<P> According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when he passed blacksmiths at work one day and thought that the sounds emanating from their anvils were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music . He went to the blacksmiths to learn how the sounds were produced by looking at their tools . He discovered that it was because the hammers were "simple ratios of each other, one was half the size of the first, another was 2 / 3 the size, and so on". </P> <P> This legend has since proven to be false by virtue of the fact that these ratios are only relevant to string length (such as the string of a monochord), and not to hammer weight . However, it may be that Pythagoras was indeed responsible for discovering the properties of string length . </P> <P> Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars . Another belief attributed to Pythagoras was that of the "harmony of the spheres". Thus the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony . </P> <P> Brewer (1894), wrote (page 2614): </P>

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