2814edo

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← 2813edo2814edo2815edo →
Prime factorization 2 × 3 × 7 × 67
Step size 0.426439¢
Fifth 1646\2814 (701.919¢) (→823\1407)
Semitones (A1:m2) 266:212 (113.4¢ : 90.41¢)
Consistency limit 17
Distinct consistency limit 17

2814 equal divisions of the octave (abbreviated 2814edo), or 2814-tone equal temperament (2814tet), 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 of 2814edo 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

Approximation of prime harmonics in 2814edo
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