[sdiy] Cheap frequency counter for oscillator calibration

[David G. Dixon]

> On Monday 26 April 2010, David G. Dixon wrote:
> > 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))]
> 
> Not quite, five cent deviation would actually be:
> 
> f(-5c) = f(0) * 2^(-5/1200)
> f(+5c) = f(0) * 2^(+5/1200)
> 
> or generally:
> 
> f(x[c]) = f(0) * 2^(x/1200) # x[c] means x in cent
> f(x[s]) = f(0) * 2^(s/12)   # x[s] means x in semitones
> 
> The error you made is small enough not to mess up your table too
> terribly, but if you were to try the same calculation with semitones
> or octaves you'd see it more clearly. :-)

Ah.  Thanks, Achim.  I didn't quite understand the concept of the "cent" of
pitch.  Of course, this makes more sense than the mixed log-linear thing I
was doing.

In any case, +/- 5 cents seems like a lot or tracking error, doesn't it?
Particularly in the midrange.