The Nautilus is a brass quintet based upon the Fibonacci sequence. The sequence determines various elements of the music, including the structure, tempo and tonality of the piece.
A Brass Quintet Based Upon the Fibonacci Sequence
For this brass quintet, I have developed my own form which uses the Fibonacci sequence in various elements of the music. The form is seen more clearly within the tempo changes and modulations, which use a formula that is relevant to the Fibonacci sequence. This decides where the tonality of the music is taken.
|The Fibonacci Sequence||1||1||2||3||5||8||13||21||34||55|
I began this composition by developing a code for all the notes on a piano, which would be paired with a number. The lowest A would be labelled 1, and the highest C would be labelled 88. By applying the Fibonacci sequence to this code, the keys would be automatically selected, which allowed for my form to have a tonal structure.
Table demonstrating the code that I have used.
There are 8 key modulations, and the number of bars for each modulation is dependent on the sequence, increasing in quantity each modulation as the sequence extends.
The tempo changes at bars 1 and 13, with the bpm values being numbers that are within the Fibonacci sequence (55, 89).
Due to the nature of the form within The Nautilus, I am restricted with the number of tempo changes in the piece, if it is to fit within the 2-minute boundary. An extended (more idealistic) version of The Nautilus would see more tempo changes following the applied formula, however the entire piece would then need to be much longer.
|Number of bars in section||1||1||2||3||5||8||13||21…|
|Tempo||Larghetto = 55bpm||Moderato = 89bpm||Vivacassimo = 144bpm…|
The Nautilus finishes at the end of bar 21. An extended edition of The Nautilus would include faster tempos and further modulations as the piece progresses.