I don't know if this will work, but here's how this came about: I was working out a schem for an octave effect, drawing waveforms to try and simulate what would happen here and there within the circuit, when I stumbled on the idea of differencing the input fundamental with a square wave of the same frequency. The idea is that with the "sine" and "square" levels equal, the difference between them will be a sort of crazy octave up mosquito like sound. At different settings, various other tones should be possible.
Improvements could include: better fundamental extraction before the comparator (i.e. a low-pass filter and maybe some limiting); possibly some coupling caps if DC levels get weird; filtering in general to tame some of the extreme fizz that is likely to be produced; limiting resistors for the gain controls.
If you build this, please let me know if it works! ;D
