Background: This composition was inspired by Claude Debussy’s ‘Reflets dans l'eau’ (1905) because of the composer's potential usage of the Fibonacci sequence that was discussed in an analysis by Roy Howat (Howat, 1994). Within the opening bars of Debussy’s piece, there are 8 rising and 5 descending chords over 3 descending notes, all corresponding to the Fibonacci numbers. There is also a larger structural concept relating to the proportions of the sequence such as the climax being arranged around 60 percent of the way into the piece, matching the golden ratio value (Howat, 1994). These ideas have greatly inspired this composition where the sequence has been used to determine the number of chords in the introduction and the proportions of sections. Additional inspiration includes Debussy’s ‘La Cathédrale Engloutie’ (1910) for the chordal passages and Maurice Ravel’s ‘Une barque sur l'océan’ (1906) for the various types of arpeggios.

Commentary: The composition opens with ascending chords over a B-flat note in the left hand. Each bar includes a new chord and the number of chords is determined by the numbers in the Fibonacci sequence (for example, bar 1 contains 1 chord, bar 2 contains 2 chords, bar 3 contains 3 chords, bar 4 contains 5 chords, etc…). The repeating B-flat note represents the larger structure of the piece through the use of a rhythmic identity that is inline with the Fibonacci numbers. This is achieved by letting a quaver be equivalent to the number 1, then the rest of the rhythms are sums of quavers. In bar 7, a chromatic melody is introduced that is derived by transforming the Fibonacci numbers into a pitch set. Furthermore, in bar 21 the greatest range of the pitch set on a piano is introduced through octaves in the bass and treble clef.

These ideas develop until a chordal section that is based upon D-flat 7 and A-flat 7 chords. The B-flat note in this section is positioned off the beat and in its correct position (in terms of the Fibonacci numbers) instead of the first beat so that this structural cue is not lost in the first chord. This chordal passage fades away into a similar theme to the introduction with modified harmonies. These chords are then developed into arpeggios and the bass clef plays the chromatic melody from bar 7 in inversions. Overall, this section is designed as a development of ideas and more creative freedom away from the sequence was allowed to occur compared to other parts of the composition.

In preparation for the climax of the composition, these ideas build until a short abrupt pause followed by an emphasised B-flat note. This section combines the chordal and arpeggiated passages together. Because of the span of the arpeggios, the performer is allowed to play them freely whilst keeping the rhythmic identities of the chords intact. The harmonies balance between chromatically spaced seventh and ninth chords before settling on a D-flat 7 chord. From this point until the end of the composition, previous melodies and harmonies are developed before ending with the note of B-flat.

(Composed for an assignment at the University of Birmingham)