PFDO: Difference between revisions

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~~{{stub}}~~

A '''''p''-FDO''' ('''''p''-mean frequency division of the octave''') is a [[period]]ic [[tuning system]] which divides the [[octave]] using {{w|Generalized mean|power means}}. For example:

'''~~pFDO~~''' (~~pth~~ mean frequency division of the octave) ~~refers to dividing~~ the octave using power ~~[https://en.wikipedia.org/wiki/Generalized_mean](~~means). p=0 corresponds to [[EDO]], p=1 corresponds to [[AFDO]], ~~and~~ p=-1 corresponds to [[IFDO]]. ~~The general formula~~ for the ~~ath~~ interval of b-~~pFDO~~ is ~~equal to~~ (a/b + 2~~<sup>~~p~~</sup> * (b-a)~~/b)~~<sup>~~1/p~~</sup>.~~

* ''p'' = 0 corresponds to [[EDO]],

* ''p'' = 1 corresponds to [[AFDO]],

* ''p'' = -1 corresponds to [[IFDO]].

Except for the case where ''p'' = 0, the [[frequency ratio]] of the ''k''-th interval in the first octave of ''n''-''p''-FDO is

$$\left( (n - k)/n + 2^p \cdot k/n \right)^{1/p}$$

[[Category:Acronyms]]

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-{{stub}}
+A '''''p''-FDO''' ('''''p''-mean frequency division of the octave''') is a [[period]]ic [[tuning system]] which divides the [[octave]] using {{w|Generalized mean|power means}}. For example:
-'''pFDO''' (pth mean frequency division of the octave) refers to dividing the octave using power [https://en.wikipedia.org/wiki/Generalized_mean](means). p=0 corresponds to [[EDO]], p=1 corresponds to [[AFDO]], and p=-1 corresponds to [[IFDO]]. The general formula for the ath interval of b-pFDO is equal to (a/b + 2<sup>p</sup> * (b-a)/b)<sup>1/p</sup>.
+* ''p'' = 0 corresponds to [[EDO]],
+* ''p'' = 1 corresponds to [[AFDO]],
+* ''p'' = -1 corresponds to [[IFDO]].
+Except for the case where ''p'' = 0, the [[frequency ratio]] of the ''k''-th interval in the first octave of ''n''-''p''-FDO is
+$$\left( (n - k)/n + 2^p \cdot k/n \right)^{1/p}$$
+[[Category:Acronyms]]
+{{Todo| discuss title }}
+{{Stub}}