austinsid:
Look, if the values that I'm getting match what I'm expecting then I'm happy. And they do. snip
Ok, they do have a point tho', ideally you should filter before ADC.
However, ideally you should pre-filter, 16-bit sample at 44KHz into a moving window buffer and and do a full 8 or 16k FFT on it.
But you can't do that with the hardware you have.
So, you have a small processor doing a cut-down approximation to a FHT on raw ADC values... and it seems to work just enough for what you want.
You did ask about values 'jumping around' - well, you have to put up with some odd things happening when the input data is not 'ideal' and the math is approximated. To get any better results, you would have to upgrade the audio and processor hardware and run better FFT software.
Yours,
TonyWilk
P.S. It might be interesting to look at the effect of aliasing on your bin values if you play a tone which is a bit above your ADC sampling frequency