855edo
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Prime factorization
32 × 5 × 19
Step size
1.40351¢
Fifth
500\855 (701.754¢) (→100\171)
Semitones (A1:m2)
80:65 (112.3¢ : 91.23¢)
Consistency limit
13
Distinct consistency limit
13
| ← 854edo | 855edo | 856edo → |
855 equal divisions of the octave (abbreviated 855edo or 855ed2), also called 855-tone equal temperament (855tet) or 855 equal temperament (855et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 855 equal parts of about 1.4 ¢ each. Each step represents a frequency ratio of 21/855, or the 855th root of 2.
855edo divides the steps of 171edo in five, and like 171edo, it is consistent to the 13-odd-limit, tempering out 1575/1573, 4225/4224, 6656/6655, 39366/39325, and 50421/50336 using the patent val.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.201 | -0.349 | -0.405 | +0.261 | +0.174 | +0.308 | +0.031 | +0.498 | +0.598 | +0.228 |
| Relative (%) | +0.0 | -14.3 | -24.9 | -28.8 | +18.6 | +12.4 | +21.9 | +2.2 | +35.5 | +42.6 | +16.2 | |
| Steps (reduced) |
855 (0) |
1355 (500) |
1985 (275) |
2400 (690) |
2958 (393) |
3164 (599) |
3495 (75) |
3632 (212) |
3868 (448) |
4154 (734) |
4236 (816) | |
Subsets and supersets
Since 855 factors into 32 × 5 × 19, 855edo has subset edos 3, 5, 9, 15, 19, 45, 57, 95, 171, and 285.