The Fibonacci Sequence and The Golden Ratio in Math and Music

The exact origin of the Fibonacci sequence is unknown. However, it is widely recognized to have first been used by Leonardo of Pisa, an Italian mathematician, to solve a breeding issue with rabbits. It has since evolved into a complex system that has been used and taught for many centuries. Whether we realize it or not, Fibonacci numbers and related ideas can be found in almost everything in our lives. A Fibonacci sequence consists of a list of numbers beginning with 0 and 1, in which each number is the sum of the two previous numbers in the sequence. For example, 0, 1, 1, 2, 3, 5 are the first numbers in the Fibonacci sequence, because 0 + 1 =1, 1 + 1 =2, 1 + 2 =3, and 2 + 3 =5. This pattern applies to any number in a Fibonacci sequence. The ratio of two fibonacci numbers that are one next to each other will always be extremely close to 1.618, the “golden ratio.” 1.618 is also known as ”phi” which originates from the 21st letter in the Greek alphabet ɸ. My research will look into the application of the Fibonacci sequence and the golden ratio in music specifically. On a foundational level, the Fibonacci sequence can be observed within a scale. The 5th note in a scale is the most important, and it happens to be the 8th note in an octave, which consists of 13 notes. Upon the division of 8 by 13, the rounded result is 0.615, a number practically identical to the golden ratio. It’s important to note that 5, 8, and 13 are all also numbers in the Fibonacci sequence. Beyond this foundational level, the Fibonacci sequence and golden ratio play a more widespread role in the composition of large musical works, such as in the first movement of a piece by Hungarian composer Béla Bartók. His piece, Music For Strings, Percussions and Celesta, is divided into two parts. Part one has 55 measures, and part two has 34 measures. When those numbers are divided, you get 1.6176, which when rounded, is 1.618 (the golden ratio). The Fibonacci sequence also makes appearances in rhythm, such as in the complex Konnakol rhythm by B.C Manjunath, which uses the first eight numbers of the Fibonacci sequence as its basis. My research will explore these occurrences of the Fibonacci sequence and the golden ratio in musical construction in order to more clearly demonstrate the parallels between music and math.