OD: Difference between revisions
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An '''OD''', or '''otonal division''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Monotonic tunings|monotonic]] tuning. | An '''OD''', or '''otonal division''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Monotonic tunings|monotonic]] tuning. | ||
Its full specification is n-ODp: n otonal divisions of interval p. | Its full specification is n-ODp: n otonal divisions of rational interval p. | ||
The only difference between n-ODp and n-EFDp is that the p for an [[EFD]] is irrational. | |||
The nth [[Overtone scale|overtone mode, or over-n scale]] is equivalent to n-ODO. So is n-[[ADO]]. | The nth [[Overtone scale|overtone mode, or over-n scale]] is equivalent to n-ODO. So is n-[[ADO]]. | ||
If you want to describe overtones 1-9 with OD you would need to use 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. Alternatively, you could describe his as an [[OS|OS, or overtone sequence]], by simply saying 8-OS. | |||
{| class="wikitable" | {| class="wikitable" | ||
Revision as of 22:12, 22 March 2021
An OD, or otonal division, is a kind of arithmetic and monotonic tuning.
Its full specification is n-ODp: n otonal divisions of rational interval p.
The only difference between n-ODp and n-EFDp is that the p for an EFD is irrational.
The nth overtone mode, or over-n scale is equivalent to n-ODO. So is n-ADO.
If you want to describe overtones 1-9 with OD you would need to use 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. Alternatively, you could describe his as an OS, or overtone sequence, by simply saying 8-OS.
| 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 |