Music of the Spheres

Music of the Spheres - interval of 1:2 called the octave ,...

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Music of the Spheres Jubal and Pythagoras Slide 3-4: Theorica Musica F. Gaffurio, Milan, 1492 Lawlor, Robert. Sacred Geometry. NY: So the Pythagoreans in their love of numbers built up this elaborate number lore, but it may be that the numbers that impressed them most were those found in the musical ratios. Lets start with this frontispiece from a 1492 book on music theory. The upper left frame shows Lubal or Jubal , from the Old Testament, "father of all who play the lyre and the pipe" and 6 guys whacking on an anvil with hammers numbered 4, 6, 8, 9, 12, 16. The frames in the upper right and lower left show Pithagoras hitting bells, plucking strings under different tensions, tapping glasses filled to different lengths with water, all marked 4, 6, 8, 9, 12, 16. In each frame he sounds the ones marked 8 and 16, an
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Unformatted text preview: interval of 1:2 called the octave , or diapason . In the lower right, he and Philolaos, another Pythagorean, blow pipes of lengths 8 and 16, again giving the octave, but Pythagoras holds pipes 9 and 12, giving the ratio 3:4, called the fourth or diatesseron while Philolaos holds 4 and 6, giving the ratio 2:3, called the fifth or diapente . They are: 8 : 16 or 1 : 2 Octave diapason 4 : 6 or 2 : 3 Fifth diapente 9 : 12 or 3 : 4 Fourth diatesseron These were the only intervals considered harmonious by the Greeks. The Pythagoreans supposedly found them by experimenting with a single string with a moveable bridge, and found these pleasant intervals could be expressed as the ratio of whole numbers ....
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