Ideas similar to this do turn up in Christopher Doll's Hearing Harmony, particularly when it comes to VI chords being kinda subdominant.Z1202 wrote: ↑Sun Oct 06, 2019 1:07 pm 1. The strongest and the primary factor is the presence of the 6th or the 7ths degree of the scale in the triad
- any triad containing the 6th degree has subdominant function (II, IV, VI).
- any triad containing the leading tone 7th degree has dominant function (III, V, VII), where the III of the major scale is rather weak as the dominant and rather falls into the third group below.
- any triad containing the natural (Aeolian) 7th degree belongs to the third functional group, the name of which I don't know, if it exists.
- the raised 6th of the melodic minor could be considered as giving rise to a special flavor of subdominant group (with a questionable member of the diminished root position chord on the 6th degree, thus instead one could rather simply apply the second rule below to the remaining II and IV chords with raised 6th degree of the scale)
- note that thereby the tonic triad is the only one not belonging to one of the above mentioned groups.
I think one problem here is the overloading of the word "function", which tends to imply a system that's designed for common-practice tonal music. I don't know the context of your reading or approach to music but I suspect the rules you have been building for yourself are a long way outside the boundaries of common-practice tonal music. Doll's book is about harmony in rock, which often doesn't use the classical cadence structure (and functions) at all.
The big problem with trying to create rules that go outside common-practice tonal is that the terms get muddy real fast. And inventing new terms for "function", "dominant" and "subdominant" isn't very practical. Doll has a go but doesn't go the whole hog, with the result that you wind up wondering what each term really means.
The core problem is that music appreciation and composition is the result of enculturation. There aren't really any rules other than rules of thumb that develop from multiple uses of the same motifs across lots of music that interact with how the brain perceives the harmonic series in individual notes. So, trying to develop a one-size-fits-all set of core rules is, frankly, doomed to failure IMO. All you can really do is say "in this style of music, this tends to happen and some styles insist on certain motifs, such as leading notes for cadences to make it seem cohesive".
You might find work in the psychology of music by people like David Huron more instructive.