One trick to get a sub-octave signal is to invert every other cycle of a waveform. I think that’s what those octaver guitar pedals do.
You basically have a comparator, which produces a pulse wave.
This pulse wave gets fed into an divide-by-2 counter to get a pulse with half the frequency, which is then used to invert the original signal.
As this method relies on zero-crossings it will only work well for monophonic signals with a strong fundamental.
If you have the csound book by boulanger handy, have a look at chapter 29 "Efficient Implementation of Analog Waveshaping". There’s a description of the process with nice diagrams.
If you’re completely lost, I have a patch lying round somewhere, I could share.