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The Fibonacci sequence appears in nature in various plants, animals, and even the human body. However, it has also been seen in many man made creations, such as paintings and pieces of music. The Fibonacci sequence shows up in scales, instrument creation, octaves, and even some of Mozart's arrangements.

For example: a scale has eight notes top to bottom. An arpeggio contains the first, third, and fifth note of a scale. While not an exact replica, this definitely contains some elements of the Fibonacci sequence. A great way to visualize this is on a piano octave.

This video helps to hear the sequence itself. Pay close attention to the patterns and colors.

Take a look at a few examples:

The Fibonacci Sequence

Any octave on a piano has thirteen notes. Of those thirteen, eight are natural, and five are sharps/flats. Of those five, they are divided into groups of three and two.

Take a look at this model:

The Fibonacci Sequence was named after Italian mathematician Leonardo of Pisa, commonly known as "Fibonacci". He first brought this sequence to Western mathematics in 1202 in his book "Liber Abaci" (Book of Calculation). The sequence started with an unspoken term 0, and continued as such: (0), 1, 1, 2, 3, 8, 13, 21, 34, 56, etc. The next term is the sum of the previous two numbers. This sequence is not anything extraordinary, except for the number of times it has appeared in nature and human patterns.

Music and Math

There are thirteen keys in total. Eight are white (naturals) and five are black (sharps or flats). The sharps have been divided into groups of two and three. Remember that the Fibonacci sequence is 1,1, 2, 3, 5, 8, 13,....

Music and math are not often thought of as closely related concepts. In fact, most people would consider them opposites. Math is equations, numbers, irrational values, and for those few who don't want to pick up a calculator. Music is an art, a talent, something that stimulates feeling. Not many people can say that they have shed a tear from the beauty of a calculus problem.

However, at their root, math and music share many similarities. Any musician can tell you that half of music is counting. Time signatures, flats, and rests all require musicians to have at least a basic knowledge of fractions. Music and math are also both derived form patterns. After you remove the lyrics and effects, music is essentially a synthetic pattern. In fact, many pieces of classical and modern music have been linked to the Fibonacci Sequence, a mathematical pattern commonly seen in nature.

Phi

Another element of the Fibonacci Sequence is "Phi", sometimes referred to as "the Golden Ratio". Phi refers to a very specific ratio best explained explained in diagram:

Fin

Essentially the ratio of the green line to the blue line is the same as the ratio of the blue line to the red line. This ratio is considered the "perfect balance", and shows up quite often in music.

Citations

  • Glydon, Natasha. "Music, Math, and Patterns - Math Central." Music, Math, and Patterns - Math Central. Pacific Institute for the Mathematical Sciences, 2011. Web. 16 May 2016.
  • "Music, The Fibonacci Sequence and Phi." Order in Chaos. Word Press, 17 May 2013. Web. 16 May 2016.
  • Miesner, Gary. "Music and the Fibonacci Sequence and Phi - The Golden Ratio: Phi, 1.618." The Golden Ratio Phi 1618. PhiPoint Solutions, 04 May 2012. Web. 16 May 2016.
  • Zhan, Cindy. "The Correlation Between Music and Math: A Neurobiology Perspective." Serendip Studio's One World |. Serendip Studio, 16 Jan. 2008. Web. 16 May 2016.
  • J, Elaine. "What Is the Golden Ratio?" LiveScience. TechMedia Network, 24 June 2013. Web. 16 May 2016.
  • "Fibonacci Number." Wikipedia. Wikimedia Foundation, n.d. Web. 16 May 2016.
  • Schwab, Gerben. "Fibonacci Sequence in Music." YouTube. YouTube, 10 Jan. 2012. Web. 16 May 2016.

The climax of most songs happens at the Phi point (61.8%).

Music and math may never be taught in the same classroom, but they will continue to impact each other. The Fibonacci Sequence and Phi are just a few examples of this. As time goes on, more and more studies are proving that there is a direct relationship between music and math in the brain. The "Mozart Effect" may not just be a fad after all.

Phi in Real Life

A violin is one model of Phi. The ratio of the entire instrument to the finger board is the same as the ratio of the neck to the neck to the entire fingerboard or the lower half of the body to the upper half.

To tie this back to the Fibonacci Sequence, by dividing the ratios of every term, the terms will converge closer and closer to Phi (1.618).

Music and the Fibonacci Sequence

Paris Geolas

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