![]() It’s an intermediate between white noise and random walk ( Brownian motion) noise. You might know 1/f noise by its other name, pink noise. Where f is frequency, on an interval bounded away from both zero and infinity. Here’s some background from Scholarpedia:ġ/f noise refers to the phenomenon of the spectral density, S(f), of a stochastic process, having the form So what does the 1/f in “1/f noise” refer to? Each group reflects the form of the whole, in pitch contour or patterns of tension and resolution or whatever. You can think of a musical fractal as groups of events combining to form larger groups of events, which themselves combine still larger groups - loops within loops within loops. It’s not so easy to imagine what the musical analog would be. It’s easy to grasp what a fractal is by looking at pictures like the one above. So it’s no big surprise that the same should be true of things we enjoy listening to as well. Basically everything we enjoy looking at has a fractal quality. Fractals are all around us: in clouds, trees, mountains, coastlines, and our own bodies. Here’s an article explaining what it is and why it’s so cool. The image above is part of the famous Mandelbrot set. Music is full of fractals, and the more fractal-filled it is, the more we like it. Power-law distributions have the nifty property of scale invariance, meaning that patterns in such entities resemble themselves at different scales. Specifically, they find that note durations, pitch intervals, phrase lengths and other quantifiable musical parameters tend to follow a power law distribution. (The paper isn’t on the open web, but here’s a poster-length version.) The authors think that fractals explain our music preferences. Quora user Marc Ettlinger recently sent me a paper by Sherri Novis-Livengood, Richard White, and Patrick CM Wong entitled Fractal complexity (1/f power law) determines the stability of music perception, emotion, and memory in a repeated exposure paradigm. See also my posts on the science of rock harmony, harmony generally, and Afro-Cuban rhythms. Continuing my series of posts on the ways that science might explain why we like the music we like.
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