1861edo

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← 1860edo1861edo1862edo →
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

1861 equal divisions of the octave (abbreviated 1861edo), or 1861-tone equal temperament (1861tet), 1861 equal temperament (1861et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1861 equal parts of about 0.645 ¢ each. Each step of 1861edo represents a frequency ratio of 21/1861, or the 1861st root of 2.

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 -11 -49 -23 -0 +48 +28 +23 -39 -10 -35
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

Music

Francium