Text: 3 3 X 2 = 6 3 X 3 = 9 (square) 3 X 4 = 12, etc. 3^1 = 3 3^2 = 9 (square) 3^3 = 27 (cube) 3^4 = 81 or 9^1 = 9 (3^2^1) 9^2 = 81 (3^2 X 3^2) (square made of 81 smaller squares) 9^3 = 243 (3^2 X 3^2 X 3^2) (cube made of 243 smaller cubes) 27 is the cube of 3. Think of a cube with 3 on each side. Such a cube can be broken up into 27 smaller cubes. 243 is the cube of 9. Think of a cube with 9 on each side. Such a cube can be broken up into 243 smaller cubes. 3 is the square root of 9. 3x3 3 is the cube root of 27. 3x3x3 9 is the square root of 81. 9x9 9 is the cube root of 243. 9x9x9 Music, arithmetic and geometry are three sides of the same triangle. Numbers 2 and 3 make up most musical notes til 5 is added in which makes everything wacko, but does fill in the missing notes. Let's do some more..... Cube Volume = diameter^3 Sphere Volume = 1/6 * PI * diameter^3 [from Mechanical Engineer's Handbook, Lionel Marks, 5th edition, 1951.] A sphere enclosed in a cube means its diameter is the same as one side of the cube or we could say the sphere diameter = the cube root of the cube. Let's use 9 as our diameter, so: Cube Volume = 243 Sphere Volume = 1/6 * PI * diameter^3 = 1/6 * 3.14 * 9^3 = 1/6 * 3.14 * 243 = 3.14 * 243/6 = 763.02/6 = 127.17 If we did the same thing with 3 as diameter we have: Cube Volume = 27 Sphere Volume = 14.13 Void = 27-14.13 or 12.87 parts of the cube This all looks uninteresting until we remember that sound expands in spherical waves - NOT linear sine wave patterns. One series of base 2 is smaller cubes and spheres than a series of 3 base. Musically this is something like: 27:14.13:: ninth 14.13:12.87:: 7th 27:12.87:: 4th?

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