Named after Leonardo of Pisa, the Fibonacci sequence is a sequence of numbers defined by the fact that each term is the sum of the previous two terms. Thus, the first fifteen terms are as follow:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377

 Leonardo of Pisa, nick named Fibonacci, was an Italian Mathematician who was a major figure in spreading the Hindu-Arabic numerals to the rest of the world. These numerals are the ones we use today and replaced the previously used Roman numerals.

The Fibonacci sequence was first presented as a solution to a rabbit problem:

Fibonacci’s sequence also frequently appears in nature in the form of a spiral. It can be seen in flowers, pine cones and pineapple fruitlets, giving the seeds the most efficient and even distribution in the space available. The most common example is in a sunflower; the seeds appear in a spiral with the seeds coming out of the centre which usually grow in formations of 55 clockwise and 89 anticlockwise; both Fibonacci numbers.

Within a lecture focusing on Fibonacci and art we drew our own spirals using Fibonacci’s numbers:

We also investigated the mystery of Phi and the Golden Ratio, it relates to the spiral also, as with each 90 degree turn it gets 1.6180 times wider. From Fibonacci numbers, you can get the ratio by taking any two successive numbers and putting them into this formula:

The Golden ratio has been commonly used in art and these are only a few examples:

My main interest, however, is in music rather than art and after the past few years of playing piano, I was amazed to find out Fibonacci played such a large role in music. Fibonacci’s sequence is a framework which appeals to many composers, possibly because the golden ratio. The Golden Ratio often features to generate rhythmic change or develop a melody line.

Fibonacci’s numbers feature in the piano keyboard:

Examining the scale of C to C, you can identify thirteen keys; eight white and five black. This can be further related to Fibonacci using the layout of the keys, with the black keys in groupings of twos and threes.

Fibonacci’s numbers also feature in an octave. Within a notes octave there is a span of thirteen notes and a scale is made up of eight notes. If you investigate a chord, the finding is that the chord’s foundation is the third and fifth notes which are based on a tone made up of the two steps, and one step from the root tone, as demonstrated below: