basic experiments

I would like to take up the comments on my sound examples and Dominik's own experience of expressive timbres in the range of low and mid frequencies compared to higher audio frequencies.

Based on the perception of loudness, the perceived strength rises approximately logarithmically between 20 Hz and 3 kHz and drops again between 3 kHz and the hearing limit.

The ratio of the amplitudes of the overtones adapts to this curve. A timbre that sounds good in the low range can be unpleasant due to overestimated dissonant overtones in a higher range.

The usually used low pass in the theremin provides some help, but is not the best solution, because even the good bass sounds have overtones up to the highest ranges and sound duller when filtered. 

I wonder what the effect would be of a filter that compensates for the volume curve? Would a created rich double-bass sound, shifted to higher pitches, also sound good?

What I mean is, imagine you fix your volume hand and move your pitch hand from low to high frequencies and the loudness you hear is always the same. The filter must then approx. follow the "audibility curve". Then, I think, a nice deep sound would also sound nice in a higher range. Because the overtones you perseives remain in the same relations.

Yes. Am sure. The "Equal Laudness Contour" first discovered by Fletcher and Munson is an important fact to consider in theremin and synthesizer sound! Usually that is done for proper mastering. Here for proper overtone relations.

Will try an active filter like this operating with overtone rich samples.

JPascal, I looked into equal loudness curves a couple of times:

http://www.thereminworld.com/forums/T/28554?post=214689#214689
http://www.thereminworld.com/forums/T/28554?post=215184#215184

It turned out to be less fruitful than I expected.  Having second order bass and treble controls does much the same thing, and is more adjustable.

Thanks, Eric. All thoughts have usually already been considered by someone. You just have to find it.

Do you mean an external equalizer like GE 7 coud do that job approximately well? Filter curve is than fix and to be adjusted only for a certain loudness. Here is the schematic diagram:
https://www.hobby-hour.com/electronics/s/ge7-equalizer.php

"Do you mean an external equalizer like GE 7 coud do that job approximately well?"  - JPascal

I don't know.  You need a master "blend" type control to adjust them all at once, and you can run into phase issues when crossfading filters, giving you responses you don't expect (though this probably happens more in the digital domain, where things tend to get crazy near Nyquist).

Low notes can have lots of harmonics, and if they sound good low then they will probably sound good high due to the reduced harmonic count.  This is how many analog Theremins do a high female voice well when played above most of the natural formant frequencies, the telltales are largely gone.  So the potential problem you are describing might actually be the opposite, where high notes are fine and low notes sound weird.  Also, the accuracy of the Fletcher-Munson curve is hazy because their methods are somewhat in dispute - I found it to be mostly a dead end for research, but I'm not trying to discourage you.

Dewster:Low notes can have lots of harmonics, and if they sound good low then they will probably sound good high due to the reduced harmonic count. 
Thank you for the respond. That's what I meant, the higher harmonics of a good sounding low timbre become dominant and unpleasant in the ear when you shift everything to a higher pitch, not the very high pitch.

I tried to reconstruct the measured time signal of the old RCA published here. If putting this to an amplifier and big speaker, the result is not really convincing. May be, the old speaker and a.f. amplifiing are significant involved for the good old sound.

Second path: listening to the old Rockmore records, if loudness is low the imagination of a voice is much more present.

Step by step. Time is scarce. The goal is a physiological loudness correction within the volume control unit. I am sure that an instrument without internal formants like the theremin will be improved this way. This is essential for overtone rich timbres and a wide spread of used pitch scales. First non perfect simulations are in work.  

Now I was able to optimize something. The volume control with integrated equal loudness contour now supports two things:

The harmonics change with the volume. Second, the amplitudes of the harmonics change from bass to higher audio frequencies at lower loudness levels. Here is the LTspice simulation. Recordings will follow next.

There must have been a blockage in my brain. If at low volume the timbre is very fine and as the volume increases it is not so good, then the volume correction must be in the opposite direction to the curves of equal loudness.

But now so many difficulties have been overcome that I can build good sounding theremins from scratch. Deep analysis of the problems (and patience) have always been the key to overcoming themselves.

My new schematics are basically different to all before and no rocket science. Less is more, knowing what every component (active or passive) really should to do. And new functions for theremin as wave shaping, volume acceleration, sliding formants, overtone behavior, very low temperature drift, hum avoiding.

Now can start the more relaxed creative part for me...