Pluck one string and you don't hear one frequency — the string vibrates in halves, thirds, quarters, all at once, stacking quiet overtones above the note you hear. That stack, the harmonic series, is identical for every note, and its first members are the octave, the fifth, and the major third. Two notes sound consonant when their overtone stacks share members: the octave (2:1) shares nearly everything, the fifth (3:2) the next-most, the major third (5:4) a little less. Dissonance is overtone collision — the tritone and minor second sit at complicated ratios whose overtones beat against each other. This is why the perfect fifth is so stable it survives heavy distortion, which is the entire power-chord business model, and why the same interval generates the circle of fifths. The physics here — which pairs of tones beat and which fuse — holds everywhere. Whether people prefer the smooth ones turns out to be a separate question, and a genuinely open one (next essay).