OD: Difference between revisions
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== Relationship to other tunings == | == Relationship to other tunings == | ||
=== | === 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 === | ||
The only difference between n-ODp and n- | 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 === | ||
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 === | ||
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 === | ||
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 ( | ! 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:Otonality]] | [[Category:Otonality]] | ||
[[Category:Harmonic]] | [[Category:Harmonic]] | ||
[[Category:Harmonic series]] | [[Category:Harmonic series]] | ||