[sdiy] Cheap frequency counter for oscillator calibration

[David G. Dixon]

This is slightly off the subject, but I was just looking for some tuning
data on the web (my personal obsession these days) and I came across a
review of the Wiard 300 system by Robert Rich from 2002:

http://emusician.com/elecinstruments/emusic_wiard_series_modular/

He gave the modules a generally good review, although he felt that they were
a bit hard to use and that the documentation was poor.  However, the point
is, he said that they track to +/- 5 cents over an 8-octave range.  I'm
trying to understand how to relate this information to actual frequencies.
I have assumed that, for any frequency F(0), the frequency 5 cents below may
be calculated thus:

F(-5c) = F(0)*[1-0.05*(1-2^(-1/12))]

and the frequency 5 cents above may be calculated thus:

F(+5c) = F(0)*(1+0.05*(1+2*(1/12))]

For octaves based on 1kHz, this gives the following frequencies (to four
decimal places):

   F(0)	   F(-5c)	   F(+5c)
-----------------------------------
   31.25	   31.16	   31.34
   62.50	   62.32	   62.69
  125.0	  124.6	  125.4
  250.0	  249.3	  250.7
  500.0	  498.6	  501.5
 1000		  997.2	 1003
 2000		 1994		 2006
 4000		 3989		 4012
 8000		 7978		 8024
16000		15955		16048

Is this correct?

Would this be considered acceptable tracking error?  (I shouldn't think so.)
I assume that the tracking is probably much better than this, and that all
of the error is at the extremes.  If so, then there should be a more precise
way to describe it.