Theoretical writings
A Changing Role for the Composer in Society
A study in the historical background and current methodologies of creative music-making.
(Peter Lang AG, European Academic Publishers, Bern 2005)
All-Interval Fractal Sets – the full picture
Abstract:
This paper replaces my paper "All-interval fractal sets - an analysis" first published in 2019 describing the process that led to my discovery of all-interval fractal sets. In it I estimated the total number of melodic phrases made up of the 6 primary intervals conforming to a set of simple rules as 256. I also challenged any mathematician to come up with an algorithm that would prove my hypothesis or find more viable sets that my cumbersome trial-and-error had missed. I am delighted to reveal that such a person has come forward in the form of Professor Carl Dettmann of the University of Bristol. Not only has Professor Dettman devised a successful algorithm but has also found 56 new sets bringing the total number to 312. In this new paper I again analyse their characteristics, revealing even more remarkable new relationships and symmetries. In an appendix I attach the actual new algorithm naming it after its originator, the Dettmann Code, plus a copy of the complete set of raw numerical date it generated. I again attach an appendix showing how the same principles of all-interval fractal sets can be applied to scales based on divisions of the octave by numbers other than 12.
All-Interval Fractal Sets and the Fibonacci Series
Abstract:
This paper presents an analysis of proportional relationships created by the multiplication of All-Interval Fractal Sets to the nth degree to produce fractal structures of infinite length. The resulting quasi-geometric series is compared with other geometric and quasi-geometric progressions such as the Corbusier Modulor and the Fibonacci Series.
Zooming into infinity - All-interval Fractal Sets and the Mandelbrot zoom.
Abstract:
This paper represents a new stage in my investigation of the properties of All-Interval Fractal Sets. My objective is to discover a way to use the sets too mimic the complex mathematical visualisations of so-called Mandelbrot zooms created in the well-known computer animations.
Sea Chords - A technical description of their derivation and use
Abstract:
Anyone who has read the programme notes of any of my works since the early 90s will have come across frequent references to something called “sea chords” and perhaps wondered what on earth they are. The sea chords are so-called because they were invented for the sea interludes of my opera “Seven Stars”. In this paper I describe how they were devised and what rules and procedures I have been able to develop to govern their use in musical composition.
The Creation Project
The Creation Project is a planned collection of settings for choir and instrumental ensemble or orchestra of texts that trace the story of scientific and cosmological discoveries over the past 600 years selected from the visionary writings of men and women of science who contributed to the advance of knowledge and understanding.
The Creation Project was prompted by my growing sense of incongruity when taking part in performances of Haydn’s “Creation”. Much as I admire Haydn’s great oratorio from a musical point of view, I can no longer take seriously a work which celebrates the now discredited biblical version of the creation of the world in seven days by an all-knowing and all-powerful god.