Contemporary Music
Ernő Lendvaï analyzes Béla Bartók's works as being based on two opposing systems, that of the golden ratio and the acoustic scale, though other music scholars reject that analysis. In Bartók's Music for Strings, Percussion and Celesta the xylophone progression occurs at the intervals 1:2:3:5:8:5:3:2:1. The French composer Erik Satie used the golden ratio in several of his pieces, including Sonneries de la Rose+Croix. His use of the ratio gave his music an otherworldly symmetry.
The golden ratio is also apparent in the organisation of the sections in the music of Claude Debussy's Image: Reflections in the Water, 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."
The musicologist Roy Howat has observed that the formal boundaries of Debussy’s La mer correspond exactly to the golden section. Trezise finds the intrinsic evidence "remarkable", but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions.
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.
According to author Leon Harkleroad, "Some of the most misguided attempts to link music and mathematics have involved Fibonacci numbers and the related golden ratio."
Read more about this topic: List Of Works Designed With The Golden Ratio
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