1861edo

← 1860edo

1861edo

1862edo →

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

1861edo is only consistent to the 5-odd-limit, and the harmonic 3 is about halfway between its steps. It has a reasonable approximation of the 2.9.5.21.11 subgroup.

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. 3722edo, which doubles it, provides a good correction to harmonics 3, 7, and 13.

Regular temperament properties

Subgroup	Comma List	Mapping	Optimal 8ve Stretch (¢)	Tuning Error
				Absolute (¢)	Relative (%)
2.9	[-5899 1861⟩	[⟨1861 5899]]	+0.0234	0.0234	3.63

Scales

• Helayo14

Music

Francium

• "Happy Apocalypse!" from Helayo EP (2023) – Spotify | Bandcamp | YouTube – helayo in 1861edo tuning