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this must have been the issue:
# then select only upper portion of 1 + bandwidth equal to period_length

ok, uhhhhhhhhhhhh so what is "bandwidth equal to period_length"
well, period_length says the period in recording samples that the wave is.

meanwhile, fft indices are frequencies in units of 1/bufsize, roughly.
so let's think about hte frequencies, roughly.

frequency 0 is DC offset. that means its period is infinite. (bufsize / 0)
frequency 1 is the first half vs the last half, its period is the
entire buffer. (bufsize / 1)
the last frequency, bufsize-1, is the nyquist frequency. its period is 2.

now what is bufsize?
the parameter of interest is the recording buffer size [continue]