The Nautilus


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 Sequence11235813213455
The Fibonacci sequence, where each number adds to it the value of the previous number

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.

Bar Number12358132134…
Number of bars in section1123581321…
TempoLarghetto = 55bpm    Moderato = 89bpm Vivacassimo = 144bpm…
Table demonstrating the structure of The Nautilus.

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.