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Level 8 - Vociferous
Join Date: Apr 2012
Location: south africa
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Re: aenima- problem 8
[edit]Music
Ernő Lendvaď analyzes Béla Bartók's works as being based on two opposing systems, that of the golden ratio and the acoustic scale,[44] though other music scholars reject that analysis.[2] In Bartok's Music for Strings, Percussion and Celesta the xylophone progression occurs at the intervals 1:2:3:5:8:5:3:2:1.[45] French composer Erik Satie used the golden ratio in several of his pieces, including Sonneries de la Rose+Croix. The golden ratio is also apparent in the organization of the sections in the music of Debussy's Reflets dans l'eau (Reflections in Water), from Images (1st series, 1905), in which "the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position."[45]
The musicologist Roy Howat has observed that the formal boundaries of La Mer correspond exactly to the golden section.[46] Trezise finds the intrinsic evidence "remarkable," but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions.[47] Also, many works of Chopin, mainly Etudes (studies) and Nocturnes, are formally based on the golden ratio. This results in the biggest climax of both musical expression and technical difficulty after about 2/3 of the piece.[citation needed]
Pearl Drums positions the air vents on its Masters Premium models based on the golden ratio. The company claims that this arrangement improves bass response and has applied for a patent on this innovation.[48]
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