{"id":241,"date":"2022-02-14T13:53:24","date_gmt":"2022-02-14T13:53:24","guid":{"rendered":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/carla-pinkney\/?p=241"},"modified":"2022-02-14T14:03:08","modified_gmt":"2022-02-14T14:03:08","slug":"great-music-and-the-fibonacci-sequence","status":"publish","type":"post","link":"https:\/\/www.lancaster.ac.uk\/stor-i-student-sites\/carla-pinkney\/2022\/02\/14\/great-music-and-the-fibonacci-sequence\/","title":{"rendered":"Great Music and the Fibonacci Sequence"},"content":{"rendered":"\n

I recently spent the weekend back in Edinburgh (my home town). Whilst I was there, I went to see the Royal Scottish National Orchestra (RSNO) in concert at the Usher Hall. The night was in honour of John Williams<\/a> who  has composed some of the most popular, recognizable, and critically acclaimed film scores<\/a> in cinematic history. I can’t quite describe the feeling of hearing live music on this scale after a long 2 years. With scores like Star Wars, Superman, E.T. the Extra-Terrestrial, Jaws, Schindler\u2019s List<\/em> and Saving Private Ryan<\/em>, it truly was an incredible night. <\/p>\n\n\n\n

Listening to these incredible film scores in this full-scale symphonic tribute got me thinking…is there a mathematical way to write music? So, I did a bit of digging around on the internet, and turns out there is! <\/p>\n\n\n\n

Whilst there seems to be no evidence of the legend John Williams using mathematical methods to create his music, there is evidence out there to suggest that other composers such as Mozart, Beethoven and Debussy (to name a few) used the Fibonacci Sequence to write their sonatas<\/a>. <\/p>\n\n\n\n

What is the Fibonacci Sequence?<\/h2>\n\n\n\n

Put simply, the Fibonacci Sequence is a series of numbers which commonly starts at 0 and 1, and in which each number is the sum of the two preceding numbers:<\/p>\n\n\n\n

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610\u2026 <\/span> <\/p>\n\n\n\n

In mathematical notation we can describe the Fibonacci Sequence as X_{n} = X_{n-1} + X_{n-2}.<\/span><\/p>\n\n\n\n

The golden ratio, denoted by \\phi <\/span>, in decimal form is approximately 1.618033988\u2026 <\/span> When dividing each term by its previous term in the Fibonacci Sequence, the golden ratio can be seen in the answer. Furthermore, this value becomes more accurate as we get farther into the sequence. For example: 13\/8 = 1.625; <\/span> 89\/55 = 1.1818; <\/span> 610\/377 = 1.61803; <\/span> and so on, converging to 1.618033988\u2026 <\/span>. This golden ratio is what is commonly known as “The Divine Proportion” due to its frequency in the natural world. <\/p>\n\n\n\n

Squares with the dimensions of the Fibonacci Sequence can be arranged in a spiral pattern:<\/p>\n\n\n\n

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Source: Wikipedia<\/em><\/figcaption><\/figure><\/div>\n\n\n\n

The corners of each square can be connected by quarter-circle arcs to form the Fibonacci spiral:<\/p>\n\n\n\n

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Source: Wikipedia<\/em><\/figcaption><\/figure><\/div>\n\n\n\n

This sequence, pattern and spiral presents itself in many things you may never have noticed before. For example, it is used in art and music:<\/p>\n\n\n\n

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The Fibonacci Sequence in Music<\/h2>\n\n\n\n

The Fibonacci Sequence is an integral part of Western harmony and music scales. Some examples are given below:<\/p>\n\n\n\n