A single harmonic is the purest sound possible: It contains no overtones or other identifying characteristics aside from its pitch and loudness. The shape of its vibration – whether it be vibrating the air so you can hear it, or causing the electrical vibrations of a voltage going up and down – is a sine wave. Most of the time, overtones have a very specific pitch relationship to each other. The first or lowest harmonic – known as the ‘fundamental’ – is the pitch of the sound, just as the lowest note of a chord is its ‘root.’ The other harmonics are higher, and spaced out as integer multiples of the fundamental: two times its frequency, three times, four times, and so forth. The first few harmonics happen to have a nice musical spacing: an octave; an octave and a fifth; two octaves. But the higher they get, the less musical they may seem. Adding or subtracting harmonics changes the character of the sound, as well as the pattern of vibrations that produces that sound – in other words, the shape of that sound’s ‘waveform’ in a synthesizer. Changing the waveshape means changing the sound, and vice versa.
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