OD: Difference between revisions

Revision as of 02:03, 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 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.

example: 4-ODO
quantity	1	2	3	4	5
frequency (f)	4/4	5/4	6/4	7/4	(8/4)
pitch (log₂f)	0.00	0.32	0.58	0.81	(1.00)
length (1/f)	4/4	4/5	4/6	4/7	(4/8)

@@ Line 1: / Line 1: @@
 An '''OD''', or '''otonal division''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Monotonic tunings|monotonic]] tuning.
-overtone mode, or over-n scale (equivalent to n-ODO)
+Its full specification is n-ODp: n otonal divisions of interval p.
-n-ODp: n otonal divisions of interval p
+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.
+An OD is a specific (rational) type of [[EFD|EFD, or equal frequency division]].
 {| class="wikitable"
-|+example: 4-ODO = 4th overtone mode = 4-ADO
+|+example: 4-ODO
 |-
 ! quantity
@@ Line 16: / Line 16: @@
 ! 4
 ! 5
-! 6
-! 7
-! 8
-! 9
 |-
-! frequency
+! frequency (f)
-|1/1
+|4/4
 |5/4
-|3/2
+|6/4
 |7/4
-|2/1
+|(8/4)
-|5/2
-|3/1
-|7/2
-|4/1
 |-
-! pitch
+! pitch (log₂f)
 |0.00
 |0.32
 |0.58
 |0.81
-|1.00
+|(1.00)
-|1.32
-|1.58
-|1.81
-|2.00
 |-
-! length
+! length (1/f)
-|1/1
+|4/4
 |4/5
-|2/3
+|4/6
 |4/7
-|1/2
+|(4/8)
-|2/5
-|1/3
-|2/7
-|1/4
 |}