# 2912edo

 ← 2911edo 2912edo 2913edo →
Prime factorization 25 × 7 × 13
Step size 0.412088¢
Fifth 1703\2912 (701.786¢) (→131\224)
Semitones (A1:m2) 273:221 (112.5¢ : 91.07¢)
Dual sharp fifth 1704\2912 (702.198¢) (→213\364)
Dual flat fifth 1703\2912 (701.786¢) (→131\224)
Dual major 2nd 495\2912 (203.984¢)
Consistency limit 7
Distinct consistency limit 7

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

Approximation of odd harmonics in 2912edo
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.