OD: Difference between revisions

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break up wall of information into helpful sections that are consistent across all arithmetic tuning pages
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== Relationship to other tunings ==
== Relationship to other tunings ==


=== vs. ED ===
=== Vs. ED ===


It is possible to — instead of equally dividing the octave in 12 equal parts by pitch, or 12-EDO — divide it into 12 equal parts by length. You will have 12-UDO.
It is possible to — instead of equally dividing the octave in 12 equal parts by pitch, or 12-EDO — divide it into 12 equal parts by length. You will have 12-UDO.


=== vs. EFD ===
=== Vs. EFD ===


The only difference between n-ODp and n-EFDp is that the p for an [[EFD|EFD (equal frequency division)]] is irrational, and therefore its pitches and intervals are all irrational too.  
The only difference between n-ODp and n-[[EFD]]p (equal frequency division) is that the p for an OD must be rational.


=== vs. ADO ===
=== Vs. ADO ===


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


=== vs. OS ===
=== Vs. OS ===


Any ODO will be equivalent to some [[OS|OS (otonal sequence)]]. E.g. 8-OD7 = 8-OS3/4, because to get from 1 to 7 you cover 6 overtones, and 6 divided by 8 is 3/4.
Any ODO will be equivalent to some [[OS|OS (otonal sequence)]]. E.g. 8-OD7 = 8-OS3/4, because to get from 1 to 7 you cover 6 overtones, and 6 divided by 8 is 3/4.


=== vs. UD ===
=== Vs. UD ===


The equivalent utonal version of an OD is a [[UD|UD (utonal sequence)]].  
The equivalent utonal version of an OD is a [[UD|UD (utonal sequence)]].  
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! 4
! 4
|-
|-
! frequency (f)
! frequency (''f'', ratio)
|(4/4)
|(4/4)
|5/4
|5/4
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|8/4
|8/4
|-
|-
! pitch (log₂f)
! pitch (log₂''f'', octaves)
|(0)
|(0)
|0.32
|0.32
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|1
|1
|-
|-
! length (1/f)
! length (1/''f'', ratio)
|(4/4)
|(4/4)
|4/5
|4/5
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|}
|}


[[Category:Overtone]]
[[Category:Overtone‏‎ series]]
[[Category:Otonality]]
[[Category:Otonality]]
[[Category:Harmonic]]
[[Category:Harmonic]]
[[Category:Harmonic series‏‎]]
[[Category:Harmonic series‏‎]]
Retrieved from "https://en.xen.wiki/w/OD"