When two notes are played on a piano an octave apart (the second note has a fundamental exactly twice the fundamental of the first or a \(1\) to \(2\) ratio) all of the harmonics line up and fall on t...When two notes are played on a piano an octave apart (the second note has a fundamental exactly twice the fundamental of the first or a \(1\) to \(2\) ratio) all of the harmonics line up and fall on top of each other and there is no dissonance. (For example a \(200\text{ Hz}\) fundamental has harmonics at \(400\text{ Hz}, 600\text{ Hz}, 800\text{ Hz}\), etc.
