US: Difference between revisions

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VisualWikitext

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 A '''US''', or '''utonal sequence''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Monotonic tunings|monotonic]] tuning.
-A US is a specific (rational) type of ALS.
+The full specification of a US is (n-)USp: (n pitches of a) utonal sequence adding by p.
-(n-)USp: (n pitches of a) utonal sequence adding by p
+A US is a specific (rational) type of [[ALS|ALS, or arithmetic length sequence]]. By varying the undertone series step size to some rational number (other than 1) you can produce a US, and varying it to an irrational number you can produce an ALS. In other words, by shifting the undertone series by a constant amount of string length, the step sizes remain equal in terms of length, but their relationship in pitch changes.
-The same principles that were just described for frequency are also possible for length: by varying the undertone series step size to some rational number you can produce a utonal sequence (US), and varying it to an irrational number you can produce an arithmetic length sequence (ALS). In other words, by shifting the undertone series by a constant amount of string length, the step sizes remain equal in terms of length, but their relationship in pitch changes.
 {| class="wikitable"
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 ! 7
 ! 8
-! 9
+! (9)
 |-
 ! frequency
-|1/1
+|28/28
 |28/25
-|14/11
+|28/22
 |28/19
-|7/4
+|28/16
 |28/13
-|14/5
+|28/10
-|4/1
+|28/7
-|7/1
+|(28/4)
 |-
 ! pitch
@@ Line 41: / Line 39: @@
 |1.49
 |2.00
-|2.81
+|(2.81)
 |-
 ! length
-|1/1
+|28/28
 |25/28
-|11/14
+|22/28
 |19/28
-|4/7
+|16/28
 |13/28
-|5/14
+|10/28
-|1/4
+|7/28
-|1/7
+|(4/28)
 |}