No Mr Pythagoras, we love dissonant music too!

NEW DELHI: Challenging one of the theorems of Greek philosopher Pythagoras, a new research has found that musical ‘consonance’, or the pleasant-sounding combination of notes, may not have to be in mathematical ratios to be appreciated by listeners as harmony.

These findings about the impact of instrument tuning on musical harmony appreciation challenge centuries-old Western music theory and throw the field open to more experimentation with instruments from different cultures.

According to Western music’s notion of harmony, certain chords will sound particularly pleasant or consonant, while others will sound relatively unpleasant or dissonant. Pythagoras’ concept of ‘consonance’ regards the pleasantsounding combination of notes to be produced by special relationships between simple numbers such as 3 and 4, they said.

However, the team of researchers, including those at Max Planck Institute for Empirical Aesthetics, Germany, said in their study published in the journal Nature Communications that in contexts of normal listening, people 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 the study’s co-author

Peter Harrison from Cambridge University’s Faculty of Music and Director of its Centre for Music and Science.

They found that when certain musical instruments less familiar to Western musicians, audiences and scholars were thrown in the mix, the role played by these mathematical ratios and relationships disappears.

“When we use instruments like the (Javanese) bonang (a collection of small gongs), Pythagoras’s special numbers go out of the window and we encounter entirely new patterns of consonance and dissonance,” 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,” he explained. “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’,” said Harrison.

We prefer slight amounts of deviation. We like a little imperfection because this gives life to the sounds, and that is attractive to us

— Peter Harrison, Cambridge University