[time-nuts] Re: Low cost synchronization, kitchen appliances

[Chuck Harris]

Alberto di Bene wrote:

>>based.  The absolute accuracy of such a system is not so good
>>Soundcards don't
>>even trim their crystals for frequency.  I would venture that the
>>typical accuracy of
>>a sound card's clock is certainly no better that +/-0.01%.
> 
> 
> Hmmm, the sound card used is the M-Audio Delta 44, a professional sound
> card, used also by musicians and composers for studio works. I don't
> know the accuracy of its time base, but certainly it is quite good.

No doubt, but even the best most gifted world class musician with
perfect pitch cannot resolve pitch to  better than 1 cent.  More usual
is around 4 cents.

Now to screw up a little math and figure out what that means:

A cent is 1/100th of the spacing between two semitones, and because
there are 12 semitones in an octave, there are 1200 cents in an octave.
The cent is, as such, logrithmic in nature.  The ratio of any two frequencies,
given in cents is:

n = 1200 log2(a/b)

If our sound card is accurate to 0.01%, the ratio of a/b would be:
1.0001  so,

n = 1200 log2(1.0001) = 1200 log2(10) log10(1.0001) = 0.03 cents!

0.03 cents is merely 33 times more precise than the very best of the
best can hear!  So, I think I would be safe in concluding that your sound
card may be super duper as a music processing device, and still be pretty
awful as a test instrument.

-Chuck