nstrumentation, and
             The intrinsic discovery 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 various initial
             ...