8 equal divisions of the 6th harmonic (abbreviated 8ed6) is a nonoctave tuning system that divides the interval of 6/1 into 8 equal parts of about 388 ¢ each. Each step represents a frequency ratio of 61/8, or the 8th root of 6.
| Prime factorization
|
23
|
| Step size
|
387.744 ¢
|
| Octave
|
3\8ed6 (1163.23 ¢)
(semiconvergent)
|
| Twelfth
|
5\8ed6 (1938.72 ¢)
(semiconvergent)
|
| Consistency limit
|
6
|
| Distinct consistency limit
|
4
|
Intervals
| #
|
Cents
|
Approximate JI ratio(s)
|
| 0
|
0.000
|
exact 1/1
|
| 1
|
387.744
|
5/4, 4/3, 6/5, 7/6, 9/7, 10/7, 9/8, 11/9, 11/10, 12/11
|
| 2
|
775.489
|
3/2, 11/7
|
| 3
|
1163.233
|
2/1
|
| 4
|
1550.978
|
5/2, 7/3
|
| 5
|
1938.722
|
3/1
|
| 6
|
2326.466
|
4/1
|
| 7
|
2714.211
|
5/1
|
| 8
|
3101.955
|
exact 6/1
|
Harmonics
| #
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
| Steps
|
3
|
5
|
6
|
7
|
8
|
9
|
9
|
10
|
10
|
11
|
11
|
| Reduced
|
3
|
5
|
6
|
7
|
0
|
1
|
1
|
2
|
2
|
3
|
3
|