UD: Difference between revisions

Revision as of 23:03, 22 March 2021

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

Its full specification is n-UDp: n utonal divisions of rational interval p. An n-UDO is equivalent to the nth undertone mode, or under-n scale.

The only difference between n-UDp and n-ELDp (equal length division) is that the p for UD is rational, while the p for ELD is irrational.

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

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 A '''UD''', or '''utonal division''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Monotonic tunings|monotonic]] tuning.
-A UD is a specific (rational) type of ELD.
+Its full specification is n-UDp: n utonal divisions of rational interval p. An n-UDO is equivalent to the nth [[Overtone_scale#Next_Steps|undertone mode, or under-n scale]].
-undertone mode, or under-n scale (equivalent to n-UDO)
+The only difference between n-UDp and [[ELD|n-ELDp (equal length division)]] is that the p for UD is rational, while the p for ELD is irrational.
-n-UDp: n utonal divisions of interval p
+An [[EDL|n-EDL]] is equivalent to a 2n-UDO (therefore EDL cannot be used to represent a UDO with an odd value for n).
-An n-EDL is equivalent to a 2n-UDO (therefore EDL cannot be used to represent a UDO with an odd value for n).
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