I've started prototyping. The first thing to do is make what I'm calling the triangle core. It's the only circuit that's generating an independent waveform. Everything else is a type of wave shaping.

I made a breadboard layout (If anyone knows of a better program than PEBBLE to use, please inform):

And then I put it on the breadboard:

Here's a video of the triangle and square waves changing frequency and symmetry (duty cycle):

http://youtu.be/w_oxIqUgWuA

The triangle sides aren't straight. I suspect either the capacitor or weird diode things. Also, the frequency range isn't as wide as I would like it. I suspect the diode of dropping too much voltage.

In any case, further testing is required!