Under such circumstances, binning the data can reveal patterns. Here is the same data grouped into four roughly equalsized bins. 
Here is the log plot with respect to bin number. 
Using a carefully chosen bin size, the plot illustrates the underlying fact that there approximately 3/2 as many notes in successively higher pitched bins.
If, instead of plotting log of the count against respective bin numbers, we choose to make the xaxis the log of the midperiod size of each bin, we would also obtain a straight line. This is because the pitch periods have a logarithmic relationship to each other other through the formula for finding the frequency of a given pitch:

F_{p} = F_{ref} 2^{d/12} 
where F_{p} is the frequency of pitch we wish to calculate, F_{ref} is the frequency of a reference pitch, and d is the intervallic distance between the two pitches as measured in semitones 
Return to Pitch Scaling.
© 2004 Harlan Brothers