Pythagoras was wrong (Picture: Getty)
Polymath Pythagoras believed the tone and tuning of musical instruments influenced our appreciation of harmony – but little did he know he was so very wrong.
New research has found that people actually prefer imperfect sounds, challenging thousands of years of Western belief of how people appreciate harmony.
The theory from Pythagoras says the ringing sounds of a blacksmith’s hammers sounded most pleasant, or ‘consonant’ when the ratio between the size of two tools involved two whole numbers, or ‘integer ratios’ such as 3:2.
This belief shaped how Western musicians play chords as Pythagoras’ theory was so influential.
However, when Dr Peter Harrison, at the University of Cambridge, and his colleagues surveyed people in the US and South Korea about their perceptions of music, their findings revealed the much-revelled theory was far from the truth.
The researchers found that listeners preferred sounds with an imperfect ratio.
From the 23 behavioural experiments, over 235,000 human judgments were produced when the researchers explored musical chords from different perspectives. They were surprised to find a significant preference for slight imperfection, or ‘inharmonicity’.
Ionic Greek philosopher and mathematician (Picture: PHAS/Universal Images Group via Getty)
‘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 Dr Harrison.
One experiment showed little difference in appeal between the sounds from instruments from around the world including the bonang, an Indonesian gong chime which uses consonances that cannot be replicated on a Western piano.
‘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,’ said Dr Harrison.
‘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”.’
The study suggests that the participants, who were not trained musicians and were unfamiliar with Javanese music, appreciated the new consonances of the bonang’s tones instinctively.
Now Dr Harrison hopes the research will encourage musicians to try out unfamiliar instruments and lead to more creative possibilities.
‘Our findings suggest that if you use different instruments, you can unlock a whole new harmonic language that people intuitively appreciate, they don’t need to study it to appreciate it,’ he added.