ALS: Difference between revisions

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An '''ALS''', or '''arithmetic length sequence''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Monotonic tunings|monotonic]] tuning.

~~shifted undertone series~~ (~~± frequency~~) (equivalent to ~~ALS)~~

Is full specification is (n-)ALSp: (n pitches of an) arithmetic length sequence adding by p. It is equivalent to an undertone series shifted ± frequency.

~~(n-)ALSp: (n pitches of an) arithmetic length sequence adding by p~~

A [[US|US, or utonal sequence]], is a specific (rational) type of ALS. By varying the undertone series step size to some rational number (other than 1) you can produce a US, and by 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.

A US is a specific (rational) type of ALS.

~~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.

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 An '''ALS''', or '''arithmetic length sequence''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Monotonic tunings|monotonic]] tuning.
-shifted undertone series (± frequency) (equivalent to ALS)
+Is full specification is (n-)ALSp: (n pitches of an) arithmetic length sequence adding by p. It is equivalent to an undertone series shifted ± frequency.
-(n-)ALSp: (n pitches of an) arithmetic length sequence adding by p
+A [[US|US, or utonal sequence]], is a specific (rational) type of ALS. By varying the undertone series step size to some rational number (other than 1) you can produce a US, and by 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.
-A US is a specific (rational) type of ALS.
-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"