Pythagoras’ ancient music harmony theory hits wrong note, study claims

CAMBRIDGE, United Kingdom — This won’t be music to Pythagoras’ ears. A new study is turning the tables on an ancient music theory as researchers have unveiled findings that could reshape our understanding of universal harmony. The study, a collaborative effort by academics from Cambridge University, Princeton, and the Max Planck Institute for Empirical Aesthetics, suggests that the traditional beliefs about what makes music pleasing to the ear may not hold the universal truth they were once thought to.

For generations, musicians and theorists have leaned on the principles laid down by the Ancient Greek philosopher Pythagoras, who posited that “consonance” — the quality of a chord that makes it sound pleasant — stems from precise mathematical relationships between the frequencies of notes. This concept has underpinned the foundation of Western music, dictating that chords adhering to specific ratios, such as 3:2 or 4:3, produce harmony, while deviation from these ratios results in “dissonance,” or an unpleasant sound.

However, this new research presents a striking counterpoint to Pythagoras’ long-standing theory.

“We prefer slight amounts of deviation. We like a little imperfection because this gives life to the sounds, and that is attractive to us,” says study co-author Dr. Peter Harrison, from Cambridge University’s Faculty of Music and director of its Center for Music and Science, in a media release.

The findings reveal that listeners do not always favor chords that fit perfectly into these mathematical ratios, challenging the notion that beauty in music is strictly a matter of numerical precision.

Researchers also ventured beyond the familiar territory of Western orchestral instruments to explore the musical textures of instruments less known in the West, such as the “bonang” from the Javanese gamelan, a type of pitched percussion that defies the conventional ratios of harmony.

“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,” explains 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.”

To gather empirical evidence, researchers set up an online laboratory where over 4,000 participants from the U.S. and South Korea engaged in 23 behavioral experiments, generating more than 235,000 human judgments on the pleasantness of various chords. This extensive study not only explored traditional Western chords but also included sounds from non-Western instruments like the bonang, revealing a significant preference among participants for slight imperfections in tuning, a phenomenon described as “inharmonicity.”

The findings suggest that the musical scales and harmonies native to the bonang and similar instruments are not only distinct from Western norms but are also instinctively appreciated by listeners, regardless of their musical background. This challenges the prevailing view that harmony must conform to a narrow set of mathematical relationships and opens the door to a richer understanding of musical aesthetics that transcends cultural boundaries.

Dr. Harrison hopes that this research will inspire musicians and producers to embrace the diverse tonal qualities offered by non-Western instruments, potentially unlocking new creative possibilities.

“Musicians and producers might be able to make that marriage work better if they took account of our findings and considered changing the ‘timbre,’ the tone quality, by using specially chosen real or synthesized instruments,” says Dr. Harrison. “Then they really might get the best of both worlds: harmony and local scale systems.”

As the study prompts a reevaluation of what makes music harmonious, it beckons a future where the exploration of unfamiliar instruments and the blending of global musical traditions could enrich the tapestry of sound that unites listeners around the world.

The study is published in the journal Nature Communications.