The Golden Ratio – Proportionality in the works of Béla Bartók
The Golden Ratio, often represented by the Greek letter phi (φ), is an irrational number approximately equal to 1.61803398875. This mathematical constant has been a subject of fascination for centuries due to its unique properties and its appearance in various aspects of nature and art. In music, one of the most prominent composers who utilized the Golden Ratio in his works was Béla Bartók, a Hungarian composer and pianist of the 20th century.
Introduction
Bartók’s music is characterized by its rich folk melodies and complex rhythms. His compositions often incorporated elements of traditional Hungarian music, which he sought to preserve and promote. In this article, we will explore how Bartók utilized the Golden Ratio in his works, particularly in terms of proportionality.
Proportionality in Music
In music, proportionality refers to the relationship between different parts or elements within a composition. The Golden Ratio can be used as a guideline for creating balanced and harmonious proportions in music. When applied correctly, it can create a sense of unity and coherence, drawing the listener into the music.
Bartók was well aware of the significance of proportionality in music. He often employed mathematical concepts, including the Golden Ratio, to create musical structures and patterns. For example, in his String Quartet No. 4, he uses the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13) to determine the length of the different sections within the quartet.
Examples from Bartók’s Works
One notable example of the Golden Ratio in Bartók’s music can be found in his Piano Concerto No. 2. The first movement is structured into four parts, each with a specific duration based on the Fibonacci sequence. This creates a sense of balance and proportion, drawing attention to the various themes and motifs within the piece.
Another example can be seen in his String Quartet Op. 18, where he uses the Golden Ratio to determine the spacing between different notes within a melody. This results in a more cohesive and harmonious sound.
Conclusion
Béla Bartók’s use of the Golden Ratio in his music demonstrates the composer’s interest in mathematical concepts and their application in art. By utilizing proportionality, he created balanced and coherent musical structures that draw the listener into the music. While the Golden Ratio is just one tool among many used by composers, its appearance in Bartók’s works highlights the ongoing dialogue between mathematics and music.
References
* Bartók, B. (1926). Piano Concerto No. 2.
* Fibonacci, L. (1202). Liber Abaci.
* The Golden Ratio
Image Credits
* 
*
Note: You need to replace “image.jpg” with your actual image file path.