UD: Difference between revisions

Revision as of 21:53, 22 March 2021

A UD, or utonal division, is a kind of arithmetic and monotonic tuning.

A UD is a specific (rational) type of ELD.

undertone mode, or under-n scale (equivalent to n-UDO)

n-UDp: n utonal divisions of interval p

An n-EDL is equivalent to a 2n-UDO (therefore EDL cannot be used to represent a UDO with an odd value for n).

example: 4-UDO = 4th undertone mode
quantity	(0)	1	2	3	4
frequency (f)	(8/8)	8/7	8/6	8/5	8/4
pitch (log₂f)	(0)	0.19	0.42	0.68	1.00
length (1/f)	(1/1)	7/8	3/4	5/8	1/2

@@ Line 13: / Line 13: @@
 |-
 ! quantity
+! (0)
 ! 1
 ! 2
 ! 3
 ! 4
-! 5
-! 6
-! 7
-! 8
-! 9
 |-
-! frequency
+! frequency (f)
+|(8/8)
+|8/7
+|8/6
+|8/5
+|8/4
+|-
+! pitch (log₂f)
+|(0)
+|0.19
+|0.42
+|0.68
 |1.00
-|1.15
-|1.31
-|1.46
-|1.62
-|1.87
-|2.12
-|2.37
-|2.62
 |-
-! pitch
+! length (1/f)
-|0.00
+|(1/1)
-|0.21
+|7/8
-|0.39
+|3/4
-|0.55
+|5/8
-|0.69
+|1/2
-|0.90
-|1.08
-|1.24
-|1.39
-|-
-! length
-|1.00
-|0.87
-|0.76
-|0.68
-|0.62
-|0.54
-|0.47
-|0.42
-|0.38
 |}