Essay on Debussy's use of the Fibonacci sequence

Words: 1386
Pages: 6

“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
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8 and 13 create 21 this is the next number shown and the 7th number of the sequence. 5 and 16 make 21 as 21 and 10 make 31, thus even if the numbers are not exactly the same as the Fibonacci sequence they still follow the formula where the two preceding numbers equate to the next number. Also this sequence is repeated at the end with the return of the A section that the piece started with and on which this graph is based.
Howat was not wrong in saying that the piece perhaps follows some conventions even though Debussy was against such. If we closely look at this piece we will see that it vaguely represents that of a sonata form.
Firstly the Form of the piece is in ABA form, A being from bars 1 – 31, B from bars 32 – 46, A returns in bar 47 – 78. Preceding A however is a bridge like section in bars 1 – 5 and again in 47 – 54. In bars 6 – 17 there is an introduction of the material, an Exposition if you will like in that of Sonata form. Bars 18- 23 show a slight development on the original A material. Bars 24 – 27, the sound thins out in terms of