Plato's Lambda is but two sides of a tetractys of 10 integers, which we shall call the "Lambda Tetractys." The three missing red integers 6, 12 & 18 are interpolated by following the rule that diagonal rows of integers follow the two geometric series of the integers forming the slopes of Λ, the Greek letter lambda. So 6 is twice 3 and three times 2, whilst 12 is twice 6 and three time 4 and 18 is twice 9 and three times 6. If we ignore the speculative cosmological context in which the algorithm of Plato's Lambda for generating the relative frequencies of the musical notes was presented and regard it and its underlying tetractys purely as a construction of Pythagorean mathematics, then both are incomplete. This is not simply because the three numbers making up the tetractys are absent from Plato's account. It is because the numbers 1, 2, 3 and 4 were the basis of Pythagorean number mysticism and its application to the study of natural phenomena such as musical sounds, whereas the number 4 is missing as a generative factor from the Lambda, which starts with the number 1 (the Pythagorean monad) and multiplies it by the factor 2 (the dyad) and the factor 3 (the triad) to generate its numbers. But what about the tetrad? 

 

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