It is believed that some composers wrote their music using the golden ratio and the Fibonacci numbers to assist them.
James Tenney reconceived his piece For Ann (rising), which consists of up to twelve computer-generated upwardly glissandoing tones (see Shepard tone), as having each tone start so it is the golden ratio (in between an equal tempered minor and major sixth) below the previous tone, so that the combination tones produced by all consecutive tones are a lower or higher pitch already, or soon to be, produced.
Ernő Lendvai analyzes Béla Bartók's works as being based on two opposing systems, that of the golden ratio and the acoustic scale. 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. 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 Debussy's Image, "Reflections in 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 φ position.
This Binary Universe, an experimental album by Brian Transeau, includes a track entitled 1.618 in homage to the golden ratio. The track features musical versions of the ratio and the accompanying video displays various animated versions of the golden mean.
|
