ery made by Pythagoras was the potential
             order to the chaos of music. Pythagoras began subdividing
             different intervals and pitches into distinct notes.
             Mathematically he divided intervals into wholes, thirds, and
             halves. "Four distinct musical ratios were discovered: the tone,
             its fourth, its fifth, and its octave." (Johnston, 1989). From
             these ratios the Pythagorean scale was introduced. This scale
             revolutionized music. Pythagorean relationships of ratios held
             true for any initial pitch. This discovery, in turn, reformed
             musical education. "With the standardization of music, musical
             creativity could be recorded, taught, and reproduced." (Rowell,
             1983). Modern day finger exercises, such as the Hanons, are
             neither based on melody or creativity. They are simply based on
             the Pythagorean scale, and are executed from v
             ...