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# Music and the Fibonacci Series

### Musical scales are based on Fibonacci numbers

 The Fibonacci series appears in the foundation of  aspects of art, beauty and life. Even music has a foundation in the series, as: 13 notes separate each octave of 8 notes in a scale, of which the 5th and 3rd notes create the basic foundation of all chords, and are based on whole tone which is 2 steps from the root tone, that is the 1st note of the scale. Note too how the piano keyboard scale of 13 keys has 8 white keys and 5 black keys, split into groups of 3 and 2.

### Musical frequencies are based on Fibonacci ratios

Notes 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:

 Fibonacci Ratio Calculated Frequency Tempered Frequency Note in Scale Musical Relationship 1/1 440 440.00 A Root 2/1 880 880.00 A Octave 2/3 293.33 293.66 D Fourth 2/5 176 174.62 F Aug Fifth 3/2 660 659.26 E Fifth 3/5 264 261.63 C Minor Third 3/8 165 164.82 E Fifth 5/2 1,100.00 1,108.72 C# Third 5/3 733.33 740.00 F# Sixth 5/8 275 277.18 C# Third 8/3 1,173.33 1,174.64 D Fourth 8/5 704 698.46 F Aug. Fifth

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.

### Musical compositions often reflect Fibonacci numbers and phi

Fibonacci 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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