Fractal Drumming and Pink Noise
Fractals, the extraordinary self-similar patterns in nature and math that repeat at every scale, have been discovered in leaves, trees, clouds, coastlines, seashells, hurricanes, and the swirling gasses in outer space. They’ve also been found in art and music, and recently in rhythms of a musical mind.
Physicist Holger Henning and colleagues at the Max Planck Institute for Dynamics and Self Organization in Gottingen, Gemany, and colleagues decided to analyze the technique of drummer Jeff Porcaro, in the 1980s Michael McDonald song “I Keep Forgettin’.” For more than a decade Porcaro, who died of a heart attack in 1992, drummed for the band Toto, and as a session musician he kept time for musical icons including Pink Floyd, Steely Dan, Michael Jackson, and Madonna. Porcaro’s technique was chosen for study because one of the researchers, Esa Räsänen of the Tampere University of Technology in Finland, is himself a drummer and admires Porcaro’s work. The scientists’ analysis of the fluctuations and dynamics of drumming in the song is published in PLOS One.
The research is also described in a Nova Next story by Anna Lieb. The signature rhythm, she writes, comes from Porcaro’s work on a pedal operated cymbal known as a hi-hat. The scientists measured the spacing between the hits and the volume of each hit and found a fractal sound pattern sometimes called “pink noise.” Lieb explains the name comes from the color of the visible light that comes from the frequency spectrum of the sound.
While the listener hears flawlessly steady drumming, Hennig knew that the fractal-like deviations he’d observed in previous studies were imperceptible to the human ear. Porcaro hit four hi-hats per beat and nearly 1,000 hi-hats by the end of the song. Hennig and his team statistically analyzed the onset times, interbeat intervals, and amplitudes of Porcaro’s sixteenth notes. Both the intervals between sixteenth notes and their volumes wavered throughout the piece, and those variations were similar on time scales, ranging from a few seconds to the length of the entire song, forming a fractal pattern. “It seems that the timekeeper in the brain not only produces fractal timing,” Hennig said, “but likely also fractal intensity or, in this case, loudness.”
The scientists noted the volume and spacing were independent of each there, suggesting Porcaro was controlling each separately.
Hennig plans to continue studying rhythmic patterns found in recorded music and produced by multiple players. Previous research by Hennig and others has shown humans prefer music that exhibit the fractal nature of time and volume patterns produced by individual musicians over computer generated music with the dogged precision of a metronome. Hennig’s new research may help him hone a computer algorithm he developed to introduce “humanizing” imperfections into computer-generated music. His software is already being used by electronic musician James Holden and other recording artists.
Hennig doesn’t think his work demystifies art He thinks the study shows how beautiful and mysterious the human brain can be. “I would say that we are totally unpredictable and somewhat predictable at the same time,” he said. “But on top of that, we expect that there’s some Jeff Porcaro magic in there.”
Fractals have been identified in many types of music. Compose and music researcher Dmitri Kormann, or instance, has analyzed fractal patterns in musical pieces that inlude Igor Stravinsky’s “Rites of Spring” and John Cage’s percussion sextet “First Construction.”
Read the PLOS One paper here and the Nova Next story here.
With thanks to Tuyen Tran.