Pythagoras was wrong when scientists discovered that there is no cosmic musical harmony

Mondo Science Updated on 2024-03-04

Recent research has challenged traditional Western theories, showing that the appreciation of harmony is not strictly limited by mathematical proportions, as previously thought, but can be enhanced by minor flaws and the use of non-Western instruments, revealing a wider range of harmonies and dissonances. This finding, made through extensive behavioral experiments, shows that there is a lot to learn from instruments and theories from other cultures, and opens up new possibilities for creativity and appreciation.

New research shows that the tone and tuning of musical instruments have the power to manipulate our appreciation of harmony. This discovery challenged centuries-old Western theories and encouraged greater experimentation with instruments from different cultures.

The ancient Greek philosopher Pythagoras believed that "harmony" – the fascinating blend of musical notes – came from the mystical connection between simple numbers such as 3 and 4.

But recent research by scholars at Cambridge, Princeton, and the Max Planck Institute for Experimental Aesthetics has revealed two major misunderstandings of Pythagorean theory. This discovery, published in the journal Nature Communications, gives us a new understanding of harmony.

In fact, in the ordinary auditory experience, we don't like chords that fit exactly these mathematical proportions. Dr. Peter Harrison, director of the Centre for Science and Science at the University of Cambridge and co-author, said: "We prefer subtle deviations, small imperfections, because they breathe life into the sound, and that vitality has an irresistible attraction for us. "What is even more surprising is that when it comes to musical instruments that are less accessible to Western scholars, audiences, and scholars, such as bells, gongs, xylophones of all kinds, and tonal percussion instruments, the influence of these mathematical proportions seems to evaporate. Special mention should be made of the "bonang", a musical instrument from Java Gamelan, which consists of a set of small gongs. "When playing an instrument like bonang, the Pythagorean numerical mystery is gone, replaced by a new and fascinating pattern of harmony and dissonance," Dr. Harrison noted. ”

The shape of some percussion instruments dictates that when you strike them, they resonate, and the frequency components of these resonances do not follow traditional mathematical relationships. It is in this context that we discover fascinating new phenomena. Dr. Harrison explained. In the past, Western research focused more on familiar orchestral instruments, but instruments used in other ** cultures, due to their unique shapes and physical properties, may produce what we call "dissonant" sounds. To delve deeper into this phenomenon, the researchers created a ** lab that attracted more than 4,000 participants from the United States and South Korea to participate in 23 behavioral experiments. These participants were asked to listen to the chords and rate the pleasure of each chord, or use sliders to adjust specific notes in the chord to make it sound more pleasing to the ear. The experiment produced a total of more than 2350,000 judgments made by humans. These experiments explore the charm of chords from multiple perspectives. Some experiments focused on specific intervals, asking participants to judge whether they preferred perfectly tuned, slightly sharpened or slightly flatter intervals. The results were surprising: people were clearly more inclined towards intervals that were slightly imperfect, or "dissonant". Other experiments have further explored the perception of harmony in both Western and non-Western instruments, including bolang drums, revealing the diversity and richness of the human quest for harmony. Researchers have found that the harmony of Bonang resonates harmoniously with specific musical scales in Indonesian culture, like the sound of heaven. These harmonies cannot be replicated on Western pianos, because they move between the gaps of the traditional scale, like elves in the wind, elusive.

"Our findings break with the conventional wisdom that there is only one way to harmonize and that chords must follow mathematical relationships," said Dr. Harrison. We demonstrate the diversity of harmonic genres and reveal why other cultures have developed these harmonies. "Surprisingly, the study showed that even untrained ** and unfamiliar Javanese ** participants could instinctively appreciate the new harmonies of the Bonan's tone.

Harrison explains, "Creation is a journey about exploring the creative possibilities of a given quality, like discovering what kind of melody you can play with your flute, or what kind of sound you can make with your mouth. Our findings suggest that by using different instruments, a whole new harmonic language can be unlocked, and people can intuitively appreciate it without having to learn it.

In contrast, many of the experiments in Western classics have been incomprehensible to listeners for the past hundred years because they involve highly abstract structures that are difficult to appreciate. However, the results of psychological research such as ours can provide inspiration for new ** that inspires listeners to appreciate intuitively. ”

Dr. Harrison is eager to see how this research will inspire artists to venture beyond the boundaries of instrumental instruments and explore uncharted areas of timbre to see if they can give birth to novel harmonies that will unveil a new era of creativity. Imagine today's pop music scene, where countless musicians try to blend Western harmonic acoustics with Middle Eastern melodies, Indian rhythms, and even the world's best elements.

While it is true that many of them have achieved some success, there is still a problem that cannot be ignored – when you play these exotic tunes with traditional Western instruments, that harmonious balance is often disrupted, like misunderstandings and estrangements in cross-cultural communication.

Dr. Harrison and his team know that timbre, or sound quality, is the indispensable soul of the world. They believe that if the artists and producers listen carefully to the findings of the study and are brave enough to try to reinvent the tone with carefully selected real instruments or innovative synthesizes, they may be able to find the key to harmony. At that time, they will truly achieve the best fusion of East and West, so that harmony and local scale systems complement each other, and together create a wonderful sound belonging to two worlds. Newbie Mentoring Program

Today, Harrison and his collaborators are immersed in a journey of discovery of various instruments, and their research continues to expand into a wider range of cultures. They were particularly eager to hear from those who excelled at playing "discordant" instruments, hoping to draw inspiration from them to see if they had internalized a very different idea of harmony from their Western counterparts. In this adventure that transcends cultures and breaks through boundaries, they look forward to discovering more beautiful notes and writing a new chapter in human history together. References: Raja Marjieh, Peter M c.Harrison, Harin Lee, Fotini Deligiannaki and Nori Jacoby, "The Timbre Effect of Harmony Unravels Psychoacoustic Mechanisms and Hints at the Perceptual Origin of the Scale," February 19, 2024.

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