Download presentation
Presentation is loading. Please wait.
Published byDarcy Houston Modified over 8 years ago
1
Fibonacci numbers
2
1, 1, 2, 3, 5, 8, 13, 21, 34 a, a, (a+a), a+(a+a), (a+a) + (a+a+a) etc. Term = sum of 2 preceding terms = GOLDEN RATIO
3
13 notes in an octave span 8 notes in an octave
4
1 st, 3rd and 5th notes of octave are chord basis
6
Examples: W. A. Mozart: Sonata A L. van Beethoven: 5th Symphony Claude Debussy: La Mer, Image Reflections in Water Erik Satie: Sonneries de la Rose Croix Béla Bartok: Music for Strings, Percussion and Celesta
7
Sonata no 1, 1st movement Sonata no 1, 1st movement: 38 bars62 bars Perfect division using natural numbers
8
Introduction to 'Dialogue du vent et la mer' in La mer: 2188513 =55 bars 5 sections Image, Reflections in Water: Sequence of keys marked by intervals 34-21-13-8 = a descending Fibonacci sequence
9
Ern ő Lendvai Music for strings, Percussion and Celesta, Movement 1 Movement 3 Other works including the golden ratio
10
Present everywhere May not be intentional As modern as you can get - Erik
Similar presentations
© 2024 SlidePlayer.com Inc.
All rights reserved.