Debussy's Use of the Fibonacci Sequence

“I can count”: Mathematics in Music

An Analysis of Debussy’s Nocturne

Math has been associated with music for many years, particularly that of the Fibonacci sequence and the Golden Ratio. In Debussy’s Nocturne, composed in 1892, I look into the use of the Fibonacci sequence and the Golden Ratio. Previously it has been noted that composers used the Fibonacci sequence and the Golden Ratio in terms of form, however in my analysis I look into the use of it in terms of notation as well. I will explore how the idea of Sonata form is used along with the Mathematical Model of the Fibonacci sequence. It is however important to mention that as this is one of Debussy’s earlier works, the extent that the ratio and sequence are explored are not as elaborate as some of his later works. I will explore the Harmonic analysis of the piece to create a better understanding of where and how structure is used by Debussy. Debussy was a perfectionist and would only give perfected scores to the printers, as such it is impossible to prove whether or not the use of the sequences were intended or not, however considering that some of his contemporaries in other arts were very much involved with the idea of the Golden Ratio it does seem plausible that it was intended. The fact remains, though, that the use of the sequences and ratio are still evidently there and can be analysed; as this essay will show.

The Fibonacci sequence is a system of numbers that equate to the two preceding numbers. In terms of music it is difficult to define how this might fit into a musical sequence; in form it makes a bit more sense when associating the golden ratio. However, there is a means to obtain a musical sequence using Fibonacci’s sequence. If we consider that there are seven main tones (excluding sharps or flats) in a general scale, before any note is repeated, we are able to find a number to create an equation that relates to the Fibonacci sequence, namely 7. If we then take the first few numbers of the...