2814edo
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Prime factorization
2 × 3 × 7 × 67
Step size
0.426439¢
Fifth
1646\2814 (701.919¢) (→823\1407)
Semitones (A1:m2)
266:212 (113.4¢ : 90.41¢)
Consistency limit
17
Distinct consistency limit
17
| ← 2813edo | 2814edo | 2815edo → |
2814 equal divisions of the octave (2814edo), or 2814-tone equal temperament (2814tet), 2814 equal temperament (2814et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 2814 equal parts of about 0.426 ¢ each.
Theory
2814edo has all the harmonics from 3 to 17 approximated below 1/3 relative error and it is as a corollary consistent in the 17-odd-limit.
In the 7-limit, it is contorted, with the same commas tempered out as 1407edo.
In the 11-limit, it supports rank-3 odin temperament.
In the 13-limit it tempers out 6656/6655 and supports the 2.5.7.11.13 subgroup Double Bastille temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | -0.036 | +0.040 | +0.044 | +0.068 | -0.016 | -0.051 | +0.142 | -0.129 | -0.153 | -0.046 |
| relative (%) | +0 | -8 | +9 | +10 | +16 | -4 | -12 | +33 | -30 | -36 | -11 | |
| Steps (reduced) |
2814 (0) |
4460 (1646) |
6534 (906) |
7900 (2272) |
9735 (1293) |
10413 (1971) |
11502 (246) |
11954 (698) |
12729 (1473) |
13670 (2414) |
13941 (2685) | |
Regular temperament properties
Rank-2 temperaments
Note: 7-limit temperaments represented by 1407edo are not included.
| Periods per 8ve |
Generator (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperament |
|---|---|---|---|---|
| 1 | 593\2814 | 252.878 | 53094899/45875200 | Double Bastille |