8edso
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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 |