# 2912edo

← 2911edo | 2912edo | 2913edo → |

^{5}× 7 × 13**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 2^{1/2912}, 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 | -45 | -2 | +18 | +14 | +32 | +13 | +31 | +4 | -43 | +39 | |

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 2^{5} × 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.