I’ve got to check that I’ve got this right, but it seems that an algorithmic analysis I’ve written of a Bach 3-part invention reveals a fractal. It’s based on a table of entropies for different basic variables (pitch, rhythm, intervals, etc). An increase in entropy is a value for a variable “x”, where a decrease in entropy is a value for “not-x”. Taking the variables as A, B, C, D, etc, there is also the values for the combined entropies of AB (and not-AB), AC, BC, etc. And also for ABC, ABD, BCD, and so on.
The raw table looks a bit like this:
But plotting this looks something like this:
What a fascinating thing that is! It should be read from left to right as an index of increasing complexity of the variables (i.e. more combined variables), with those at the far left the simplest basic variables. From top to bottom is the progress in time of the music.
My theory is that music continually creates an anticipatory fractal, whose coherence emerges over time. The fractal is a selection mechanism for how the music should continue. As the selection mechanism comes into focus, so the music eventually selects that it should stop – that it has attained a coherence within itself.
Need to think more. But the power of the computer to visualise things like this is simply amazing. What does it do to my own anticipatory fractal? Well, I guess it is supporting my process of defining my own selection mechanism for a theory!