I started my investigation by watching some videos on Youtube. This is how I learned much of what I know about music theory, and I find it can make information quickly and easily understood.
Here is one which does a good job explaining the idea I am investigating. The creator explains how to find the first few overtones of a note on a keyboard, and how to use them to play particularly consonant major chords.
A commenter said that notes of a minor chord share a common overtone. I investigated on my own keyboard and found this is true: two octaves and a perfect fifth above the root is an overtone shared by all three notes. I noticed that by dropping the chord’s third down an octave, we can make this overlap happen an octave lower, and it creates a very nice sound. In an example of how confusingly music theory uses and reuses numbers as names, what I made there is also called a “drop 2 chord,” because it drops the third, which is the second highest note. (It’s also the second note up. It’s called the “third” because it’s the third note of a major scale starting at the root 🙄.)
Next I looked for articles on Google Scholar. I found this one, which is fairly compelling and explains the history of main scientific hypotheses for our experience of consonance and dissonance. I also started reading this one, but didn’t get very far through it before I was distracted by an idea from it. In audacity, I messed around with some sounds to see what pitch I perceived when a sound wave was played containing a periodic gap.
the audio clips played are as follows:
440 sine: a sine wave at 440 Hz
gapped sine: the same sine wave but with a gap of half a period inserted every four cycles
98 string: a combination five sine waves in decreasing intensity and increasing pitch, meant to roughly resembling the overtones of a string with fundamental frequency 98 Hz. They are 98, 196, 294, 392, and 490 Hz. I made this because I noticed that pattern in the spectrum of the gapped sine wave.
saw 440: a sawtooth wave at 440 Hz
gapped saw: same sawtooth wave, gapped the same way as earlier
saw 391: a sawtooth wave at 391 Hz, which is theoretical frequency of the “long pattern” that comprises the four cycles and a gap. Notice it is also very close to the third harmonic above 98 Hz. If my method of introducing a gap in the sound had been more exact, I expect those numbers would have been identical.
Here is another video I skimmed. I didn’t really like the presentation and knew most of the content already. However, for someone who is new to music theory or its associated math, it could be a good crash course.
Finally, I found a this music stack exchange thread which indeed places the minor chord within a harmonic series. I haven’t quite understood where that fits on a keyboard yet but I expect to at some point.