2912edo
| ← 2911edo | 2912edo | 2913edo → |
2912 equal divisions of the octave (abbreviated 2912edo or 2912ed2), also called 2912-tone equal temperament (2912tet) or 2912 equal temperament (2912et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2912 equal parts of about 0.412 ¢ each. Each step represents a frequency ratio of 21/2912, or the 2912th root of 2.
2912edo is consistent to the 7-odd-limit, but the error on 3 and 5 is quite large, commending it to a dual-fifth interpretation. As a dual-fifth system, its sharp and flat approximations to 3/2 come from two notable systems - 364edo and 224edo (see the template to the right).
Aside from the patent val, there is a number of mappings to be considered. 2912dd val provides a tuning close to POTE tuning for the tokko temperament, and 2912e val tunes skadi. 2912edo can be used with 2.7.9.11.15.19 subgroup.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.169 | -0.187 | -0.007 | +0.074 | +0.056 | +0.132 | +0.055 | +0.127 | +0.014 | -0.177 | +0.160 |
| Relative (%) | -41.1 | -45.5 | -1.8 | +17.8 | +13.5 | +32.0 | +13.5 | +30.8 | +3.5 | -42.8 | +38.8 | |
| Steps (reduced) |
4615 (1703) |
6761 (937) |
8175 (2351) |
9231 (495) |
10074 (1338) |
10776 (2040) |
11377 (2641) |
11903 (255) |
12370 (722) |
12790 (1142) |
13173 (1525) | |
Subsets and supersets
Since 2912 factors as 25 × 7 × 13, 2912edo has subset edos 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 91, 104, 112, 182, 208, 224, 364, 416, 728, 1456.