Summary: New research challenges Pythagoras’s ancient theory on musical consonance, revealing our preference for slight imperfections in chords rather than the perfect integer ratios traditionally associated with beautiful music.
The study highlights how the mathematical relationships deemed crucial for a chord’s beauty disappear with instruments unfamiliar to Western traditions, such as the Javanese gamelan’s bonang.
Over 4,000 participants from the US and South Korea, through online experiments, demonstrated a significant preference for these “inharmonic” sounds, indicating a broader and instinctive appreciation for varied musical harmonies beyond Western norms.
This opens up exciting opportunities for exploring new harmonic languages that resonate with listeners without prior musical training, encouraging musicians and producers to experiment with diverse instruments for innovative musical expressions.
Key Facts:
- Imperfection Preferred: Listeners actually favor chords with slight deviations from perfect mathematical ratios, finding beauty in minor imperfections.
- Cultural Diversity in Harmony: Traditional Western focus on specific musical instruments limits the exploration of harmony, while instruments like the bonang introduce new consonance and dissonance patterns.
- Universal Appreciation for New Harmonies: Even without musical training, people instinctively enjoy the unique consonances of non-Western instruments, challenging the notion of a universal harmonic language based on mathematical ratios.
Source: University of Cambridge
According to the Ancient Greek philosopher Pythagoras, ‘consonance’ – a pleasant-sounding combination of notes – is produced by special relationships between simple numbers such as 3 and 4.
More recently, scholars have tried to find psychological explanations, but these ‘integer ratios’ are still credited with making a chord sound beautiful, and deviation from them is thought to make music ‘dissonant’, unpleasant sounding.
But researchers from Cambridge University, Princeton and the Max Planck Institute for Empirical Aesthetics, have now discovered two key ways in which Pythagoras was wrong.
Their study, published in Nature Communications, shows that in normal listening contexts, we 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, Dr Peter Harrison, from Cambridge University’s Faculty of Music and Director of its Centre for Music and Science.
The researchers also found that the role played by these mathematical relationships disappears when you consider certain musical instruments that are less familiar to Western musicians, audiences and scholars.
These instruments tend to be bells, gongs, types of xylophones and other kinds of pitched percussion instruments. In particular, they studied the ‘bonang’, an instrument from the Javanese gamelan built from 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,” Dr Harrison said.
“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 researchers created an online laboratory in which over 4,000 people from the US and…
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