If it helps any, the OC-2 sound is simply a low-passed square wave with a good bit of resonance.
It does seem like that would be the case, but actually what's up is trickier than that.
So the logic portion of the circuit generates a square wave that's an octave lower (or 2) than the input. That part's well understood, Google "flip flop circuit" for details.
But the synthesized square wave is not actually used at the output - instead, it's used to switch a FET on and off. The FET is connected to an opamp gain stage which is setup in such a way that it's non-inverting, but when the FET is switched on, the opamp becomes inverting. So the result is that the opamp is flipping the phase of your instrument signal every other cycle. That gives a wave much like the drawing I've attached. Then the output is filtered, in hopes of removing the upper harmonic (the little valley at each peak/little peak at each valley). But because the filter can't be all that steep without a ton of extra parts, the upper harmonic is never filtered out completely.
We now have a nice fundamental that's an octave below your input pitch (note that this is not a synthesized tone, but a mangled version of your actual input). However, because we now have 3 little peaks for every 1 fundamental peak, we also get a third harmonic, which is an octave and a fifth above the fundamental (the fundamental, confusingly, is the octave down).
Put more simply, the OC-2 in 1 oct down mode generates an octave down, plus a harmonic a fifth up from your original note. This goes a long way toward explaining why the OC2 and all the other analog octavers based on it sound so fat. It also explains why it's not that simple to get that sound without the octave down - and why it can't be done polyphonically.