People have long known that professional musicians don’t keep time with the dogged precision of a metronome. However, in deviating from a perfectly steady beat, one professional drummer makes patterns in his timing and loudness that have a particular mathematical form—a fractal—a new study shows. Previous research has shown that the fractal nature of time deviations makes music sound distinctly human.
A fractal is a pattern that looks "self-similar" on many different scales. For example, statistically, a coastline may look just as jagged on the scale of 10 kilometers as it does on the scale of 1000 kilometers. Fractals can emerge in temporal patterns, too, and researchers have observed rhythmic fractal patterns in many controlled musical experiments. Such work sheds light on the unique signatures that musicians impart into their work, and it could help researchers make the rhythmically perfect music generated by computers and drum machines sound more human.
Holger Hennig, a physicist at the Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany, and colleagues decided to analyze the technique of prolific drummer Jeff Porcaro, one of the more famous musicians most people have never heard of. For more than a decade he drummed for the band Toto, and as a session musician he kept time for an extensive list of musical icons including Pink Floyd, Steely Dan, Michael Jackson, and Madonna. Porcaro died of a heart attack in 1992. Hennig and his colleagues chose to study Porcaro’s technique because the paper’s lead author, physicist Esa Räsänen of the Tampere University of Technology in Finland, is himself a drummer and admires Porcaro’s work.
As a representative sample of Porcaro’s timekeeping skills, the research team focused on the studio recording of the 1982 hit “I Keep Forgettin’ ” by singer Michael McDonald. The rapid, high-pitched tink-tink-tink-tink keeping the beat is the hi-hat, a clamshell arrangement of two small cymbals that a drummer opens and closes with a foot pedal and simultaneously strikes with a drumstick. With one hand, Porcaro hit the hi-hat four times on every beat, in subbeats known as sixteenth notes, and motored out almost 400 of them in every minute of the song.
To the listener, the tinks sound flawlessly steady. But Hennig knew that the fractallike deviations he’d observed in previous studies were imperceptible to the human ear, and he wondered whether Porcaro’s rhythm would obey the same mathematical laws. He was also curious about what he’d find if he analyzed the volumes of the tinks, which Porcaro clearly modulates. So Hennig and his team pored over the 1982 recording and 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. 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.”
Psychologist Edward Large, director of the Music Dynamics Laboratory at the University of Connecticut, Storrs, who was not involved in the study, agrees that the fractal patterns Hennig’s team discovered in amplitude are exciting. “That, in a way, is the stronger analysis in this particular paper,” he says.
What’s more, timing and volume varied independently, so that the fractals formed by each were different. That observation surprised and enticed Large. “If most of my colleagues had seen that [loudness and timing] were highly correlated, they would have said, ‘of course,’” Large says, because musicians tend to play faster music louder, and vice versa. But instead, “there’s some independent control going on that’s really subtle.”
Hennig plans to continue studying rhythmic patterns found in recorded music and produced by multiple players. That work should 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 many other recording artists.
Hennig doesn’t feel that his work demystifies a raw human art form. In fact, 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 says. “But on top of that, we expect that there’s some Jeff Porcaro magic in there.”