Theremin and capacitance

Today Google were leading with an obscure anniversary for a theremin player. The theremin was the first electronic instrument. Its inventor was trying to come up with a proximity sensor. Watch this to see it being played: https://www.youtube.com/watch?v=MJACNHHuGp0 Notice that she changes the sound without touching the instrument. It turns out that her hands are acting as the Earthed plates of a capacitor. Consider this:

A capacitor is a break in a circuit. It acts to stop current flowing. But with AC current flows backwards and forwards. As the frequency increases, the gap affects the flow of current less and less. Capacitors are used as high pass filters allowing only high frequencies through.

An inductance is basically an electomagnet. It generates a moving magnetic field with AC. That moving magnetic field is responsible for generating a back emf in the circuit. This is bigger when the frequency is high, by Faraday's Law which says that induced emf is directly proportional to the rate of change of flux linkage. Thus high frequencies are blocked by an inductance. It is a low pass filter.

Now put the two together.They do opposite things. Careful study show that the phase of the current oscillation in them is 180 degrees so when current goes right through the inductance it is going left through the capacitance. Ah! Current will flow in a self-sustaining loop. The frequency of this resonance depends on the values of inductance and capacitance chosen. In the theremin the inductance is fixed. The hand acts as one plate of the capacitor and its size is affected by the distance from the other plate. This changes the frequency and thus the note.