Today, the Greek philosopher Pythagoras, known mainly for the theorem of the right triangle, tried to understand the beauty of ** with mathematics.
As a result, the harmonious combination of notes known as ** consonants relies on a simple "integer ratio" in the frequency or tone of the sound to sound appealing. What's more, the philosopher insisted that it was true no matter what the instrument was.
An international research team surveyed the responses of 4,272 volunteers to certain chords and found otherwise. Mathematically, these reactions show a preference for **, but there are some flaws in it.
Listening survey. 
Participants were asked to rate the sounds they heard (Marjieh et al.).，nature communications，2024）
Peter Harrison, a ** psychologist at the University of Cambridge, said: "We prefer slight deviations. ”。We like a little bit of imperfection because it brings the sound alive, which appeals to us. ”
The team also found that the integer ratios that Pythagoras were so fond of could be completely ignored when it came to instruments less familiar to Western listeners: bells, gongs, xylophones, and a series of gongs known as boons.
Research responses to this Indonesian instrument have revealed entirely new patterns of harmony and disharmony. These patterns match the scales used in Indonesian culture and cannot be accurately mapped to the preferred scales in places like the United States and Europe.
In other words, timbre (the part that makes the sound sound like it belongs to a particular instrument) can also affect the consonant, which may have surprised Pythagoras. These results show that listeners can recognize pleasing sounds even if they are not homemakers or familiar with the instrument.
"The shape of some percussion instruments means that when you strike them and resonate, their frequency components (tones) don't respect those traditional mathematical relationships," Harrison said. ”。That's when we'll find out that something interesting is happening. ”
This relationship between timbre and consonants may be why some cultures have ended up adopting a different note scaling system than the one we Westerners are most familiar with.
"These results provide an empirical basis for the idea that cultural differences in scale systems may be driven in part by the spectral properties of the instruments used by these different cultures," the researchers wrote in **. ”。
The team hopes that their findings – which cover a total of 235,440 human judgments – will shed light on what is pleasant and what is not—especially when it comes to lesser-known instruments.
Both the home and the listener can benefit from a little experimentation, as well as from stepping out of our comfort zone, the researchers say. Future research plans to analyse a wider range of instruments and cultures, particularly with regard to what may have previously been considered "dissonance".
"If the family and producers had taken into account our findings and had thought about changing the tone and quality through the use of specially selected real or synthesized instruments, they might have made the marriage work better," Harrison said. ”。
And then they can really have the best of both worlds: harmony and a system on a local scale. ”