Fibonacci numbers.  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.

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Presentation transcript:

Fibonacci numbers

 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

13 notes in an octave span 8 notes in an octave

 1 st, 3rd and 5th notes of octave are chord basis

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

 Sonata no 1, 1st movement  Sonata no 1, 1st movement: 38 bars62 bars Perfect division using natural numbers

 Introduction to 'Dialogue du vent et la mer' in La mer: =55 bars 5 sections  Image, Reflections in Water: Sequence of keys marked by intervals = a descending Fibonacci sequence

 Ern ő Lendvai  Music for strings, Percussion and Celesta, Movement 1  Movement 3  Other works including the golden ratio

 Present everywhere  May not be intentional  As modern as you can get - Erik