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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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- Fall '10