OD
An OD, or otonal division, is a kind of arithmetic and monotonic tuning.
Its full specification is n-ODp: n otonal divisions of interval p.
The nth overtone mode, or over-n scale is equivalent to n-ODO. So is n-ADO.
An OD is a specific (rational) type of EFD, or equal frequency division.
note there's a kinda tricky aspect which is that if you just want overtones 1-9 you need 8-OD9 because there are only 8 steps from 1 to 9. You could think of it like 9 is the 8th overtone, so you're really dividing 8 by 8. You're dividing the number of overtones.
| quantity | (0) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| frequency (f) | (4/4) | 5/4 | 6/4 | 7/4 | 8/4 |
| pitch (log₂f) | (0) | 0.32 | 0.58 | 0.81 | 1 |
| length (1/f) | (4/4) | 4/5 | 4/6 | 4/7 | 4/8 |