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Fibonacci Numbers

Concepts of Mathematics Presentation

Matthew Topping

on 20 April 2010

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Transcript of Fibonacci Numbers

Math and Music Fibonacci Numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 Golden Ratio Questions How are Fibonacci numbers and the golden ratio used by composers and musicians? What does the Fibonacci sequence sound like when applied to music? What are the different ways the Fibonacci numbers can be used in music? Which composers have used the Fibonacci numbers and golden ratio in their music? Can we compose our own music using Fibonacci Numbers? The Fibonacci ratio is approx. 1.618 approx. 1.618 Composers Beethoven Mozart Bartok Used the golden ratio in placing musical phrases in his 5th Symphony Divided his piece, Concerto in C, in half using the golden ratio First section is 32 measures, Last section is 68 measures In his piece for Strings, Percussion, and Celesta, Bartok uses the Fibonacci sequence in melodic and rhythmic motifs Our Composition Composers like Mozart, Beethoven, and Bartok
use the golden ratio and Fibonacci sequence to determine riffs and song structure If modified and applied correctly, fibonacci numbers and the golden ratio in music can sound just like any other composition Through applying the sequence to rhythmic and melodic motifs and using the golden ratio to determine the form of the piece of music. Mozart, Beethoven, Bartok, and more YES.
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