Music and the Fibonacci SeriesMusical scales are based on Fibonacci numbers
Musical frequencies are based on Fibonacci ratiosNotes in the scale of western music have a foundation in the Fibonacci series, as the frequencies of musical notes have relationships based on Fibonacci numbers:
The calculated frequency above starts with A440 and applies the Fibonacci relationships. In practice, pianos are tuned to a "tempered" frequency to provide improved tonality when playing in various keys. * A440 is an arbitrary standard. The American Federation of Musicians accepted the A440 as standard pitch in 1917. It was then accepted by the U.S. government its standard in 1920 and it was not until 1939 that this pitch was accepted internationally. Before recent times a variety of tunings were used. It has been suggested by James Furia and others that A432 be the standard. A432 was often used by classical composers and results in a tuning of the whole number frequencies that are connected to numbers used in the construction of a variety of ancient works and sacred sites, such as the Great Pyramid of Egypt. The controversy over tuning still rages, with proponents of A432 or C256 as being more natural tunings than the current standard. Musical compositions often reflect Fibonacci numbers and phiFibonacci and phi relationships are often found in the timing of musical compositions. As an example, the climax of songs is often found at roughly the phi point (61.8%) of the song, as opposed to the middle or end of the song. In a 32 bar song, this would occur in the 20th bar.
Musical instruments are often based on phi
Fibonacci and phi are used in the design of violins and even in the design of high quality speaker wire.
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