Why Some Chords Sound Happy

Play a major chord and it sounds bright; play a minor chord and it sounds sad. The difference is tiny: usually just one note moved down by a half-step. Why does so small a change flip the mood? Notes are really vibrations at certain frequencies. When frequencies fit together in simple ratios (like 2:3), the sound waves line up often and we hear it as smooth and 'consonant'. A major chord stacks notes whose frequencies fit especially neatly, giving that stable, open feeling. A minor chord shifts the middle note down slightly, changing those ratios into ones that don't lock together quite as cleanly. Our ears register that subtle roughness as tension or melancholy. So the emotional 'colour' of a chord traces back to the maths of how its frequencies overlap.