Musical Idea 27: Context Threshold
04.05.2014 § Leave a comment
There are not parts of music, but parts of music in context, that what matters is the transition.
There’s really just two properties:
The number of elements, like if it’s three then you’re dealing with A, B, and C
The context threshold, meaning how far you care to look. Perhaps it is an open question whether it matters to look only one direction, forward or backward. Threshold 1 means that you consider B sandwiched between two A’s to be different than a B between an A and B. However, you wouldn’t distinguish the middle B in AABAA from AABAB; the fifth character is two away from the middle one so it wouldn’t “see” it.
So when implementing a context fractal, you basically just consider the set of all clusters of the size determined by your context threshold. Then attempt to lay them on top of each other, offset by one each time, to progress through, and end up perfectly by the end having gone through every element’s possible contexts. It can also be thought of as a tree whereby each node branches into each element, but you can only choose to move to the next node if it will not result in the repetition of a previous sequence of length according to the context threshold. Thus while it is not necessarily a means toward maximum evenness of distribution of the elements on a macro scale, it is a perfectly efficient document of all micro scale distributions.
Combining the different possible iterations of the same parameters in sequence or unison can give rise to interesting textures.
Context fractals can be applied to music at scales ranging all the way from form, through melody, to timbre.