How look this signals before and after the volume control, measured with the oscilloscope?
It definitely gets more squared at the lower tones but honestly I don't think it's the VCA because using the spectroid app I was able to look at the frequencies coming out of my speaker and the entire 0-500Hz range is missing. When the waveform pitch is at the lowest frequencies eg 0-200Hz, the speakers output in the 2kHz range more than in the lower range - seriously!
This is a video of what the VCA does, basically exactly what I expect. https://youtu.be/hXPcDzrCX2s
There is a slight problem in that the 0-300Hz signals have a more squared shape, one would then conclude that the following is happening:
1. VCA introduces distortion on lower frequencies
2. Frequency spectrum of lower frequencies, due to distortion, have introduced high frequencies components
Therefore VCA induced clipping, case closed.
HOWEVER
Linear signals and systems tells us a square wave is made of series of higher frequency components with falling amplitudes, the characteristic frequency is always the highest.The high frequency overtones should have a lower magnitude than the low frequency characteristic frequency so VCA distortion doesn't explain to me why high frequency components are heard over the low frequency components.
If you remove the VCA altogether and throw the signal into the speaker you get similar but less buzzy sound behaviour.
My own conclusion are:
1. The VCA is introducing coupling because it gets its power rails from the voltage source before regulation. Why would that cause coupling? I don't know but it explains the low frequency shape change - but nothing else.
2. The bass dropout is entirely due to the speakers used. Bass dropout is also causing the theremin as a whole to sound whiny.
If the circuit can be adjusted to allow direct speaker drive with some trash like this then great: https://www.jaycar.com.au/76mm-all-purpose-replacement-speaker/p/AS3006
If it can't then I'll have to return to the speaker issue when I have better audio equipment.