As I said previously, I am not an electronics expert. However, I have been following the theremin engineering threads here for five years and the general consensus amongst the skilled electronics guys is that it's darned hard to make a commercial quality theremin. This is reinforced by the number of designs that do not produce playable instruments.
An ideal instrument would have a linear pitch response over a useful number of octaves. By this I mean that if the player makes the same hand movement in any part of the field, it will produce the same interval change in pitch - for instance from closed fist to fingertips stretched towards the pitch rod might be an octave - a doubling in frequency. I believe the natural tendency of capacitative fields is to obey an inverse square law which is in contradiction of this.
From my background in computer programming I note that the theremin pitch circuit combines two different functions - those of frequency determination and waveform synthesis - in a single functional unit - which sets of a little alarm bell - my supposition is that it will be hard to adjust one functionality without affecting the other.
I also think that the various sounds of theremins and ondes martenots - both heterodyne synthesisers, are distinct from those synthesised by other technologies, and are a large part of the attraction of the theremin to me. I think part of it - for the theremin - is to do with FM synthesis - the waveform of a theremin is not fixed, but varies as the player's pitch hand modulates its frequency. To do this it samples the player's position very rapidly - at radio frequencies. I think a lot of information is lost when a theremin's audio is converted to a representation of pitch and volume alone, discarding timbral changes, making this blended functionality an essential aspect of theremin design.
[i]I cannot stretch my brain far enough to be able to call an electronic oscillator "organic"[/i]
I can. :-) Well, not quite. But I can call it cybernetic. Correct me if I am wrong, but I understand that the player's hands are acting as capacitor plates, making them - literally - part of the circuit - like the cybernetic organisms of science fiction - and also in the Norbert Weiner sense of being part of a feedback loop which includes the theremin, the loudspeaker and the thereminist who is constantly correcting pitch and volume based on audio feedback.