I was recently introduced to a "trick" sometimes known as the "minor arpeggio secret". It can be summarized as following:
If we can maintain the same tension while plucking twice, 3 times, 4 times that length, etc. the undertone series will unfold downwards, containing the minor triad. Similarly, on a wind instrument, if the holes are equally spaced, each successive hole covered will produce the next note in the undertone series. (Source)
In other words, if you keep the distance between your fingers constant and shift your hand, you are able to play a pure minor triad on a string regardless of where you start (since they are found following eachother in the overtone and undertone series). It is demonstrated in this video by Chris West.
While I somehow understand this phenomenon, I have some troubles to intuitively grasp which undertone series I am playing when using this trick, for example starting with a minor third A-C (followed by C-E and E-A).
In other words, how can I formalize the relation between the minor arpeggio secret and the undertone/overtone series?