Glad to hear my explanations are appreciated! So let me see if I can find time and inspiration to continue on the topic of mutation stops.
First, the Resultant Bass 32', or whatever the stop is named. As you all know, sound is air waves. Before we go to this deep bass sound, let's have a look at more common pitches. Perhaps you know that concert pitch is often defined as A = 440 Hz. What does that mean? Well, if we play an A on an instrument that is tuned to concert pitch, the instrument (strings or pipes or whatever) will make the air oscillate 440x per seconds. To write it more concise, the Hertz unit has been invented, so we can write 440 Hz. On top of that, you will find oscillations of the harmonics, so oscillations of 880 Hz and 1320 Hz and so on.
Now, a bass tone has fewer oscillations per second, for example 20 Hz for one of the lowest pipes of a 32' stop. What about the harmonics of this tone? The second harmonic be 40 Hz and the third 60 Hz.
Now we are going to remove this tone. Instead, we will generate two different musical tones. One of them, a 16', sounds in this case at 40 Hz, and the other, a 10 2/3', at 60 Hz. What will happen?
An oscillation can be represented as a regular pattern of peaks and dips. Perhaps from high school you remember the waveform patterns of the sinus and cosinus graphs. We have to add up two of these graphs, one with 40 oscillations and one with 60 oscillations per second. If the peaks of both graphs are aligned, we get an extra high peak. If the dips are aligned, it sums up to an extra low dip. If a peak of one graph aligns to the dip of the other, they cancel out.
Let's suppose the peaks are aligned at the beginning of the graph. An extra heigh peak results. How much do we have to move on before the peaks are aligned again? Try to visualize it. Here is the answer: 1/20 part of a second. After 1/20 part of a second, the 40 Hz tone has completed 2 oscillations, and the 60 Hz tone has completed 3 oscillations. The peaks are aligned again. So every 1/20 second we have an extra heigh peak.
There it is, the resultant: every 1/20 second, so at 20 Hz. Even though we removed the original 20 Hz tone, we get it back (in a slightly different form) by addition of a 40 Hz and a 60 Hz tone, in the form of recurring extra heigh peaks in the oscillations of the air.
See
https://de.wikipedia.org/wiki/Residualton for a graph (using different numbers).
By the way, I do not reject the psychoacoustic explanation given by OrganoPleno. At this moment, to me it is an open question where physics ends and where psychology begins in the realm of music, and what the role is of the physiology of the ear.