One thing that kinda stands out to me is the "parallel" "Maj_i2, Maj_i1, Maj", "min_i2, min_i1, min" lines. Those lines somehow are a beautiful thing.

Zwaarddijk wrote:One thing that kinda stands out to me is the "parallel" "Maj_i2, Maj_i1, Maj", "min_i2, min_i1, min" lines. Those lines somehow are a beautiful thing.

Yes, well if nothing else, I'm learning more about chord type relationships and things like what is similar and what is different in chord inversions.

I've been thinking about this some more and especially about something someone said earlier in the thread that both maj and min chords contain a min3rd interval. In the min chord it's between the root and third but in the major chord it's between the M3 and P5. Yet we still hear the minor as very different from major. That makes me think the m3 interval from the M3 to P5 must not be as important. With this in mind I weighted the m3 intervals based on if they were from a root harmonic, a M3 harmonic or P5 harmonic.

Also, there's something very different if these "dissonant" intervals are going up in frequency or down in frequency. That is, a landing on a m3rd is somehow different than landing on a M6. So I decided to only look up in frequency for m2, M2, and m3 dissonance.

Again, I took this out to 7 harmonics. (and I color coded the chord families) and got:



Which to my eyes suggests a lot of structure can be found in the chords just by looking at this very basic information.

And for a very different take on the op's question I recommend this guy, who seems to know a thing or two about what he's talking about. In any case, there are worse ways to spend an hour.