My first orchestral work Tocco (written for the LSO’s Panufnik Composers Scheme in 2011) took as its starting point the process of change-ringing, the method used by bell-ringers to determine the order of bells within a peal. Indeed, much of my recent music has concerned itself with types of process and pattern, and of how to balance the rigour inherent in these processes with a more intuitive, ‘composerly’ approach. Mindful of this, I read D’Arcy Thompson’s seminal book On Growth and Form, which seeks to explain why organisms and physical phenomena take the forms they do, and was inspired to investigate a more mathematical approach towards formal organisation.

The form of Spiral is strictly governed by the proportions of a Fibonacci spiral, being divided into a number of sections, each one being shorter and faster than the last. Therefore, the temporal dimensions of the piece are constructed according to the following ratio: 233 / 144 / 89 / 55 / 34 / 21 / 13 / 8 / 5 / 3 / 2 / 1 / 1.

The cumulative effect is of a gradual ratcheting up of tension, as the initially contemplative material becomes ever more probing and animated. In a nod to the self-similar nature of fractals (in which of course the Fibonacci sequence plays a large part), the final, shortest section is itself then divided up according to the ratio 5 / 3 / 2 / 1 / 1, the last of which sub-sections (the period between the final tom-tom and temple block hits) has a duration of 1/24 of a second. This is the ‘singularity’ at the heart of the spiral, in which the form implodes, disintegrating under its own momentum.

As well as informing the overall shape of the piece, the Fibonacci sequence is also used on a smaller scale to generate both melodic and harmonic material: specifically, a line which rises or falls by 1, 2, 3, 5, 8 (and, in some cases, 13 and 21) semitones, occasionally ‘verticalised’ into a chord. The simultaneous use of the same numerical sequence on both the macro and micro levels is again intended as an allusion to the fractal world.

from notes by Alastair Putt © 2016