Andreas has sent me a link to a fairly strait forward Theremin build. I’m not a Theremin guru, but the design seems easy to implement with only 2 4069 Hex Inverter ICs and other inexpensive parts. The description of the circuit operation is a nice read as well. From what I can decipher the pitch of one oscillator is controlled by the capacitance of the body’s relative position to the antenna. Another oscillator is adjusted and set to have a similar frequency of around 73kHz, that is roughly 4 times higher then the normal hearing range. What happens next is the key to Theremin operation. These 2 frequencies are actually subtracted from each other, giving a frequency that is within audible range. This typically is not the way most Optical Theremins work where a single oscillator is controlled by resistance and the resulting frequency happens to be within the audible range. Either way there are lots of cool case designs and info on this page.
An audio sample of the theremin can be heard on this arrangement.