I’ve been googling self-similarity in music. It seems there was interest in finding fractal orders in music 10-20 years ago. These are some of the papers I’ve found:
- Using self-similarity for sound/music synthesis
- Automatic composition: Experiments with self-similar music
- Self-similarity of the”1/fnoise”called music
- Self-similar pitch structures, their duals and rythmic analogues
- Profile: a musical fractal
I’ve only skimmed over them, but their appropriation of self-similarity seems simplistic. It is mostly applied to melody and rhythm. That’s my first observation.
My second observation is that Perlin Noise introduces an extra dimension that I suspect is what helps it achieve that particular resonance with reality. Perlin Noise is typically applied over an area … that is: over 2 dimensions. Most sound parameters can only be mapped in 1 dimension (typically time).
In fact, I’ve found a definition of Perlin Noise that specifically makes that point
Perlin noise is function for generating coherent noise over a space. Coherent noise means that for any two points in the space, the value of the noise function changes smoothly as you move from one point to the other — that is, there are no discontinuities (from here).
Perlin Noise can then be extended to a 3rd dimension, which will typically be time.
So my thinking now is that to explore Perlin Noise in the audio domain, it would be best to start with audio parameters which can be described using 2 dimensions.