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Journalism of Courage
You may know Pythagoras for the theorem that tells you about the sides of a right-angled triangle but the ancient Greek was a polymath in the true sense of the word, dabbling in philosophy, mathematics and many other fields. But now, a new study has found that one of his theorems may have been wrong.
Pythagoras proposed that “consonance,” or the pleasant-sounding combination of notes is produced by the special relationship between simple numbers. Many researchers have tried to find psychological explanations but these “integer ratios” the ancient Greek philosopher talked about are still often credited with making chords sound beautiful, and it deviating from them is thought to make music “dissonan,” or sound unpleasant.
But a new study published in the journal Nature Communcations this month found two key ways in which Pythagoras was wrong. It showed that it normal listening contexts, humans do not actually prefer chords to be perfectly in these mathematical ratios.
“We prefer slight amounts of deviation. We like a little imperfection because this gives life to the sounds, and that is attractive to us,” said co-author, Peter Harrison, from Cambridge’s Faculty of Music and Director of its Centre for Music and Science, in a press statement. The study was conducted by researchers from University of Cambridge, Princeton and the Max Planck Institute for Empirical Aesthetics.
Further, they found that the role played by these mathematical relationships disappears when you consider some musical instruments that are less familiar to Western musicians, audiences and scholars. These instruments could include bells, gongs, xylophones and other pitched percussions instruments. The researchers particularly focused on the “bonang,” an Indonesian instrument that consists of a collection of small gongs.
“When we use instruments like the bonang, Pythagoras’s special numbers go out the window and we encounter entirely new patterns of consonance and dissonance. The shape of some percussion instruments means that when you hit them, and they resonate, their frequency components don’t respect those traditional mathematical relationships. That’s when we find interesting things happening. Western research has focused so much on familiar orchestral instruments, but other musical cultures use instruments that, because of their shape and physics, are what we would call ‘inharmonic’, ” added Harrison.
For the study, the researchers created an online lab with over 4,000 participants from the United States and South Korea participating in 23 behavioural experiments. Chords were played and the participants were asked to give a numeric pleasantness rating or to use a slider to adjust the particular notes to make it sound more pleasant.
The researchers were surprised when they found a major preference for slight imperfection or “inharmonicity.” Other experiments also produced similar results.
