Audio feedback affects Theremin tone?

I can speak to part of that. I had dabbled with cheap diodes for use as varactors even before I came across Fred's discussion of it, but this was for improving pitch linearity, and seeing his writings reinforced the idea that it might work.  Back when I was looking at ways to add a little linearity shaping to the basic Etherwave I was doing some experiments with back-biased rectifier diodes (what I had on hand that had large reverse capacitance) in series with a various values of fixed caps to tame the overall capacitance change.  This was purely a concept test to see if I could easily get the diode in the oscillator circuit and biased without too much trouble and to see how the oscillator would behave.

It was actually quite interesting to see in action.  I connected an arbitrary waveform generator to the "varactor" diode and was able to create all kinds of warbling effects, noise, and even vibrato.  The relationship between the diode voltage and the capacitance change and ultimately the frequency change was terrible and would have required a contoured diode voltage, but that was worth doing if it looked promising.  And I never did look into better diodes - I still have some abrupt and hyperabrupt varactors around here somewhere from my dielectric-resonator VCO days, but I'm pretty sure that the capacitance is way too low to be of value.  At the time I think I was conditioning the pitch-proportional output voltage from an EW Plus CV board to feed the varactor bias to pull or push the middle and stretch the compressed high end.  This was many years ago, and of course this all got dropped like a hot potato when Dewster's D-Lev came along with a better way to do it.

But what you are talking about for timbre alteration certainly seems possible, at least as a pretty easy experiment. It's hard to predict favorable outcomes, but I'm wishing I had thought of this to try at the time.  It might not take much, even with a terribly non-linear rectifier diode for a varactor, to get some surprisingly good or terrible timbre changes. 

Thank you, pitts8rh, it is very remarkable and interesting for me. I dropped the idea of using varicaps in the pitch oscillator because they are too temperature dependent. But for volume or time dependent filter effects that influence the timbre I will use it later. Now I want to do some "basic experiments" concerning the influence of on-board speaker.

A second question: is there an influence of mechanical resonances within the box due to the external speaker behind the player? The circuitries of old theremins looks like rats nests with a lot of swinging potential? And the third thing is a back-closed versus a back-opened speaker-box, where I suppose different formant effects.   

In a general sense, audio phase feedback is how FM synthesis generates various timbres.  Even the simplest of feedback can give odd or all harmonics, and varying the strength of the feedback varies the timbre level (indeed this is how the D-Lev software audio oscillators work - and a huge side benefit is alias suppression).  So clearly there is a direct mechanism that could be at work (I'm stating the obvious here).

Fred said he noticed a timbre enhancement at low frequencies rather than higher, which he felt ran counter to his hand / antenna capacitance reasoning, but I'd say it is actually consistent with happening in the far field because being nearer to the null point dramatically magnifies the difference frequency.

That said, pushing anything through an actual speaker - even an extremely good one - will introduce all sorts of extra content due to the relatively large distortion levels, frequency dips and peaks from the cabinet and room, and gobs of (continuous, really) room delays.  So it's usually a safe bet to chalk any "enhancements" to the tone to that before anything else.  Open back baffles plus intentionally introduced speaker distortion raise this to even higher levels of complexity.

I wonder if a good guitar & amp simulator, the kind that give realistic feedback type effects when there is none, might be a point of reference in any experiments?

I've noticed that movie audio has gotten quite good at matching the natural ambience of any overdubbed lines, which I suspect is due to the general availability of convolutional reverb, where the impulse response of the room can be taken and used directly on a dry signal.

"A second question: is there an influence of mechanical resonances within the box due to the external speaker behind the player? The circuitries of old theremins looks like rats nests with a lot of swinging potential?"

If you are talking about the theremin case being subject to microphonics through tube vibrations or whatever else (coils, wiring) is acoustically sensitive I suppose it's plausible - I never gave it much thought.  But knowing that the enclosure is probably quite sound-deadening to higher frequencies by virtue of its mass, and on top of that the old speakers might have been pretty lacking in bass (or volume, right behind the player's head) I can't imagine that this would have too much effect.  If I ever get a chance to play the RCA at the Pavek Museum in Minneapolis again I'll give the cabinet a whack when no one's looking and report back .

"And the third thing is a back-closed versus a back-opened speaker-box, where I suppose different formant effects."

By today's standards those open-back speakers must be a big old mess.  Having the bass attenuation of an open speaker isn't entirely bad fit for a theremin's output which can be bass heavy, at least modern ones.  But I would hate to have that as a monitoring speaker with its peaks and valleys and where boosted bass is actually better for balanced pitch perception over the full range. I've never had a chance to see or use a real RCA speaker, so I really don't know what I'm talking about.

Really good discussion! I wonder if the fm synthesis is here at work allone. The frequency  - and the amplitude -  of audio-output modulate mechanically the variable pitch oscillator (hand capacitance). But is there a significant effect on timbre?

Have done first ultimative tests now. Loudspeaker of a 40W guitar amplifier should give enough power...