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Harmonograph

38 amPliTuDe circles, polygons, flowers and another circle Much variation can be obtained from a rotary ratio by having unequal sizes in the two circular motions. Opposite we see two frequencies related by a major sixth 53. A lower frequency note begins to be influenced by, combines with and is then more or less replaced by a higher frequency one. When the two notes are at equal volume the lines all pass through the centre see pages 5657. Notice that the sequence is not symmetrical. Below we see the first three overtones. For the spikiest shapes simply invert the amplitudes. For polygons, square them first. If you have ever played with a Spirograph, the harmony is determined by the cogging ratio, and it is the amplitude which is adjusted when you change penholes on the wheel.
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