Investigation Of Applications Of Fibonacci Sequence And Golden Ratio In Music

Abstract

In studies presented in the literature, relationships between music and mathematics can sometimes be observed. Leonardo Fibonacci (1170-1250) is well known in mathematics with the Fibonacci Sequence and this sequence used to identify numbers in various music elements, too. In related studies, these numbers have been used to demonstrate the existence of the ‘Golden Ratio’ using methods and theories borrowed from the components of music. Nevertheless, this relationship has subsequently been seen inaccurate. The studies that previously based some works of Chopin, Mozart, Beethoven, Bach and Bartók on Fibonacci Sequence and Golden Ratio are critically examined in the context of musical and mathematical theories in this study. Qualitative and quantitative research methods were used together in this interdisciplinary research in the field of mathematical sciences and critical musicology. It was examined basically the measure or rhythms (sound duration) within the musical works that allegedly used the Fibonacci Sequence and the Golden Ratio, and it was found these studies yielded values close to the terms of the Fibonacci Sequence and the determined values of the Golden Ratio were 0.618, 1.618, and 0.382. It is determined that mathematical, historical and music theoretical data and findings could not provide enough to support the claims of the related studies. Thus, it was determined that the accuracy of the Fibonacci Sequence and Golden Ratio expressed in the works of the related composers are controversial within the framework of the relevant studies.