# 6edt

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 ← 5edt 6edt 7edt →
Prime factorization 2 × 3
Step size 316.993¢
Octave 4\6edt (1267.97¢) (→2\3edt)
Consistency limit 7
Distinct consistency limit 2
Special properties

6 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 6edt or 6ed3), is a nonoctave tuning system that divides the interval of 3/1 into 6 equal parts of about 317 ¢ each. Each step represents a frequency ratio of 31/6, or the 6th root of 3.

## Theory

Since 6edt contains one interval of 2edt and two intervals of 3edt, it introduces 2 new notes unseen in previous edts. These new notes happen to approximate 6/5 and 5/2 very well, the former being only 1.351 cents sharp. 6edt is therefore the smallest edt other than 5edt to accurately approximate 5-limit harmony, as well as some elements from the 13-limit inherited from 3edt. 6edt allows for construction of chords such as 2:5:6:15:18:26:31:45:54...

### Harmonics

Approximation of harmonics in 5edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -59 +0 -118 -124 -59 +55 -176 +0 -182 +33 -118
Relative (%) -15.5 +0.0 -30.9 -32.5 -15.5 +14.4 -46.4 +0.0 -48.0 +8.7 -30.9
Steps
(reduced)
3
(3)
5
(0)
6
(1)
7
(2)
8
(3)
9
(4)
9
(4)
10
(0)
10
(0)
11
(1)
11
(1)

## Intervals

Degrees Cents hekts ApproximateRatios
0 1/1
1 316.993 216.667 6/5, 65/54
2 633.985 433.333 13/9
3 950.978 650 19/11, 26/15
4 1267.97 866.667 27/13
5 1584.963 1093.333 5/2 (5/4 plus an octave)
6 1901.955 1300 3/1