What is the difference between major and minor, and why does minor sound sad?
One note, the third, separates them: 4 semitones up is major and bright, 3 is minor and dark. The sadness is mostly learned association.
Major and minor differ by one note: the third. In a major chord it sits a little higher (brighter); in minor, a little lower (darker).
Why sad? Partly the sound itself, partly a lifetime of hearing minor keys under sad scenes. Your ear learned the association the way you learned that certain music means a movie villain arrived.
Technically: a major triad spans root-4-7 in semitones, minor root-3-7. Scales likewise: natural minor lowers the 3rd, 6th and 7th of major. That lowered third is the emotional hinge.
The perception has two layers. Acoustically, the major third aligns more simply with the overtone series, which some hear as more consonant or settled. Culturally, Western listeners absorb thousands of pairings of minor with lament and major with celebration.
Training the distinction is fast: focused major-versus-minor drilling usually becomes reliable within a week or two, and it is the standard first chord-hearing skill.
Cross-cultural studies complicate the pure-physics story: the sad-minor association is strongest in listeners raised on Western tonal music, and some traditions use "minor-like" collections for joyful music. The safest summary: a modest acoustic seed, heavily amplified by enculturation.
The minor system is also richer than one scale: natural, harmonic (raised 7th for a functional dominant) and melodic (raised 6th and 7th ascending) minors coexist in real pieces, which is why minor-key harmony has more variety than major.
For the ear, the operational skill is catching the third: sing root, then third, and judge bright versus dark. Everything else in quality-hearing builds on that reflex.