Why some notes sound sweet together and others seem to fight

Play C and E together and they sound sweet. Play C and C sharp and they buzz. The notes aren't the problem: the clash only happens when they meet.

Every musical note is secretly a stack of harmonics at 2, 3, 4… times its pitch. When two notes play, those harmonics either land on the same frequencies or sit just close enough to beat against each other, which your ear hears as roughness. Simple ratios like 3:2 line the ladders up. Drag the interval below and watch it happen.