8 equal divisions of the superoctave is a super-pitch tuning system that tetratively divides the superoctave into 8 equally spaced steps.
8edso is notable for containing a close approximation to 3/1 (as well as log2(3)) according to the analytic extension of the tetration developed by Kneser, hereby producing a strong approximation to the super-pitch equivalent of the Pythagorean tuning. Furthermore, it provides good representation of 5/1 as well as log2(5), thus being a strong 2.3.5 super-subgroup tuning and therefore being the best candidate for the super-pitch equivalent of 12edo.
Intervals
| Step
|
Linear value
|
Cents
|
Tetrative intervals
|
Common JI approximation
|
| 0
|
1
|
0.000
|
|
1/1 exact
|
| 1
|
1.11149118
|
182.996
|
|
10/9
|
| 2
|
1.22436140
|
350.435
|
log(log(5)) = 5/1 reduced
|
5/4, 11/9
|
| 3
|
1.33973255
|
506.334
|
|
4/3
|
| 4
|
1.45878181
|
653.717
|
|
16/11, 19/13
|
| 5
|
1.58278746
|
794.961
|
log(3) = 3/1 reduced
|
8/5, 11/7, 19/12
|
| 6
|
1.71318047
|
932.013
|
|
12/7
|
| 7
|
1.85160598
|
1066.533
|
|
11/6, 13/7
|
| 8
|
2
|
1200.000
|
|
2/1 exact
|
