https://www.cam.ac.uk/research/news/pythagoras-was-wrong-there-are-no-universal-musical-harmonies-study-finds Home * Study at Cambridge * About the University * Research at Cambridge * For Cambridge students * For staff * For alumni * For our researchers * Business and enterprise * Colleges and Departments * Email and phone search * Give to Cambridge * Libraries * Museums and collections Search [Search ] Search Search [ ] Search * Study at Cambridge * Undergraduate + Courses + Applying + Events and open days + Fees and finance * Postgraduate + Postgraduate courses + How to apply + Fees and funding + Postgraduate events * International students * Continuing education * Executive and professional education * Courses in education * About the University * How the University and Colleges work * Term dates * History * Map * Visiting the University * Annual reports * Equality and diversity * News * A global university * Events * Public engagement * Jobs * Give to Cambridge * Research at Cambridge * For Cambridge students * For staff * For alumni * For our researchers * Business and enterprise * Colleges and Departments * Email and phone search * Give to Cambridge * Libraries * Museums and collections * Home * Research * News * Pythagoras was wrong: there are no universal musical harmonies, study finds Research * Research home * News * Our people * Spotlights * About research + About research overview + Animal research o Animal research overview o Overseeing animal research # Overseeing animal research overview # The Animal Welfare and Ethical Review Body o Animal welfare and ethics o Report on the allegations and matters raised in the BUAV report o What types of animal do we use? # What types of animal do we use? overview # Chickens # Guinea pigs # Mice # Naked mole-rats # Non-human primates (marmosets) # Other birds # Rats # Sheep # Xenopus # Zebrafish o Non-technical summaries o Animal Welfare Policy o Alternatives to animal use o FAQs o Further information + Funding Agency Committee Members + Research integrity + Horizons magazine + Strategic Initiatives & Networks + Nobel Prize + Interdisciplinary Research Centres + Open access + Energy sector partnerships + Podcasts o Podcasts overview o S2 ep1: What is the future? o S2 ep2: What did the future look like in the past? o S2 ep3: What is the future of wellbeing? o S2 ep4 What would a more just future look like? * Business and enterprise * Research impact Pythagoras was wrong: there are no universal musical harmonies, study finds Pythagoras was wrong: there are no universal harmonies! | Cambridge research The tone and tuning of musical instruments has the power to manipulate our appreciation of harmony, new research shows. The findings challenge centuries of Western music theory and encourage greater experimentation with instruments from different cultures. There are many more kinds of harmony out there Peter Harrison 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 the University of Cambridge, 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'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," said Dr Harrison, a Fellow of Churchill College. "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 South Korea participated in 23 behavioural experiments. Participants were played chords and invited to give each a numeric pleasantness rating or to use a slider to adjust particular notes in a chord to make it sound more pleasant. The experiments produced over 235,000 human judgments. The experiments explored musical chords from different perspectives. Some zoomed in on particular musical intervals and asked participants to judge whether they preferred them perfectly tuned, slightly sharp or slightly flat. The researchers were surprised to find a significant preference for slight imperfection, or 'inharmonicity'. Other experiments explored harmony perception with Western and non-Western musical instruments, including the bonang. Instinctive appreciation of new kinds of harmony The researchers found that the bonang's consonances mapped neatly onto the particular musical scale used in the Indonesian culture from which it comes. These consonances cannot be replicated on a Western piano, for instance, because they would fall between the cracks of the scale traditionally used. "Our findings challenge the traditional idea that harmony can only be one way, that chords have to reflect these mathematical relationships. We show that there are many more kinds of harmony out there, and that there are good reasons why other cultures developed them," Dr Harrison said. Importantly, the study suggests that its participants - not trained musicians and unfamiliar with Javanese music - were able to appreciate the new consonances of the bonang's tones instinctively. "Music creation is all about exploring the creative possibilities of a given set of qualities, for example, finding out what kinds of melodies can you play on a flute, or what kinds of sounds can you make with your mouth," Harrison said. "Our findings suggest that if you use different instruments, you can unlock a whole new harmonic language that people intuitively appreciate, they don't need to study it to appreciate it. A lot of experimental music in the last 100 years of Western classical music has been quite hard for listeners because it involves highly abstract structures that are hard to enjoy. In contrast, psychological findings like ours can help stimulate new music that listeners intuitively enjoy." Exciting opportunities for musicians and producers Dr Harrison hopes that the research will encourage musicians to try out unfamiliar instruments and see if they offer new harmonies and open up new creative possibilities. "Quite a lot of pop music now tries to marry Western harmony with local melodies from the Middle East, India, and other parts of the world. That can be more or less successful, but one problem is that notes can sound dissonant if you play them with Western instruments. "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 synthesised instruments. Then they really might get the best of both worlds: harmony and local scale systems." Harrison and his collaborators are exploring different kinds of instruments and follow-up studies to test a broader range of cultures. In particular, they would like to gain insights from musicians who use 'inharmonic' instruments to understand whether they have internalised different concepts of harmony to the Western participants in this study. Reference R Marjieh, P M C Harrison, H Lee, F Deligiannaki, and N Jacoby, ' Timbral effects on consonance disentangle psychoacoustic mechanisms and suggest perceptual origins for musical scales', Nature Communications (2024). DOI: 10.1038/s41467-024-45812-z --------------------------------------------------------------------- Creative Commons License. The text in this work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Images, including our videos, are Copyright (c)University of Cambridge and licensors/contributors as identified. All rights reserved. We make our image and video content available in a number of ways - on our main website under its Terms and conditions, and on a range of channels including social media that permit your use and sharing of our content under their respective Terms. --------------------------------------------------------------------- Read this next [globe_headphones_590x288] Musical preferences unite personalities across the globe Composite image of Cambridge musicians University of Cambridge commits to a major new centre for music performance [stormzy] 11 hip-hop artists who had something to say about mental health Soundwave Scientists find upper limit for the speed of sound --------------------------------------------------------------------- Media enquiries Tom Almeroth-Williams External Affairs and Communications Share Published 27 Feb 2024 Image A man playing a bonang Credit: Andrew Otto via Flikr under a CC license [88x31_0] Search research Keyword search [ ] Go Sign up to receive our weekly research email Our selection of the week's biggest Cambridge research news and features sent directly to your inbox. 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