Pop music in the 1980s was full of weirdness, but no amount of Madonna or “The Safety Dance” will prepare you for what scientists recently found in a Michael McDonald song—fractals.
Physicist Holger Henning and colleagues at the Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany found self-similar patterns in the drum pattern of a recording of the 80s hit song “I Keep Forgettin’.” This pop classic features drummer Jeff Porcoro, who was a member of Toto and has played for other big names like Steely Dan, Madonna, and Pink Floyd.
Loosely speaking, a fractal pattern is distinctly recognizable no matter how much you zoom in or out, a property known as self-similarity. For example, if you show a pattern to a person looking through a microscope and to an astronaut looking down from orbit with a telescope, and they describe the same thing, then that pattern is self-similar. Fractal patterns show up both in mathematics and nature, from the intricate contours of the Mandelbrot set to the mesmerizing florets of the broccoli-like vegetable romanesco . Scientists recently noticed that when people make musical rhythms, the resultant pattern of sound has a fractal nature.
The signature rhythm in “I Keep Forgettin’” comes from Porcaro’s handiwork on pedal-operated cymbal known as a “hi-hat.” Porcaro fires off four “hi-hats” per beat, for a total of nearly 1,000 hi-hats by the end of the song. The study authors analyzed the distinctive sound of a hi-hat in order to filter out all the other instruments. They then looked at two properties of the pattern of hi-hats: the spacing between hits, and how loud each hit was.
Here’s Kerry Klein, reporting for Science News:
Both the intervals between sixteenth notes and their volumes wavered throughout the piece. Moreover, those variations were similar on time scales ranging from a few seconds to the length of the entire song (3 minutes and 39 seconds), showing that the pattern formed fractals, the researchers reported on 3 June in PLOS ONE. “It seems that the timekeeper in the brain not only produces fractal timing,” Hennig says, “but likely also fractal intensity or, in this case, loudness.”
Hennig and his team found that both the intervals and volumes could be described by a fractal pattern called “1/f noise.” In this kind of noise, each octave carries the same amount of energy per unit time. The description is sometimes referred to as “pink noise” because visible light whose spectrum has this property is a pink color. The self-similarity comes up in how the pause between two hi-hats depends on the pauses already played. If the size of the space between two hi-hats is just as correlated with the five preceding spaces as it is with the preceding 50 or 500—that is, if it depends on the entire song so far—then the pattern of pauses is self-similar. The loudness followed the same idea.
What’s more, the loudness and spacing were independent of each other, suggesting Porcaro was controlling them separately. The work, a glimpse into the brain of a talented and prolific musician, offers a fascinating picture of what makes human music human.
Photo credit: Gamma Ray Productions/Flickr (CC BY-SA)