In 1983 it came to me to develop a new kind of mathematics which I call harmonic mathematics.
It is a way to create changes in the data of one of the senses (audio and/or visual) such that chaos continually changes into order, and back into chaos again
but in a way that is determined not by randomness, but by utilising the laws of harmonics, applied to movement or to other kinds of changes.
Applying it to visual motion or colour changes can create beautiful, exhilarating sequences of abstract visual action.
Applying it to timbre creates a series of deeply relaxing tonal changes – an orchestral richness of harmonics within a single tone.
Application to melody is also enormously exciting. One such application of melodic Harmonic Mathematics was a system of pieces called “Number Rays”.
These emerged in the spring of 1984, and were for me a colossal breakthrough in understanding how to create new dimensions of control and intricacies of change in music.
I also applied these techniques to creating many of my scores, including all of my 1st Symphony, and 3/4 of my 2nd, spanning the next 20 years and more.
The first melodic breakthrough was in rhythmic phase.
The composer Steve Reich created a series of pieces called Pianophase; Violinphase &c.
where performers playing an identically repeating figure are instructed that one overtakes the other, extremely gradually.
This is difficult to do with human performers, but with computer programming – although it is harder to program than one realises -
one can not only do it beautifully – but can extend the number of melodic streams going in and out of phase from 2 up to as many as one wishes (I have used up to 16).
The effect of 16 automated musicians playing this gradual phase change music is wondrous in the extreme, it challenges the mind to hear so so many beautiful details.
The next breakthrough I made was to alter the melodic loop as the streams were going on their magical “in and out of phase” journeys.
This gives an added interest to the musical texture, as now the rhythms AND the melodic patterns are both shifting and transforming magically.
In the Method Music album, I use spliced fragments of these sequences, some like these, others a more advanced design, but that gives a basic vivid idea.
To go back to the basic principle, when an array of points (points could be notes in a melody, or the position of a downbeat, or objects on a screen) change their position in a way that the speeds of change are harmonic
one at speed 1, the next at speed 2,then 3,4,5,6,7,8,9,10 &c, up to possibly 100s
then the changes behave like the natural harmonics of a tone, and they have all the beauty of the harmonics of a tone, and in some ways even more.
The late computer filmmaker John Whitney discovered the very basics of harmonic maths, which he calls “differential dynamics”, but he applies it only to actual motion, not to more sophisticated, or algebraic or abstract changes.
On youtube there are pendulum systems, (look up harmonics + pendulum), which are “differential dynamics” unplugged,
where one can see the most elementary form of this beauty of transformation that harmonic motion produces.
Even at this level one can see almost unbelievably satisfying changes that are as good as magic, if not actually, magical.
In the Method Music album, these mathematically magical sequences of melody and rhythms are edited with deliberation.
The intricate patterns of melodically and rhythmically evolving loops are loaded into and edited in a sequencer.
My program creates giant marathon slabs of this contrapuntal chocolate, which can be broken off into usable chunks.
I used such pieces of these richly woven mega-strands, laid them down and edited them, to maximise their “speaking”.
In the Lifehouse-Method portraiture there are streams of combinable sounds auto-generated,
but everything is done without human intervention, it is a sealed system,
an automatic generation is the only option for online portraiture.
Method Music – the double album – is released on January 31st 2012 by Navona Records, available on Amazon and iTunes