f 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 soon 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 various initial pitches. Creating a foundation for musical representation, works became recordable. From the Py
             ...