# 2814edo

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 ← 2813edo 2814edo 2815edo →
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 2814ed2), also called 2814-tone equal temperament (2814tet) or 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 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 (%) +0.0 -8.4 +9.4 +10.3 +15.9 -3.7 -12.0 +33.2 -30.3 -35.9 -10.8
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