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Unformatted text preview: by the Pythagoreans. Further, they are made up of the first four numbers 1, 2, 3, 4 of the tetractys . Filling in the Gaps He took the interval between the fourth and the fifth as a full tone. It is 3/2 4/3 = 3/2 x 3/4 = 9/8 Plato then has his creator fill up the scale with intervals of 9/8, the tone. This leaves intervals of 256/243 as remainders, equal to the half tone. Thus Plato has constructed the scale from arithmetic calculations alone , and not by experimenting with stretched strings to find out what sounded best, as did the Pythagoreans. Project: Repeat Plato's calculations and see if you do indeed get a musical scale....
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 Fall '10
 KarenRoberts

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