User:Cmloegcmluin/AS: Difference between revisions

Revision as of 21:53, 22 March 2021

An AS, or ambitonal sequence, is a kind of arithmetic and monotonic tuning.

An AS is a specific (rational) type of APS.

(n-)ASp: (n pitches of an) ambitonal sequence adding by p (equivalent to 1D JI lattice of p)

These are sequences which are rational but ambiguous between otonality and utonality, such as a chain of the same JI pitch.

example: AS5/4 = 1D JI lattice of 5/4 = 5/4 chain
quantity	(0)	1	2	3	4	5	6	7	8
frequency (f)	(5⁰/4⁰)	5¹/4¹	5²/4²	5³/4³	5⁴/4⁴	5⁵/4⁵	5⁶/4⁶	5⁷/4⁷	5⁸/4⁸
pitch (log₂f)	(0)	0.32	0.64	0.97	1.29	1.61	1.93	2.25	2.58
length (1/f)	(1/1)	4/5	16/25	64/125	256/625	1024/3125	4096/15625	16384/78125	65536/390625

@@ Line 13: / Line 13: @@
 |-
 ! quantity
+! (0)
 ! 1
 ! 2
@@ Line 21: / Line 22: @@
 ! 7
 ! 8
-! 9
 |-
-! frequency
+! frequency (f)
-|1/1
+|(5⁰/4⁰)
-|5/4
+|5¹/4¹
-|25/16
+|5²/4²
-|125/64
+|5³/4³
-|625/256
+|5⁴/4⁴
-|3125/1024
+|5⁵/4⁵
-|15625/4096
+|5⁶/4⁶
-|78125/16384
+|5⁷/4⁷
-|390625/65536
+|5⁸/4⁸
 |-
-! pitch
+! pitch (log₂f)
-|0.00
+|(0)
 |0.32
 |0.64
@@ Line 45: / Line 45: @@
 |2.58
 |-
-! length
+! length (1/f)
-|1/1
+|(1/1)
 |4/5
 |16/25