Background: The main inspiration for this composition was Claude Debussy’s ‘Les sons et les parfumes tournent dans l’air du soir’ (1911), particularly because of the arrangement of harmonies and phrases. Within the melody of the ‘Hidden Passageways’, the pitches were computed through converting the numbers of the Fibonacci sequence onto an octatonic scale. To compute this, the pitches were calculated through a modulus of 8. A few rules were set in place before starting the compositional process, such as only using the numbers to establish the melody and allowing rhythms or harmonies to be created without the sequence's influence. Furthermore, the lengths of sections were also determined by the golden ratio, a number that directly correlates to the Fibonacci sequence. Lastly, the sequence would have to develop chronologically, but phrases were allowed to be repeated to aid the musical process (this can be seen in bars 12-13, where bar 13 is a repeat of bar 12, this aspect will be discussed further in the conclusion). Additional inspiration included Maurice Ravel’s ‘Sérénade grotesque’ (1893) for the different types of contrasts and tonalities.

Commentary: The composition opens with a repeating note on C with a resultant ascending flourish. This idea is repeated whilst gradually adding more notes to the flourishes before abruptly stopping at the end of bar 11. All of the melodic notes in these phrases are based upon the Fibonacci numbers where C = 0, C-sharp = 1, D-sharp = 2, E = 3, F-sharp = 4, G = 5, A = 6, A-sharp = 7 and the idea behind the repeated note of C is to show how without manual intervention to the sequence, the number 0 (or the note C) will infinitely repeat. Harmonic and rhythmic content are not based upon the sequence and this is the case throughout the composition. The first example of this is in bar 2 with the addition of the note of A. For the remainder of the composition, phrases are arranged into two bars each, similar to the previously mentioned Debussy prelude.

Throughout this composition, contrasts are brought to the forefront. This is mostly achieved through the use of staccato and legato notes that help differentiate the fragments of musical material from one another. The Fibonacci sequence and the end of the first section finishes in bar 25 and the resultant section is created by inverting the melody of the first section around the note of C. Inspiration for inverting this section came from researching Béla Bartók’s work with symmetry or inversion of musical material in their piano compositions (Pearsall, 2004). This section continues until bar 52, transitioning into a developmental section.

The penultimate section develops the material created in the previous two sections. There is also a distinct shift towards more tonal harmonies as contrasts become less frequent. The coda at bar 69 utilises the opening material and slowly fades away to a singular staccato note. Additionally, throughout the composition there is a recurring low E note. This is most recognisable in the last few bars where there is an evident retrograded rhythmic Fibonacci identity. The rhythm of this note is not interrupted and is repeated multiple times such as in bar 19, 57, 65, 69 and 72.

Finally, the proportions of each section have been chosen inline with the golden ratio, or a modified Fibonacci sequence. Here, the number of beats are closely in proportion with this constant so that the introduction lasts 31 beats, the first section lasts 50 beats, the second section lasts 81 beats, the development lasts 50 beats and the coda lasts 31 beats. From this, a symmetry of the lengths of sections is created.