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The decagon has ten corners. A geometrical symbol of the Decad (10), which was regarded by the Pythagoreans as "All Perfect" because it represented closure of the set of integers needed to express any integer, the decagon contains 61 yods when its sectors are tetractyses. The 31 internal yods symbolize the 31 sounds playable with the two tetrachords of the first octave A-A′, the centre denoting the starting note A. The 30 yods on the boundary of the decagon symbolize the 30 sounds playable in the second octave A′-A′′. Here is a geometrical representation of the Greater Perfect System. The 60 yods surrounding the centre represent the 60 sounds that can be made with its four tetrachords when played separately one, two, three or four notes at a time.
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