Multiplexing and electric capacitance

The fact that theremins use heterodyne mixers has nothing to do with RF. The 'antennae' are not antennae in the classical, RF sense. The capacitance explanation is correct.

Capacitors and Theremin 'Antennae'

The simplest type of capacitor is a parallel-plate capacitor. That means the capacitor consists of two metal plates separated by some material called the dielectric. The equation for the capacitance of such a capacitor is C=εA/d, where ε is the permittivity of the dielectric (ε≈8.8541878176..×10^−12 F/m for air).

When you are operating a theremin, your hand is one plate (your hand is effectively grounded), the antenna is the other, and the air between the two is the dielectric. As you move your hand, you vary the capacitance between ground and the antenna. Both hands will affect both antennae, as they act like two plates in parallel, increasing the total area.

The two antennae are at right angles because that reduces the impact your left hand will have on the right antenna and vice versa. For example, as you move your hand up and down above the volume antenna, it maintains a relatively constant distance from the pitch antenna, thus it's contribution to the overall capacitance is constant (and small).

Theory of Operation

Note/Update: Please refer to FredM's Answer for a more detailed description of the oscillator.

Both antennae capacitors are part of two different, complex active LC oscillators. The 'L' refers to inductors, which store energy in a magnetic field; the 'C' refers to capacitors, which store energy in an electric field. In an LC oscillator, energy is constantly flowing back and forth between the two, changing from electric potential to magnetic potential.

The frequency of the pitch oscillator is beyond audio frequencies, so it can't be directly used. The theremin has a third oscillator that operates at a fixed frequency. The pitch oscillator and the fixed oscillator's outputs are fed into a heterodyne mixer, resulting in an output that includes the sum and difference frequencies of the two inputs. The sum frequency is even higher than the original signal, thus it is useless and is filtered out. The resulting signal is a single frequency (plus harmonics) in the audio range.

The frequency of the volume oscillator is used to control how much the audio signal is amplified. As you move your hand, the frequency changes, so the amplifier's gain changes, and thus the output volume changes.

For the H bridges, if the motor voltage is low i.e. less than 10V, please consider the implications of some types of H bridge listed in this answer. For the multiplexing of the potentiometers you can use a serial/SPI controlled analogue switch such as the ADG714 - it has 8 normally open switches but is restricted to logic level voltages.

Providing PWM control isn't needed (difficult to multiplex) the ADG714 can probably also help out - use the analogue switches to control enable and direction pins. Note that 2 ADG414s can be cascaded from one serial SPI bus so no extra pins are required.

If you are happy with constant speed I'd stick with it but you could implement a slow/fast speed regime by gating a 50:50 square wave oscillator to the FETs. You could take this further by using the LTC6992 PWM control chip - it needs an analogue input that could be provided from a serial DAC.