2912edo

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← 2911edo2912edo2913edo →
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.