| As composition becomes increasingly important in the world of jazz, composers in this genre looking for new organizational techniques have found inspiration in the possibilities inherent in a mathematical series known' as the Fibonacci numbers. Along with its close relative, the golden ratio, the Fibonacci numbers present composers with a wide palette of aesthetic choices.;One attractive aspect of the Fibonacci numbers for composers is the series' reverberance throughout nature. From nautilus seashells, pine cones, leafing plants, and sunflowers, to the shape of galaxies, and DNA molecules, to the ebb and flow of the stock market, the Fibonacci series quietly makes its presence known.;My research on this fascinating numerical sequence inspired me, as it has countless others in the arts, to integrate the Fibonacci numbers into the compositional process for several works I was composing for jazz orchestra. The resulting three-part suite, and its analysis, is the focus of this discourse. This study unveils the various properties of the Fibonacci numbers, details its appearances and uses in nature and the arts throughout history, and speculates on the psychological and aesthetic implications inherent in its unconscious perception. My primary goal, however, is to introduce a useful compositional tool to a rising generation of composers who might not be aware of the inherent beauty of such a device.;In regard to music analysis, an investigation of Fibonacci and golden proportion relationships can greatly enhance various aspects of a traditional analysis. By highlighting the temporal and spatial connections of important structural events across the time span of a composition, the psychological ideas of tension, stability, ambiguity, and certainty are brought into greater relief, addressing the question: How does the application of the Fibonacci numbers to a system of composition affect the music experientially?;The answer is perhaps in how we perceive ambiguity and resolution and how those concepts translate (through music) into the natural dynamic symmetry of growth and recession, helping to balance and order seemingly unrelated events in our unconscious mind. |
