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Continued fractions
A continued fraction is a method to find the simplest fractions that come closest to a given number. In music, the number to approximate is the size of the fifth measured in octaves, about 0.585. The method gives the fractions 3/5, 7/12, 24/41 and 31/53, each closer than the one before. The bottom number of each fraction is a number of equal notes per octave that contains a good fifth. Twelve is on the list, and it is the first one where the fifth is so close to pure that most people cannot hear the difference.