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.
-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]].
-An OD is a specific (rational) type of [[EFD|EFD, or equal frequency division]].
+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.
-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.
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