OD: Difference between revisions

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|-
|-
! quantity
! quantity
! (0)
! 1
! 1
! 2
! 2
! 3
! 3
! 4
! 4
! (5)
|-
|-
! frequency (f)
! frequency (f)
|4/4
|(4/4)
|5/4
|5/4
|6/4
|6/4
|7/4
|7/4
|(8/4)
|8/4
|-
|-
! pitch (log₂f)
! pitch (log₂f)
|0.00
|(0)
|0.32
|0.32
|0.58
|0.58
|0.81
|0.81
|(1.00)
|1
|-
|-
! length (1/f)
! length (1/f)
|4/4
|(4/4)
|4/5
|4/5
|4/6
|4/6
|4/7
|4/7
|(4/8)
|4/8
|}
|}



Revision as of 21:40, 22 March 2021

An OD, or otonal division, is a kind of arithmetic and monotonic tuning.

Its full specification is n-ODp: n otonal divisions of interval p.

The nth overtone mode, or over-n scale is equivalent to n-ODO. So is n-ADO.

An OD is a specific (rational) type of EFD, or equal frequency division.

note there's a kinda tricky aspect which is that if you just want overtones 1-9 you need 8-OD9 because there are only 8 steps from 1 to 9. You could think of it like 9 is the 8th overtone, so you're really dividing 8 by 8. You're dividing the number of overtones.

example: 4-ODO
quantity (0) 1 2 3 4
frequency (f) (4/4) 5/4 6/4 7/4 8/4
pitch (log₂f) (0) 0.32 0.58 0.81 1
length (1/f) (4/4) 4/5 4/6 4/7 4/8