Back in the late 70s, when I was in high school, I used to build these and give them to girls I had a liking for. I even managed to get a date or two from some of the recipients. Heh, the life of a high school science geek. Well, anyway...
The first few specimens I built used three 555 IC oscillators slaved to each other. After those first few I'd made of 555 chips I started thinking about how to make an equivalent circuit out of fewer, cheaper, more clever parts. Like 4xxx series CMOS inverter gates. After all, almost anyone can build a three-oscillator circuit using off-the-shelf oscillator IC chips (or a microcontroller, for the more sophisticated).
Step 1: Theory (such as it is) - waveforms
Why CMOS? High circuit impedance and very low current requirements lead to long battery life and, as we'll see below, lower parts cost and better "character" in the finished toy. Why CMOS 4xxx series? Because they can be run from a wide voltage supply: from 3 to 18 Volts -- just the thing for a toy using a 9V battery as a supply.
Aside from its extremely low current requirements digital CMOS provides a few other advantages in this analog application. First, the extremely high impedance of CMOS circuits leads to increased "noise susceptibility" -- the opposite of noise immunity -- which is something that we want in this application. Nose susceptibility adds character to the Tribble. The extremely high impedance and low internal leakage of CMOS also allows us to use small capacitor values and high resistor values in our RC networks. Resistors (of a given precision and thermal dissipation capacity) generally cost the same regardless of their Ohmic value. The same is not true of capacitors; the higher capacitances tend to cost more, and be of larger physical size, than the lower ones.
But perhaps the main attraction of using CMOS gates is the satisfaction of knowing that you are using digital logic blocks to do an analog task. A corruption of logic ... so to speak.
Some of you may have seen oscillator circuits that use simple inverters, and you could certainly build our three oscillators from a single hex inverter IC, but then you would still need a way of multiplying (AND-ing) the outputs together. Worse, since the inverter circuits require two gates per oscillator they are not the most clever, parsimonious way to build this particular toy. Therefore, the IC that I've selected for this version of the Tribble is the 4093B quad 2-input NAND Schmitt Trigger. It can provide all three oscillators as well as do the multiply/mixing of the signals.
(Actually, I would have used a hex Schmitt Trigger inverter, the 40106B, if I could have found one at the store. As I'll show below an oscillator using a Schmitt Trigger needs only a single inverter. Perhaps I'll do that one another day because it is even more interesting than the current design as an example of Micky Mouse logic and applied bullshit.)
Figure 1 shows the voltage vs. time graph of the three signals we want to mix (and the mixed result). Red traces are the RC voltages. Blue traces are the outputs from the "inverters" (actually NAND Schmitt Trigers) of the stages.
Figure 2 shows the three signals multiplied (AND-ed) together.
Note that the frequency ratios in the figures are not to scale.