I understand that the mathematical frequency ratios between certain intervals will correlate with the overtones that are present when a note sounds in a fundamental frequency. Certain predictable overtones will occur naturally at frequencies that are integer multiples of the fundamental note.
Sound waves produced by musical instruments (including the voice) translate into corresponding vibrations in the basilar membrane and other mechanical components of the inner ear. These vibrations produce their own overtones that work the same way as a plucked string on a musical instrument - producing certain predictable overtones in our auditory system that are integer multiples of the fundamental.
A perfect fifth in just or pure tuning based on the harmonic overtone series would obviously be more naturally consonant because the vibrations set off in the inner ear would flow together and not beat against one another. So theoretically, tuning to the perfect integer multipliers which match the harmonic overtone series would yield a more pleasing harmonious blending of notes than say equal temperament tuning of modern instruments.
I know that equal temperament tuning is a compromise to allow fixed tuning instruments such as a piano or guitar (with intervals determined by fret spacing - bending of notes notwithstanding) to be played in any key without being terribly out of tune in any one key (only slightly out of tune in every key). But tempering the tuning literally means stretching or shrinking the intervals such that they are no longer truly consonant and some dissonance is interjected by necessity.
I will acknowledge that it is likely that as we grow up listening to "out of tune" equal temperament tuned music - we develop a tolerance for and acceptance of it (some may argue even a preference for it but that is highly debatable). However, it seems to me that perfect consonance in keeping with the pure harmonic overtones, would naturally and instinctively be more pleasing to our ears without the need for (and in spite of) conditioning.
Given that the human voice is capable of microtonal adjustments to an infinite degree and not limited by the fixed tuning imparted upon an instrument such as a piano - I am wondering if singers who harmonize with the lead vocalist subconsciously adapt and instead of singing a equal tempered third or fifth actually sing something closer to a justly intoned harmonically natural interval.
If this does occur, it might help explain why some singers sound so incredible harmonizing together. I have been privileged to hear some performances where the vocal harmonies actually gave me shivers up and down my spine and seemed to touch my soul with their sensual richness.
Have there been any studies (or is there compelling evidence) which attempt to ascertain if trained and capable singers who sing harmony - instinctively gravitate towards pure intonation verses singing the notes they have learned to associate with equal temperament tuned instruments? In other words if they are singing a fifth above, would the instinctive control center of their brain override their musical training and adaptation and lead them towards singing a perfect natural fifth or would they sing something closer to a equal tempered fifth that a piano would play?
If some do and some do not, have any studies attempted to determine if there is a clear listener preference for pure harmonies vs. harmonies based on adapted and learned tempered tuning?
My personal hypothesis is that pure and natural harmonies that approximate the frequencies found in the harmonic overtone series would provide a more enjoyable listening experience unless said harmonies clashed directly with equal tempered tuned accompanying instruments. In many cases the vocals (including harmony) are not sung in unison with chords or corresponding melody notes. But it still may work better in a cappella singing (such as a trio or quartet).
But I will defer to the more educated music theorist and trained practitioners in the SE community for a more accurate assessment.