The answer to why major keys sound bright and minor keys sound dark has been found.
Humans feel uneasy with unstable vibrations such as trembling and unnatural movements, while they feel comfortable with static and natural vibrations.
The waveform of a minor scale is inherently unstable in its harmonic structure. The best combination of notes that align with pure tuning in harmonics is the major scale.
Music created by combining sounds that harmoniously conform to the laws of nature is perceived by us as bright and comfortable.
Then, where does the source lie that makes us feel complex emotions beyond brightness and darkness, joy and sadness, according to the structure of chord progressions?
To understand this, it was necessary to first know the principles of chord progression.
Why does the leading tone want to resolve to the tonic?
The degree of resonance varies depending on the distance between notes, and by unfolding the harmonic structure, one can see that the next note resonates best with the previous one.
Arranged in this way, the intervals in order of best harmony are the octave, perfect fifth, perfect fourth, major third, minor third, major second, and minor second. This means that the further back you go, the more unstable it becomes, and humans instinctively want to return these unstable intervals to stable ones.
Therefore, the minor second interval, which appears only at the end of the 16th overtone (and is barely audible), is naturally returned to the existing larger harmonic notes.
In this process, humans feel satisfaction that instability has been resolved. This satisfaction can be said to be the source of how chord progression evokes emotions. What I want to further research is how various harmonies composed of complex intervals induce specific feelings in a clear and established manner.