	[57 -55 13⟩, [91 -12 -31⟩	⟨1861 2950 4321]	-0.0422	0.0818	12.69
2.3.5.7	95703125/95551488, 359661568/358722675, 160163466183/160000000000	⟨1861 2950 4321 5224]	-0.0036	0.0973	15.08
2.3.5.7.11	3025/3024, 19712/19683, 26796875/26763264, 102538515387/102400000000	⟨1861 2950 4321 5224 6438]	-0.0028	0.0871	13.51
2.3.5.7.11.13	3025/3024, 4096/4095, 4459/4455, 765625/764478, 18302823/18279040	⟨1861 2950 4321 5224 6438 6887]	-0.0163	0.0850	13.18
2.3.5.7.11.13.17	1225/1224, 2431/2430, 4096/4095, 4459/4455, 42500/42471, 22000363/21970000	⟨1861 2950 4321 5224 6438 6887 7607]	-0.0192	0.0790	12.25