There is no "true theremin sound".
All of the theremins that Lev Termen built in the 1920's & 30's had tone controls on them, making available to the player a variety of different sounds which could be changed depending on the piece being played. In his original theremin demonstration concerts and recitals, Lev used all sorts of different tones and FX with his instruments. The custom instrument Lev made for Clara Rockmore had several possible tone settings on it (I think it was about seven???) but Clara only used one of them.
The RCA had no tone controls because adding them to the design would have made the instrument more expensive and RCA wanted to keep costs down. If the theremin had been the marketing success that RCA had hoped it would be in 1930, modifications would have been made to successive generations of instruments. There were already plans to integrate the speaker into the cabinet (as it is in Samuel Hoffman's RCA) and eventually tone controls would have been added. Unfortunately, as we all know, none of this ever came to pass.
The sound of Clara's theremin has, for many people, become the "gold standard" for tone. Ironically, that "sound" has a great deal to do with the way Clara played the instrument. In the hands of other players, it no longer has the distinctive tone that we associate with it when Clara played it herself. In fact, the sound of Clara's theremin today is so different that people tend to think that something has happened to it that changed its tone. The real "flavor" of the instrument was never in the theremin, it was in Clara.
This is a common phenomenon with the musical instruments of great virtuosos. Heifetz dies and leaves his violin to someone who can never make it sound the way it did when Jascha played it. Ditto for Andres Segovia's guitar and Pablo Casals' cello. With acoustic instruments the explanation for this seems obvious because the player is actually creating the sound and then shaping it. With the theremin, the player is only shaping but that is a far, FAR more important process than most people realize.
These days, the big question seems to be, what makes a particular sound a "theremin sound"? Does it have to be produced through the heterodyne process in order to qualify? If so, then the Moog SERIES 91 instruments are not theremins. They are VCO's. For many people, if it sounds like a theremin it IS a theremin. There are many recordings that claim to be theremins, but are actually MIDI keyboard samplers and synthesizers playing vaguely theremin-like spooky SciFi FX.
Maybe the "true theremin sound" is the theremin sound you like best.
