If there were a soundtrack to accompany this edition of The Arts Paper it would certainly include works by Béla Bartók (1881-1945), whose music is as rich in folk melodies as it was informed by the composer’s fascination with the so-called Fibonacci series.
As explained in musicologist David Cooper’s Bartók: Concerto for Orchestra (Cambridge University Press, 1996), “the Fibonacci series is a number series derived from a recursive formula in which each subsequent element is the sum of the previous two … and has the property that the ratio between neighbouring pairs of numbers increasingly approximates the so-called ‘golden mean’ … (which) can be understood as the point on a line which divides it into two segments … such that the ration between the segments … is the same as that between the longer segment and the entire line.”In his Connections: The Geometric Bridge Between Art and Science (The McGraw-Hill Companies, 1991), New Jersey Institute of Technology professor Jay Kappraff wrote: “Bartók based the entire structure of his music on the golden mean and Fibonacci series – from the largest elements of the whole piece, whether symphony or sonata, to the movement, principal, and secondary themes and down to the smallest phrase.”
While mathematical principles help us understand these patterns and ratios – and how they’re applied to composition and other art forms – it is their appearance in nature that inspired Bartók and other artists to incorporate them into their work.
Bartók wasn’t so much trying to compose according to a mathematical formula as he was taking his cue from the beauty we see in naturally occurring patterns, such as that of the seeds on the head of a sunflower.
Kappraff wrote in Connections: The Geometric Bridge Between Art and Science: “Bartók believed that every folk music of the world can finally be traced to a few primeval sources.”
While scientific analysis helps us understand Bartók’s work and its inspiration, it is important to remember that he was striving not for mathematical perfection but to express as best he could the beauty that informed the richness of his melodies.
David Brensilver is the editor of The Arts Paper. This is his opinion.