US: Difference between revisions

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Line 20: Line 20:
|-
|-
! frequency (f)
! frequency (f)
|28/28
|(28/28)
|28/25
|28/25
|28/22
|28/22
Line 28: Line 28:
|28/10
|28/10
|28/7
|28/7
|(28/4)
|28/4
|-
|-
! pitch (log₂f)
! pitch (log₂f)
|0.00
|(0)
|0.16
|0.16
|0.35
|0.35
Line 39: Line 39:
|1.49
|1.49
|2.00
|2.00
|(2.81)
|2.81
|-
|-
! length (1/f)
! length (1/f)
|28/28
|(28/28)
|25/28
|25/28
|22/28
|22/28
Line 50: Line 50:
|10/28
|10/28
|7/28
|7/28
|(4/28)
|4/28
|}
|}



Revision as of 22:23, 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: 8-US(3/4)
quantity (0) 1 2 3 4 5 6 7 8
frequency (f) (28/28) 28/25 28/22 28/19 28/16 28/13 28/10 28/7 28/4
pitch (log₂f) (0) 0.16 0.35 0.56 0.81 1.11 1.49 2.00 2.81
length (1/f) (28/28) 25/28 22/28 19/28 16/28 13/28 10/28 7/28 4/28