How does a Theremin “antenna” work?

this is the best explanation I've found for people who don't understand most of the technical stuff:https://youtu.be/KDG15-iTJLw

Thx for the note.  my intention was to produce an explanation that would be understood by most.  for those attempting to design their own theremin, i was hoping that i could create some knowledge that would help in getting things designed correctly and working properly.

"I agree that this paper has inacuracies in the equations.  it appears they hid some 'Cooks Variable Constants' in their work so that the numbers worked out.  However, they did attempt to create an equation to describe the relationships."  - jgdpeng

They should have been more up-front about how horrible their mutual C equation is.  It's all plausibility and hand waving, and it's total crap for true linearity studies (i.e. if you're looking for a way to mathematically linearize the field).

"The objective of the paper was to prove that the relationship between hand proximity and musical notation is approximately linear and sharping my pencil and correcting errors in the document will only make the result a little more linear, which is only a moot point."

The simple algebraic C between two plates equation is actually pretty close, particularly in the far field.  I think I would use that and work it back through the LC resonance equation.  The linearity differences between a plate and a rod antenna aren't that great, and the hand behaves a lot like a plate.

Thank you for sharing your paper about pitch linearity. There is a lot of work you have done well. But the equations from the 1998 paper "Physics of the Theremin" are indeed doubtfully. 

A proper and robust formula for rod antennas please find in my thread "basic experiments". Your result, that beat frequency is nearly linear to the hand capacitance, is a basic fact for all theremins and this is based on the LC oscillator formula itself. The fact, that theremins with a high inductance antenna coil use the lowest oscillator frequency range, I fully agree with. See also my simulations and surrounding math. Your conclusio, that linearity is not given for lowest and highest beat frequencies, is right for the highest beat frequencies. But using a proper offset for nulling you can linearize into the the lower beat frequencies quite well. This can be also find in the thread mentioned. 

I would be very pleased for oscillograms of the pitch control of your valve based theremin. At C18, and "out" with respect to the swiches "old school" and diodes. 

When will pitch linearity be available for guitars, violins, violas, cellos and basses?
Those frets just keep getting closer together the higher the pitch.
And organ pipes! Why do you need a 64 foot tube to make a bass note?
Why cannot the octaves on organ pipes be a reasonable one foot per octave???
That would save space and lead! Unless they are making them from wood.

Yes Rupert, the logarithm to the base of the mathematical constant e.  The physics of the universe seems to dislike linearity.  All your examples support this fact.  Fortunately for the theremin, there is an opposing ln(x) which counteracts the e^x.  this creates a situation where linearity is approximated.  

BTW: It's basically wrong to use the term linearity here. What we feel as linear (equal tone spacing) is basically an exponential thing since f = a * 2 ^ (b * x)

BTW: It's basically wrong to use the term linearity here. What we feel as linear (equal tone spacing) is basically an exponential thing since f = a * 2 ^ (b * x)

Thx. And as I am interested in understanding the physics,  can u define ‘a , b, and x’.  I assume ‘x is distance from pitch antenna?

BTW: It's basically wrong to use the term linearity here. What we feel as linear (equal tone spacing) is basically an exponential thing since f = a * 2 ^ (b * x)

I've thought about your post (i was on a long vacation and just got back) and now that i got a moment, i would like to respond.  yes, the relationship of distance of hand from antenna and frequency is exponential.  what confused me was using '2' as the base and not 2.78(the base for natural logarithms).  In any case, the relationship is exponential.  however, the relationship between frequency and the musical scale is exponential as well, but with an opposite sign.  when you combine these two equations to determine the relationship of distance of hand from antenna and the musical scale, one gets a linear equation in the form of n=mx+b.

I'm not disagreeing that the relationship between distance of hand to antenna to frequency is exponential, i am saying that the musician experiences a somewhat linear (there are physical properties in the instrument design and construction that precludes a perfect linear relationship) relationship between distance of hand from antenna to musical notes.  the musician is not concerned that the frequency has increased exponentially.  he is trying to, for example, create an Augmented Fifth from middle C to G#, not thinking of jumping from 261.63Hz to 415.30Hz.