I'm not searching for a right waveform. I'm searching for a lot of "right" waveforms and a few wrong ones too. If you understand the sound, you can create a theremin that sounds like any theremin you want (that doesn't mean you will sound like any thereminist you want). Anyone who wants to create a digital theremin, they better well understand the sound unless they let you enter your own waveforms (then you need to know). The Open.Theremin project is very interesting in that regard. A theremin with one sound does not interest me as much as a theremin with 100 sounds. That way I only have to ever by one more theremin - if it works well.
The sound of the theremin interests me greatly. And I think it somewhat a fallacy to say almost any sound is acceptable because a good player will make it musical. A good player will make any instrument musical. I totally agree great theremin players have a style and often you can tell immediately who is playing.
But its interesting to look at the sound of an instrument - especially if you want to try and recreate it.
Let's take the Open.Theremin case. Here's the Standard wavetable and a wavetable they say is based after the Keppinger theremin. Well someone took the time to try and figure out what the basic wave shapes should be here - because with the digital theremin you absolutely must know about this subject unless you just want to experiment - and that's fine too.
If my goal is to create acceptable theremin simulations to create mockups of pieces, I need to know what's going on here.