851edo

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← 850edo 851edo 852edo →
Prime factorization 23 × 37
Step size 1.41011¢ 
Fifth 498\851 (702.233¢)
Semitones (A1:m2) 82:63 (115.6¢ : 88.84¢)
Consistency limit 15
Distinct consistency limit 15

851 equal divisions of the octave (abbreviated 851edo or 851ed2), also called 851-tone equal temperament (851tet) or 851 equal temperament (851et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 851 equal parts of about 1.41 ¢ each. Each step represents a frequency ratio of 21/851, or the 851st root of 2.

851edo is consistent to the 15-odd-limit or the no-17 no-23 25-odd-limit. As an equal temperament, it tempers out the luna comma in the 5-limit; 2401/2400 (breedsma) and 33554432/33480783 (garischisma) in the 7-limit; 3025/3024 and 19712/19683 in the 11-limit; and 2080/2079, 4096/4095, and 4225/4224 in the 13-limit. It provides the optimal patent val for 13-limit newt, the 270 & 581 microtemperament, as well as neonewt, its no-17 19-limit extension.

Prime harmonics

Approximation of prime harmonics in 851edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.278 +0.055 -0.083 +0.033 -0.105 -0.608 +0.019 +0.633 -0.200 -0.030
Relative (%) +0.0 +19.7 +3.9 -5.9 +2.4 -7.4 -43.1 +1.4 +44.9 -14.2 -2.1
Steps
(reduced)
851
(0)
1349
(498)
1976
(274)
2389
(687)
2944
(391)
3149
(596)
3478
(74)
3615
(211)
3850
(446)
4134
(730)
4216
(812)

Subsets and supersets

Since 851 factors into 23 × 37, 851edo contains 23edo and 37edo as its subsets.