TimV
Error on my part re "Rounding up 31.7666536334 = 4 cents."
Using the example of 31.766xxxx as the total amount of deviation it would be 32 cents.
Had that 4 cents per Hz stuck in my mind and my mind left me...
And yes this is more valid in reference to A440 and pitch, as I mentioned in my real world examples as a tuner.
In a piano, inharmonicity  & 'stretching' octaves will alter the 4c=1Hz.   
m