You can look at a root as the 0th overtone, but in minor do you know some "deductive" reason for the -2nd overtone to be a root of the minor chord?
An illustrating explaining what I'm talking about:
You can look at a root as the 0th overtone, but in minor do you know some "deductive" reason for the -2nd overtone to be a root of the minor chord?
An illustrating explaining what I'm talking about:
It sounds like you're homing in on the idea of harmonic dualism, a concept heavily discussed by nineteenth-century German music theorists.
In short, the notion of harmonic dualism states that, if major triads are built upwards from the overtones of a given root/fundamental, the minor triad is built downwards by finding different roots/fundamentals that generate that starting tone.
Thus, starting on C, the opening partials of the C harmonic series create C, E, and G. But moving downwards from that same C, the first fundamentals to create that C end up being F, A♭, and C.
I've briefly discussed dualism further in my answer to Is the IV chord a perfect fifth in disguise?
Harmonic dualism is experiencing something of a comeback these days in its updated guise of negative harmony. If you're interested, check out the negative-harmony tag.
The minor scale descending IS very close to a major scale:
major asc. = C (+2) D (+2) E (+1) F (+2) G (+2) A (+2) B (+1) C min desc. = C (-2) B♭(-2) A♭(-1) G (-2) F (-2) E♭ (-1) D (-2) C
So the only difference is the interpolation of the last two steps. If you replace the D in the min descending with D♭, then you have A♭ Major or f minor.
It's actually a pretty interesting observation, but to answer your question in a simpler way-- the 2nd overtone of a series is the dominant, so the 2nd "subtone" would be that inverted: the subdominant.