It's a direct result of heterodyne detection performing a frequency subtraction, which is inharmonic. A tiny shift in pitch by the bat - remember pitch is about RATIOS - results in a HUGE shift in pitch by the detector. The detector slaps and bangs, but the bat just did a graceful swooping whistle.
Thanks! Will research further
An example - detector tuned to 50kHz. Bat calls at 52kHz - detector emits 2kHz. Bat drops to 51kHz - a gentle bluesy bend of 1/3 semitone - the detector drops to 1kHz. An octave! It seems sane - the bat dropped 1kHz, so did the detector - but the result does NOT preserve harmonic relationships.