This is last nights thought or opinion from the witching hour  6.02.19
(This is new science, I am learning and open to the opinion of others)

“Think in terms of a transformer that transfers its energy through an inductive field.”

The Electrodeum transfers energy through a capacitance field. The linearity happens by some constant “unknown” to me.

There is an engineer out there that might read this and get an idea of what is going on.

This energy transfer is “almost independent” of the relationship of the pitch oscillator tank frequency vs. the resonant frequency of the Electrodeum. Without the L4 base choke the spring will only resonate at a pitch oscillator frequency of about ~900 kHz, with the base 3.3 mh choke the tuning becomes very broad.

If the Electrodeum is not resonating the L4 choke at its base is a 5 ohm dc short to ground. My guess the same would happen if using the standard pitch antennas of today. With L4 removed and the spring not resonating behaves as any standard pitch antenna would in the normal non linear fashion. 

L4 protects the electronics from dc static discharge, the weakest point of theremin design.

“If the Electrodeum is resonating with L4 the linearity magic is happening.”

If you want five linear octaves and not three linear octaves you need more “current flow” into the Electrodeum which is accomplished by using Higher Q oscillator circuits.

This is why I use heavy duty ferrite chokes for the pitch oscillator coils as they have larger gauge wire and lower resistance for a Higher Q.

I have often wondered if seven linear octaves are possible. There are no half octaves in a linear pitch field out of linearity. It either resonates with 3 or 5 octaves or it does not.

Using the Null tuning knob the octaves can be of any width and still be linear to fit the size of your hand.

The octaves expand out further or better when you have the least resistance through the environment or best earth-ground. In analog theremin’s earth-ground also has purpose in generating a clean RF wave shape which transposes into the audio wave shape.

In other words with a no earth-ground connection the Electrodeum octaves are still linear just compressed inward towards this pitch electrode and the sound will be more distorted.

Test: Scope measure the p-p voltage of the Electrodeum with it resonating and not resonating. Then measure the p-p without the 3.3 mh choke to direct earth-ground.