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Harmonograph

9 8 overTones anD inTervals harmonic ratios in and outside the octave How are musical scales constructed Listen very carefully as you pluck a string, and you will hear not only the main note, or tonic, but also a multitude of other harmonics, the overtones. The principle is one of harmonic resonance, and affects not only strings and ringing hammers, but columns of air and plates too. Touching a string with a feather at the halfway or third point, as shown below, encourages regularly spaced stationary points, called nodes, and an overtone can be produced by bowing the shorter side. The first three overtones are shown opposite top. Musicians, however, need notes with intervals a little closer together than the overtone series, which harmonise within an octave. The lower diagram opposite shows the overtone series on the left, and the intervals developing within the octave on the right, in order of increasing dissonance, or complexity. All discord harmony not understood wrote Alexander Pope. The brain seems to grasp easily the relationships implicit in simple harmonies, an achievement bringing pleasure but with increasing complexity it falters and then fails, and failure is always unpleasant. For most people enjoyment fades as discord increases, towards the end of the series opposite. And, as we shall see, that is where the harmonograph drawings fade too.
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