>>12049575The 12edo major chord approximates a 4:5:6 frequency ratio, while a 12edo minor chord approximates a 1/6:1/5:1/4 ratio (or, a 10:12:15 ratio).
The major chord, being small numbers on the overtone series, bears a very strong consonance. 4 is also two octaves above 1, so the 4 harmonizes with sum and difference tones between the three frequencies (for example, {400 Hz, 500 Hz, 600 Hz} will generate difference tones at 100 Hz and 200 Hz. These simple relationships are easily picked up by our ears.
The minor chord is an undertone series, and its root does not lie on an octave. This generates dissonance. A minor chord {400 Hz, 480 Hz, 600 Hz} generates difference tones at 80 Hz, 120 Hz, and 200 Hz, which is more complex than the major chord. Our ears have to work harder to pick out the greater amount of information, which is stress and dissonance. However, the minor chord is not too dissonant. Its complexity allows it to express more musical nuance than major chords, which is why classical composers were quite fond of it.
To tie in the emotions of "powerful" and "sad", notice that a lot of sensations are related to emotions.
Warmth (belonging), light (clarity), sweetness (enjoyment), major. These are all associated under "happiness", and tend to be very simple emotions.
Coldness (isolation), darkness (confusion), bitterness (disgust), minor. These are associated under "sadness", and represent the complexity and struggle that give meaning to life and happiness.
tldr
major is simple like happiness
minor is complex like sadness
