Shocktave
I was "shocked" that this worked as well as is did, hence the name. This circuit produces an octave-down effect which tracks effectively across the fretboard. The sound is not clean, but works well enough.

The circuit consists of a high-gain preamp stage, followed by a frequency-to-voltage convertor, which in turn drives an oscillator. The oscillator is tuned so that it can only keep up with every other cycle, resulting in the octave-down effect which can be mixed with the original signal.


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