Music is pleasing when it mixes expectation and surprise in the right amount. But what you may not know is that pleasing music also follows a pattern that can be frequently found in nature.
Let "f" equal "frequency." "1/f" noise lives between "white," or undifferentiated, noise, and "brown noise," where each note is closely related to the prior note - resulting in a rather linear pattern to the human ear.
Musical sounds, however, will generally trace a separate profile. Science journalist Samuel Arbesman:
In between though, is what is known as 1/f noise. Sometimes also called pink noise, this music has some correlation, but less than brown music and more than white noise. It is defined as a power law decay in the correlations between pitch over time. The equivalent in motion include what are called Lévy flights, which are similar to how bank notes travel around the United States: sometimes traveling very short distances, and at other points hopping across the country. (Note: This type of power law is related to the normal type of power laws that many of us have heard of, where the “popularity” of phenomena follows a heavy-tailed distribution.)
Most music that we actually listen to is 1/f noise. It has the right combination of pattern and unexpectedness, and is pleasing to the human ear. And as a fun bonus, if you look at the shape of the curve described by 1/f music, it has a fractal shape. Just as shapes in nature are often fractals — self-similar objects at all scales — so is it true with human-created music.
If I understand the algorithm correctly, 1/f pattens should be infinitely recursive as well. It's probably too big a stretch, but I wonder if that is responsible for some of the transcendence I experience listening to Beethovan's Ninth Symphony or the cello and piano denouement in the second half of OneRepublic's "Waking Up," or the searing and haunted strains from the film "Watlz with Bashir."