What makes a pair, or a trio, of notes sound beautiful when played together in a chord, while another might send your hands flying to your ears?

Western musical tradition holds that chords sound beautifully ’consonant’ when the fundamental frequencies of the individual tones have a low, simple ratio — when that ratio is 2:1, for example, or 3:2. Deviations from this are thought to make for unpleasant, dissonant chords. It’s been argued — by the Ancient Greek philosopher, Pythagoras, no less — that this ‘rule’ of musical harmonies is universal. In other words, it should apply to chords played on all instruments, in all cultures.

But a recent paper in Nature Communications suggests that this is not correct. In fact, through a series of online studies that involved more than 4,000 people and 235,440 individual musical judgements, Raja Marjieh at Princeton University and colleagues found two key discrepancies between what has long been assumed to underpin consonance and what listeners felt actually made a chord sound pleasant.

The first key discovery was that Western participants didn’t actually most prefer chords in which the frequencies of the constituent notes were in perfect mathematical ratios. In fact, these listeners rated chords with slight deviations from a perfect ratio as being the most pleasant. Exactly why they found these more enjoyable isn’t clear, but the team believe that the answer may lie in the slow, pulsating beats which slight deviations create. They suggest that listeners may enjoy these “for the feeling of richness that they convey.”

The other major discovery, from an analysis of reports from participants from South Korea as well as the US, was that while chords from non-Western percussion instruments, in particular, did not follow the ‘rule’ of simple mathematical tone ratios at all, they could still sound pleasant.

As an example, the team cites the bonang, a Javanese instrument made up 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,” commented co-author Peter Harrison of Cambridge University in a statement.

This seems to be a product of the shape of the bonang gongs, which have a different ‘timbre’ or tone quality to Western instruments. When these gongs are struck, and they resonate, they produce different sound frequencies that just don’t match the notes in Western musical scales or fit with Western mathematical ‘rules’ of music. However, the team found that they did fit with the ‘slendro’ musical scale from Indonesia. “These results provide an empirical foundation for the idea that cultural variation in scale systems might in part be driven by the spectral properties of the musical instruments used by these different cultures,” the researchers write.

Harrison suggests that if more Western musicians used instruments from non-Western cultures, they could “unlock a whole new harmonic language that people intuitively appreciate.” He also warns that taking a piece of music composed for an Indonesian gamelan orchestra, for example, and playing it on Western instruments may well not work, because the different resonances could mean that Indonesian music on Western instruments could sound dissonant. Instead, he advises musicians or music producers seeking to create fusion music to use instruments (or synthesized versions of instruments) with the ‘correct’ timbre for the musical scale system. “Then they really might get the best of both worlds: harmony and local scale systems,” he comments.

In overturning a long-held ‘universal’ theory of consonance, this research also represents yet another finding that Western musical rules do not necessarily apply globally. It follows other research concluding that there are cultural variations in pitch perception, for example. The new work clearly highlights, once again, the need for investigations into our responses to music to include people from non-Western cultures.

Read the paper in full.