User:Cmloegcmluin/APS: Difference between revisions

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fix table
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|-
|-
! quantity
! quantity
! (0)
! 1
! 1
! 2
! 2
! 3
! 3
! 4
! 4
! 5
! 6
! 7
! 8
! 9
|-
|-
! frequency
! frequency (f)
|1.00
|(1)
|1.19
|1.19
|1.41
|1.41
|1.68
|1.68
|2.00
|2
|2.38
|2.83
|3.36
|4.00
|-
|-
! pitch
! pitch (log₂f)
|0.00
|(2⁰⸍⁴)
|0.25
|2¹⸍⁴
|0.50
|2²⸍⁴
|0.75
|2³⸍⁴
|1.00
|2⁴⸍⁴
|1.25
|1.50
|1.75
|2.00
|-
|-
! length
! length (1/f)
|1.00
|(1)
|0.84
|0.84
|0.71
|0.71
|0.59
|0.59
|0.50
|0.5
|0.42
|0.35
|0.30
|0.25
|}
|}


[[Category:Equal-step tuning‏‎]]
[[Category:Equal-step tuning‏‎]]
[[Category:Equal divisions of the octave‏‎ ]]
[[Category:Equal divisions of the octave‏‎ ]]

Revision as of 21:53, 22 March 2021

An APS, or arithmetic pitch sequence, is a kind of arithmetic and monotonic tuning.

(n-)APSp: (n pitches of an) arithmetic pitch sequence adding by p (equivalent to rank-1 temperament with generator p)

An AS is a specific (rational) type of APS.

equal multiplications https://en.xen.wiki/w/Equal-step_tuning#Equal_multiplications

example: 4-EDO = rank-1 temperament w/ generator 300¢ = APS⁴√2 ≈ APS1.189
quantity (0) 1 2 3 4
frequency (f) (1) 1.19 1.41 1.68 2
pitch (log₂f) (2⁰⸍⁴) 2¹⸍⁴ 2²⸍⁴ 2³⸍⁴ 2⁴⸍⁴
length (1/f) (1) 0.84 0.71 0.59 0.5