d-n, did it again. I had a long comment explaining that in the real world there's always noise, just from fluctuation around the average number of photons per second that pass the energy that pass the energy (or fluctions about the average of arrival times of electons at the end of the connector wire for resistors) then lost my internet connection.

Off to get breaksfast and see if I can get an oscilloscope to put directly across the speaker terminals in my computer to see what BASIC sound command really sends it. Then I'm going to dig out an old fast Fourier transform program I wrote and the BASIC programs that generate data points to feed it. The heart of the the output graphics display program for it is in the in the two programs on my website.