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Legend holds that ancient Greek philosopher and polymath Pythagoras discovered the laws of harmonics fundamental to so much of Western music by listening to blacksmith apprentices at work. As the story goes, by divine will, Pythagoras happened to pass a blacksmith shop, from which he heard a cacophony of hammering, some of which sounded beautiful. He decided to investigate and found that certain ratios of the weights of two hammers playing together formed the most beautiful sounds: Two-to-one created the harmony of the octave, three-to-two the major fifth, and four-to-three the perfect fourth.

Whether the legend is true or not, simple ratios between tones, known as harmonics, underlie the 12-note chromatic scale and most of the chords and melodies we hear on the radio and in concert halls in the Western world today. But outside of the West, some musical styles rely on very different voicings, patterns, and sequencing. Many of these are considered “inharmonic,” which simply means they don’t obey the math of whole number ratios. Indian classical songs known as ragas, for example, are based on 72 different melodic scales with combinations of half tones that are often inharmonic. 

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Javanese gamelan music tends to feature a harmonic instrument or voice in combination with an inharmonic melody played by a bonang, a collection of small gongs. The gamelan songs follow one of two unique musical scales, including the slendro, which divides the octave into five roughly equidistant notes. In recent decades, some research has suggested that how beautiful, or consonant, different kinds of tonal combinations sound to different listeners will be shaped by their personal cultural experiences with music.

You end up finding new patterns of pleasantness and unpleasantness.

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But in a Nature study published last month, Peter Harrison at the University of Cambridge and colleagues found that perceptions of musical pleasantness may also vary significantly depending on the timbre—or tone quality—of the musical instrument playing it. For example, the timbre of a violin may be smooth or strident, depending on how the player pulls the bow across the strings. The timbre of a Gamelan bonang is often described as brassy or bright. The new study found that listeners from both the United States and Korea liked some chords and combinations of notes considered inharmonic when played by certain instruments, even when these combinations were unfamiliar. The results, they say, provide evidence that cultural variation in musical styles and scales may be driven in part by the properties of the musical instruments used by different cultures.

“If you change the instrument you’re playing your tones on, you can actually end up producing pleasant harmonies that have none of these special mathematical relationships that Pythagoras is talking about,” Harrison says. “You end up finding new patterns of pleasantness and unpleasantness.” Many percussion instruments, including bells and gongs, are always inharmonic, for example, because the way they are built results in overtones whose relationship with the underlying notes violates simple mathematical relationships.

For the study, Harrison and his colleagues collected online responses to different tones and chords in 23 large-scale behavioral studies with a total of 4,272 participants—some participants participated in multiple experiments. The listeners rated the pleasantness of certain combinations of sounds and timbres, or sometimes dragged a slider to manipulate the tone until they found the one that sounded most appealing.

The data they collected sketches a complex picture of musical harmony—one that begins to resolve a longstanding paradox, Harrison says. Modeling from the study of human sound perception, known as psychoacoustics, had already suggested that the kind of instrument played should influence the pleasantness of certain combinations of notes. But in experiments with actual people, the study results were inconclusive. The new study went a step further than previous research by testing sounds that fall between the notes of Western 12-tone chromatic scales and adjusting the timbre of the tones in a more systematic way.

“This is a very elegantly conducted study with an exceptionally large sample size, giving credence to the conclusions drawn based on the results,” says Imre Lahdelma, a postdoctoral researcher in music psychology at Durham University who wasn’t involved in the newly published research. In a smaller study, Lahdelma and colleagues had also described the importance of timbre to the perception of consonance.

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In addition to finding that the timbre of an instrument influences perceptions of musical pleasantness, the researchers found, overall, a preference for slightly inharmonic tonal combinations among study subjects. This is often called dissonance. The contrast between consonance and dissonance is one of the qualities that makes music emotionally meaningful.  “It drives a lot of the emotional experience of music when we hear the ebb and flow of dissonance and we experience the corresponding tension and emotional journey,” says Harrison.

He hopes to devote future research to a better understanding of how consonance and dissonance work together to influence music perception and appreciation, like when a satisfying harmony resolves an unsettling musical phrase. “But before we can really get that far, we need to understand the building blocks.”

Lead image: untungsubagyo / Shutterstock

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