The idea of an RCA "sound" direct from the instrument is like talking about taking the sound direct from the larynx and feeding this to an amplifier.. It wouldn't sound sound like a voice.
Back in the '30's there was no such thing as "line out" - One didnt have hi-fi separates, or synthesisers, or any of the stuff we (since the '60s) have taken for granted - Every electronic thing one wanted to hear had to actually produce the sound as sound.. It had to have its own amplifier and loudspeaker - it was a complete instrument - not a "module" one connected to some standard amplifier and speaker with standard (flat) frequency response.
And IMO it is this difference which had underpinned our misunderstanding when talking about 'capturing' or 'replicating' old instruments.
When Lev designed / prototyped / built his instruments, these were built as a composite - the waveform being fed into the amplifier / speaker was tailored (as much as possible) to interface with the amplifier / speaker.. ) These did not have a even remotely flat frequency response - severely high harmonic levels on the signal would be cut by the amplifier and speakers roll-off... And if the amplifier was changed or loudspeaker changed, the instruments sound would change. The whole instrument was crafted - not just the 'front-end - the amplifier was crafted at the same time as the front-end.. This can be clearly seen on Clara's theremin, where the tone controls are actually operating on the power amplifier feedback.
These days we can take any modern instrument and plug it into any modern amplifier / speaker, and it will sound the same - but take an RCA signal and feed it into a modern amplifier / loudspeaker (which you cannot actually do because the potential on the RCA output is lethal) and it would sound harsh and horrible.
Then there is also the recording medium on which original recordings (that define our understanding of what theremins are "supposed" to sound like) to take into account - What we hear is not what the audience listening to the performance heard - the sound was picked up with microphones that themselves colored the sound, and recorded on early recorders which again colored the sound.
The result of combined colorations (amplifier, loudspeaker, physical resonances, microphone coloration, tape coloration) and non linearities means that what we hear on old recordings will be hugely different to the tone the designer crafted. The ONLY people who can get close to the sound the designer intended are those with access to complete original instruments - THESE people could capture with modern microphones, the most reasonably close samples.
But looking at the electrical waveforms in an RCA isn't going to help (other than for showing technical data on, for example, the change in waveform as pitch changes) . The closest one can come to the "original" recorded sound of the RCA is probably by recording a harsh theremin played through a bad amplifier / loudspeaker with a poor quality microphone into a recorder with low-fi qualities (say compact cassette) and add some noise and mains hum.
Take an EW signal with brightness cranked up, feed this into some vintage plug-ins on your DAW, tailor the frequency response, and you can get quite close to something like the RCA sound heard on OLD recordings.. The thing which makes it unconvincing isnt, IMO, the sound, as much as the fact that performers of that time could play! Particularly IMO with theremins, where the waveform actually changes proportional to pitch rate-of-change, vibrato and skillful playing actually changes the harmonic qualities of the sound. As I have said many times - there is an essential component of the theremin that cannot be replicated - in fact, the player becomes an actual physical component of the theremin, and in real, practical terms, one cannot have a Claramin unless on has a Clara, a LydiaVox without a Lydia, or a PringlePro without a Pringle!
To get close to what those who actually listened to a live rendition of an original instrument heard, we need to record an original complete instrument using modern recording technology, and one really hears these instruments in their glory only when such a setup os played by a master.
Fred.