US: Difference between revisions

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A '''US''', or '''utonal sequence''', is a kind of [[Arithmetic tunings|arithmetic]] and [[Monotonic tunings|monotonic]] tuning.
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"
{| class="wikitable"
Line 19: Line 17:
! 7
! 7
! 8
! 8
! 9
! (9)
|-
|-
! frequency
! frequency
|1/1
|28/28
|28/25
|28/25
|14/11
|28/22
|28/19
|28/19
|7/4
|28/16
|28/13
|28/13
|14/5
|28/10
|4/1
|28/7
|7/1
|(28/4)
|-
|-
! pitch
! pitch
Line 41: Line 39:
|1.49
|1.49
|2.00
|2.00
|2.81
|(2.81)
|-
|-
! length
! length
|1/1
|28/28
|25/28
|25/28
|11/14
|22/28
|19/28
|19/28
|4/7
|16/28
|13/28
|13/28
|5/14
|10/28
|1/4
|7/28
|1/7
|(4/28)
|}
|}

Revision as of 02:09, 22 March 2021

A US, or utonal sequence, is a kind of arithmetic and monotonic tuning.

The full specification of a US is (n-)USp: (n pitches of a) utonal sequence adding by p.

A US is a specific (rational) type of 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.

example: 9-US(3/4)
quantity 1 2 3 4 5 6 7 8 (9)
frequency 28/28 28/25 28/22 28/19 28/16 28/13 28/10 28/7 (28/4)
pitch 0.00 0.16 0.35 0.56 0.81 1.11 1.49 2.00 (2.81)
length 28/28 25/28 22/28 19/28 16/28 13/28 10/28 7/28 (4/28)
Retrieved from "https://en.xen.wiki/index.php?title=US&oldid=63723"