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Divisions of the World Soul as Musical Intervals

# Divisions of the World Soul as Musical Intervals - by the...

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Divisions of the World Soul as Musical Intervals Relating this to music, if we start at low C and lay off these intervals, we get 4 octaves plus a sixth. It doesn't yet look like a musical scale. But Plato goes on to fill in each interval with an arithmetic mean and a harmonic mean. Taking the first interval, from 1 to 2, for example, Arithmetic mean = (1+2)/2 = 3/2 The Harmonic mean of two numbers is the reciprocal of the arithmetic mean of their reciprocals. For 1 and 2, the reciprocals are 1 and 1/2, whose arithmetic mean is 1+ 1/2 ÷ 2 or 3/4. Thus, Harmonic mean = 4/3 Thus we get the fourth or 4/3, and the fifth or 3/2, the same intervals found pleasing
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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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