I soldered together an oscillator from a 555 chip this afternoon and it pretty much works. It's got a Control Voltage input, an output and a big old 1meg pot for pitch control. The switch turns it on and off.
It "pretty much works" in that it definitely puts out a loud square wave, but the pitch only goes up and down so much before cutting out, despite there being throw left on the dial (about 1/5 of a turn in either direction). I'll tinker with it and see if swapping out the resistor in the circuit (100k) for one of a different value does anything. Look for a video when I've got it in a more, um, respectable state.
In the meantime, can anyone out there point me in the direction of a 555 cookbook for basic (read: BEGINNER) circuits? I'd like to get better at this using something other than trial and error as a guide. Thanks!