PFDO: Difference between revisions

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'''''p''-FDO''' ('''''p''-mean frequency division of the octave''') refers to dividing the octave using [[Wikipedia: Generalized mean|power means]]. For example:  
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:  
* ''p'' = 0 corresponds to [[EDO]],  
* ''p'' = 0 corresponds to [[EDO]],  
* ''p'' = 1 corresponds to [[AFDO]],  
* ''p'' = 1 corresponds to [[AFDO]],  
* ''p'' = -1 corresponds to [[IFDO]].  
* ''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>.
Except for the case where ''p'' = 0, the [[frequency ratio]] of the ''k''-th interval of ''n''-''p''-FDO is  
 
$$\left( (n - k)/n + 2^p \cdot k/n \right)^{1/p}$$


[[Category:Acronyms]]
[[Category:Acronyms]]