Friedrich, the issue is whether one can consciously perceive (i.e. actually hear) difference tones, regardless of what Levitin or anyone else might say about ear/brain function. I cannot hear them under normal listening conditions and nobody I have ever met can either - even when I take them into a church or my studio and experiment on them! I have only come across one person who claims he can hear them under normal listening conditions, and that was only on the basis of an email so I was not able to confirm it personally. I do not know him otherwise.
Can you hear them? If so, what does music sound like to you? It must sound very different to how I perceive it, because you will hear (say) tenor C when you play middle C and the G above it simultaneously.
If sounded as two notes at a time, I will probably hear them as such. The Sesquialtera phenomenon – play one note on a North-German Sesquialtera, consisting of a slightly sharp twelfth and a flat seventeenth, and you will hear those notes apart, as I do. Start playing lines and runs throughout the compass, and the separate notes will vanish, giving way to a glassy and nasal fundamental. According to Levitin, that is a product of our brain processing and ordering environmental sounds. Jehan Alain knew all that instinctively and made use of it in his compositions, e. g. towards the end of the Second Fantasy, where at least my brain struggles to shake off the illusion of hearing a harmonic that belongs to another fundamental, and to perceive the diminuendo line at the actual pitch.
As a violinist, I used to make use of difference tones when practicing double-stoppings. You can train yourself to perceive them quite quickly. If a major third “drones”, it will work in solo playing, but rarely in ensemble. When I practiced scales in thirds, I tried to get rid of the drone, sharpening the major thirds and narrowing the minor ones in order to arrive at something approaching equal temperament; when I practiced fourths, I sought the drone, because without it the fourth would sound foul. (I gave up that kind of practice, useful as it proved, because of lack of time, and after all, I did not make it my profession.)
I find the subject as fascinating as you do, and think it is one of special importance to the organ; in fact, it singles out the organ as the one instrument that extensively makes use of the effects of difference tones as perceived by the human brain, in order to give the music a special colour. In my ears, a Grand Plein Jeu with sub-harmonics in the order of 5 1/3’ and even 10 2/3’ sounds fascinating, even when no actual fundamental rank is present.
At Lausanne cathedral, Fisk included blind features with the Great mixtures: The sub-unison ranks only come on if the respective fundamental rank is drawn (16’ or 32’ open). That’s smart, but I think it’s slightly beside the point in certain styles.
I even am tempted to say that the fundamental is grossly overestimated in organ sound.