Has there been any discussion regarding the relationship between the harmonic series and tonal tendencies like this?
Yes. For example, this is clearly mentioned in “Great Songwriting Techniques,” which is one of the references on this site:
The stability or instability of each tone is measured by each of the tones’ place in the harmonic series. Those closest to the fundamental are the most stable.
(Perricone, Jack. Great Songwriting Techniques (p.87). Oxford University Press. Kindle Edition.)
The overtone series also serves as the basis for the stability of major chords, so it can be said that the stability of each tone can also be considered as either the development or the source of that theory.
