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The Fascinating Role of the Fibonacci Sequence in Music

It may sound unbelievable, but the Fibonacci Sequence and the Golden Ratio play significant roles in Western harmony and musical scales. Their patterns are often found in literature, film, visual arts, and even in the structure of musical compositions.


The Fibonacci Sequence in Musical Scales

An octave on the piano consists of 13 notes: 8 white keys and 5 black keys. Within a scale of 8 notes, the third and fifth notes form the foundation of a basic chord. The dominant note is the fifth note, which also happens to be the eighth note in the full set of 13 notes that make up the octave. Interestingly, 8 divided by 13 is approximately 0.615, close to the Golden Ratio of 0.618. Notice the pattern? These are all Fibonacci numbers: 3, 5, 8, 13.

Historical Use by Composers

For centuries, composers and instrument makers have utilized the Fibonacci Sequence and the Golden Ratio to craft music. Wolfgang Amadeus Mozart, for instance, structured many of his works around the Golden Ratio, particularly his piano sonatas.

A traditional sonata has two parts:

  1. Exposition – Introduction of the musical theme.
  2. Development and Recapitulation – The theme is developed and repeated.

 

Mozart arranged his sonatas so that the ratio of bars in the development and recapitulation to those in the exposition approximates the Golden Ratio. For example, in the first movement of his Piano Sonata No. 1 in C Major, the exposition has 38 bars, while the development and recapitulation have 62 bars. Thus, 62 divided by 38 equals approximately 1.63, close to the Golden Ratio of 1.618.


Other Notable Composers

Experts claim that Beethoven, Bartók, Debussy, Schubert, Bach, and Satie also employed this technique in their sonatas, but the exact reason for its effectiveness remains a mystery.

Stradivari and Instrument Making

Antonio Stradivari, the master violin maker, created some of the most beautiful and sonorous violins, partly due to his use of the Fibonacci Sequence and the Golden Ratio. These ratios are evident in the specific lengths of various parts of his violins, contributing to their superior sound quality. The Golden Ratio is also used in crafting saxophone mouthpieces, speaker wires, and even in the acoustic design of some cathedrals.

Sebanev’s Research

Russian composer Sebanev delved into the presence of the Golden Ratio in music, analyzing numerous compositions. He found that the highest percentages of the Golden Ratio appear in the works of great composers. Among 1,770 compositions by 42 composers, the Golden Ratio appears 3,275 times, with one variant appearing in 1,338 compositions. Beethoven, Haydn, Mozart, Chopin, and Schubert show the highest occurrences, with Chopin’s 27 etudes containing 154 golden sections.


Modern Usage

Even contemporary artists like Lady Gaga have used the Fibonacci Sequence in their music, highlighting its timeless relevance.

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