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Golden Section

38 39 MeloDy harMony in search of the lost chord Harmonics number in time was one of four disciplines studied in the Pythagorean Quadrivium, together with Arithmetic pure number, Geometry number in space, and Spherics number in space and time. The golden section is a theme common to all. In the Platonic tradition, the intention was to lift the soul out of the realm of mere opinion doxa, by attunement with the ratios and proportions contained in the harmonies and rhythms of music. This allows the soul to pass into the Intelligible realm of knowledge episteme, moving through the realm of mathematical reasoning dianoia up into direct intuition noesis of the world of pure Forms, the ratios themselves. The structure of both rhythm and harmony is based upon ratio. The most simple and pleasing musical intervals, the octave 21 and the fifth 32, are the first Fibonacci approximations to the golden section. The series continues with the major and minor sixths 53 and 85. The scale itself holds the next step 138, for astonishingly, if we include the octave, musicians play eight notes in a scale, taken from thirteen chromatic notes. Finally, simple major and minor chords consist of the 1st, 3rd, 5th and 8th notes of the scale. The golden section has been used by composers from Dufay opposite top after Sandresky to Bach, Bartok, and Sibelius, as a way of structuring a work of music. Russian musicologist Sabaneev discovered in 1925 that the golden section particularly appears in compositions by Beethoven 97 of works, Haydn 97, Arensky 95, Chopin 92, including almost all of his Etudes, Schubert 91, Mozart 91, and Scriabin 90.
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