# Harmonograph

28 The roTary ocTave 21 hearts and triangles From rotary motion with a 21 ratio come some of the most beautiful of all harmonograph drawings simple, graceful and often surprising. Remember, all that is happening here is that two circular motions, one almost exactly twice as fast as the other, are being added together. Contrary motion produces a trefoil shape with many fine variations right hand images opposite. Starting with a smaller size or amplitude in the faster rotation produces a triangle, or pyramid. The octave in concurrent motion produces a heartshaped form with a simple inner loop left hand column opposite. Here there is a link with the ancient tradition of the music of the spheres, for this is the shape an observer on Uranus would ascribe to the movement of Neptune, or vice versa. This is because the planets orbit the Sun concurrently, Uranus in 84 years and Neptune in 165, approximately performing an octave. The planet Mercury sings a perfect octave all by itself, as one of its days is two of its years. Nearmisses in the ratios of rotary drawings set the designs spinning lower row opposite. 29