US: Difference between revisions

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{| class="wikitable"
{| class="wikitable"
|+example:
|+example: 9-US(3/4)
|-
|-
! quantity
! quantity
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|-
|-
! frequency
! frequency
|
|1/1
|
|28/25
|
|14/11
|
|28/19
|
|7/4
|
|28/13
|
|14/5
|
|4/1
|
|7/1
|-
|-
! pitch
! pitch
|
|0.00
|
|0.16
|
|0.35
|
|0.56
|
|0.81
|
|1.11
|
|1.49
|
|2.00
|
|2.81
|-
|-
! length
! length
|
|1/1
|
|25/28
|
|11/14
|
|19/28
|
|4/7
|
|13/28
|
|5/14
|
|1/4
|
|1/7
|}
|}

Revision as of 01:51, 22 March 2021

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

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

(n-)USp: (n pitches of a) utonal sequence adding by p

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.

example: 9-US(3/4)
quantity 1 2 3 4 5 6 7 8 9
frequency 1/1 28/25 14/11 28/19 7/4 28/13 14/5 4/1 7/1
pitch 0.00 0.16 0.35 0.56 0.81 1.11 1.49 2.00 2.81
length 1/1 25/28 11/14 19/28 4/7 13/28 5/14 1/4 1/7