Non-tonal Centricity

Debussy

A Debussy example. A look at a piano prelude, ...Danseuses de Delphes. Some of the tools used:

tonal (functional) harmony
pentatonic scales
pedal sounds
parallel movement of chords (atonal)
motivic framework
The Fibonacci series of numbers

Musical metaphor and gentle innovation.

Bartok's use of the Fibonacci series and of the golden mean. His chord (E-G-C-E flat).

The Fibonacci series of numbers:

0,1,1,2,3,5,8,13,21,34,55,.... is obtained by adding two adjacent members of the series in order to obtain the next one. The ratio between two adjacent members of the series is very close to that obtained by the golden mean relation:

		a / b  =  b / a+b

It was used extensively in the past in architecture, painting and music.