Arduino Theremin With Variable Pitch and Volume

My intention was to build an easy and cheap theremin, using the arduino. I’ve already finished a classic variant (the model 144;; but now I wanted something cheaper. The theremin was invented by Leon Theremin in 1919. Classically a theremin consists if two oscillating circuits, one fixed and one variable. The variation is achieved by moving the hand in front of an antenna. When those two slightly different oscillations are being mixed you get beats. The frequency of those beats is the difference between the frequencies of the two oscillations. This signal can be heard.”