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Harmonograph

5 4 The Discovery of harmony on passing a blacksmith To understand what the harmonograph does we need first to glance at the elements of musical theory. Pythagoras, some 2500 years ago, is credited with discovering that the pleasing experience of musical harmony comes when the ratio of the frequencies consists of simple numbers. A widely recounted story tells how taking a walk he passed a blacksmiths shop. Hearing familiar harmonies in the ringing tones of the hammers on the anvil, he went in and was able to determine it was the weights of the hammers which were responsible for the relative notes. A hammer weighing half as much as another sounded a note twice as high, an octave 21. A pair weighing 32 sounded beautiful, a fifth apart. Simple ratios made appealing sounds. The picture opposite shows experiments the philosopher went on to make from Gafurios Theorica Musice, 1492, as he found that all simple musical instruments work in much the same way, whether they are struck, plucked or blown. Deeply impressed by this link between music and number, Pythagoras drew the metaphysical conclusion that all nature consists of harmony arising from number, precursor to the modern physicists assumption that nature conforms to laws expressed in mathematical form. Looking at the picture you will see that in every example, hammers, bells, cups, weights or pipes, the same numbers appear 16, 12, 9, 8, 6 and 4. These numbers can be paired in quite a few ways, all of them pleasant to the ear, and, as we shall see, also pleasant to the eye.
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