Why One Note Contains Hidden Higher Notes

Watch what I am doing here — I pluck this one string and you think you hear a single note. But I am actually giving you a whole hidden chord at once. When I pluck the string, it vibrates along its full length and makes the lowest, strongest pitch — that is the fundamental, the note you think you are hearing. But at the same moment, the string also vibrates in smaller sections: two halves, three thirds, four quarters, and so on. Each of those smaller vibrations makes its own quieter, higher pitch. Those extra pitches are called overtones, or harmonics, and they stack up in a precise order called the harmonic series. Here is how the series runs above a fundamental C: the string splits into two halves, each vibrating twice as fast — that gives you C one octave higher. Split into three thirds at three times the speed — that is G. Four quarters at four times the speed — C again, two octaves up. Five fifths at five times the speed — E. Six sixths at six times the speed — G again. Notice that each step up is one more segment, one more multiple of the original vibration rate. This overtone recipe also explains two things you have probably wondered about. First, it explains timbre — why a violin and a flute sound different on the same note. Each instrument has a different shape, so it emphasizes different overtones, giving it a different tonal color. Second, it explains consonance — why C and G together sound smooth and pleasing. Their overtones line up closely, so the combined sound is stable. C and D-flat together share very few overtones, so they clash. If you are unsure where a pitch belongs in the series, count the string segments: one segment vibrating is the fundamental, two segments give the first overtone, three segments give the second overtone, and so on — the number of segments always equals one more than the overtone number.