A major and a minor triad differ by one semitone in the middle note, and the emotional difference is enormous. That seems out of proportion to the change.
Is there an acoustic reason, or is it something we are taught to hear?
Accepted Answer
Both, and the acoustic half is smaller than people expect.
The physical part: a major third sits close to the ratio 5:4, which appears early in the harmonic series of the root. A minor third is nearer 6:5, further up the series, so the triad aligns less neatly with the overtones already present. That gives a measurable difference in roughness, but it is subtle.
The learned part does most of the work. The major and minor association with happy and sad is strong in Western listeners and much weaker or absent in listeners from other traditions. Studies with people unfamiliar with Western tonal music find the association does not reliably appear.
So the ratio gives you a small physical difference, and a few centuries of convention amplify it into the meaning you hear.
Worth resisting the "minor equals sad" shorthand, since it falls apart on contact with actual repertoire.
A great deal of dance music from the Balkans, Turkey and Eastern Europe is in minor keys and is unambiguously joyful. Plenty of funeral music is in major.
Tempo, rhythm, articulation and register carry at least as much of the emotional weight. Play a minor triad fast and loud with a driving rhythm and almost nobody hears sadness.
The third is doing something structural too. It is the note that tells you which mode you are in, which is why leaving it out gives you a power chord that sits comfortably in either.
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