# 7edt

 ← 6edt 7edt 8edt →
Prime factorization 7 (prime)
Step size 271.708¢
Octave 4\7edt (1086.83¢)
Consistency limit 2
Distinct consistency limit 2

7 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 7edt or 7ed3), is a nonoctave tuning system that divides the interval of 3/1 into 7 equal parts of about 272 ¢ each. Each step represents a frequency ratio of 31/7, or the 7th root of 3.

## Theory

Since one step of 7edt approximates a 7/6 subminor third (4.84 cents sharp) quite nicely, three steps are almost exactly 8/5 (tempering out 1728/1715, the orwellisma), and four steps are very nearly 15/8 (tempering out 2430/2401, the nuwell comma). 7edt is the lowest equal division of the tritave to accurately approximate some 7-limit harmony, along with some elements of the 11-limit, such as the 11/8 major fourth. Seven steps make up a tritave, meaning that 7edt tempers out 839808/823543, the eric comma.

Due to the proximity of the step size with 7/6, 7edt supports orwell temperament. One step of 7edt is almost identical to 12\53, the 53edo orwell generator, at about 271.698 cents. 7edt is also a good tuning for Electra temperament, with two steps of 7edt being a close approximation to 15/11.

### Harmonics

Approximation of harmonics in 7edt
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -113 +0 +45 -69 -113 -108 -68 +0 +89 -76 +45
Relative (%) -41.7 +0.0 +16.7 -25.5 -41.7 -39.9 -25.0 +0.0 +32.9 -27.9 +16.7
Steps
(reduced)
4
(4)
7
(0)
9
(2)
10
(3)
11
(4)
12
(5)
13
(6)
14
(0)
15
(1)
15
(1)
16
(2)

### Prime harmonics

Approximation of prime harmonics in 7edt
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) -113 +0 -69 -108 -76 -93 -14 +65 +6 -124 +33
Relative (%) -41.7 +0.0 -25.5 -39.9 -27.9 -34.3 -5.2 +23.9 +2.2 -45.5 +12.0
Steps
(reduced)
4
(4)
7
(0)
10
(3)
12
(5)
15
(1)
16
(2)
18
(4)
19
(5)
20
(6)
21
(0)
22
(1)

## Scale degrees of 7edt

Degrees Cents Hekts Approximate Ratio Electra notation (J = 1/1)
0 1/1 J
1 271.708 185.714 7/6 K
2 543.416 371.429 15/11, 11/8 L
3 815.124 557.143 8/5 M
4 1086.831 742.857 15/8 N
5 1358.539 928.571 11/5 (11/10 plus an octave) O
6 1630.247 1114.286 18/7 (9/7 plus an octave) P
7 1901.955 1300 3/1 J