Hello Dominique,
Because you bring up one of the most fascinating threads from the past I must respond. I am just a garage hacker with a little amateur radio background. WD6EDZ - Fred below (RIP) does a nice intellectual reasoning of how theremin sound color comes about, using a transformer. I also figured this out a few years earlier, this approach is on my PCB dated 2013, the only commercial board I ever had made. There are many reasons why a first theremin design will not work properly but she is a good teacher and will discipline you as you go along. She will humble most engineers, no.... all of them.
I could give you some simple tips to aid in your journey but I do not want to spoil your fun... ok one, a 1N914 diode works fine for me mixing RF and detecting the audio signal, used with vacuum tube or transistor oscillators. I always found cooperative RF blending before the diode to be the real trick. Shaping the sound starts with the pitch oscillator right on to and thru the speakers.
In this older thread we are messaging I am avatar RS Theremin, today the theremin has seasoned and aged me, so now oldtemecula.
Good luck on your adventure.
Christopher
FredM said: Unlike you, I am not absolutely convinced that tubes add anything which cant be created more simply using modern components.. I have no interest in cumbersome electronics and HV supplies etc unless these are absolutely required for "good" sound.
My thinking is in the lines that IF tubes are "needed" then they will be needed probably for the mixer and (perhaps) output stages only - the mixer being by far the most likely important role. I cannot see any sonic benefit in replacing oscillators with tube ones, but there might be a thermal / stability benefit.
I also think (and Thierry is the person who got me to look more closely at this) it likely that to get the "classic" mixer sound, the mixer needs to drive a transformer, and the characteristics of this transformer (and related resonant components) will be critical in 'coloring' the tone.