2814edo
| ← 2813edo | 2814edo | 2815edo → |
2814 equal divisions of the octave (abbreviated 2814edo or 2814ed2), also called 2814-tone equal temperament (2814tet) or 2814 equal temperament (2814et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2814 equal parts of about 0.426 ¢ each. Each step represents a frequency ratio of 21/2814, or the 2814th root of 2.
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 enfactored, 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) | |
Subsets and supersets
Since 2814 factors into 2 × 3 × 7 × 67, 2814edo has subset edos 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938 and 1407.
Regular temperament properties
Rank-2 temperaments
Note: 7-limit temperaments represented by 1407edo are not included.
| Periods per 8ve |
Generator* | Cents* | Associated Ratio |
Temperament |
|---|---|---|---|---|
| 1 | 593\2814 | 252.878 | 53094899/45875200 | Double bastille |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct