How timbre influences the harmony we find pleasing in music

The traditional mathematical guidelines to achieve musical harmony might be more adaptable than we had previously believed.

According to established Western musical theory, chords sound most appealing when they contain notes which are separated by specific intervals (SN: 5/9/23). For instance, intervals in which the frequencies of notes have straightforward ratios like 2:1 (an octave) or 3:2 (a fifth).

Yet, new scientific findings suggest that the harmonies people actually prefer may depend on the timbre of the notes. In other words, timbre is the unique flavor of sound produced by distinct instruments, explaining why the same note played at the same volume can sound diverse on various musical instruments such as the piano, guitar, or gong.

These discoveries, announced on February 19 in the publication Nature Communications, indicate that the recipe for appealing harmony involves more than a fundamental set of mathematical relationships. The findings could also help illustrate why different worldwide cultures - with instruments that produce different timbres - have generated diverse musical scales.

Tuomas Eerola, a scholar of music cognition at Durham University in England who was not part of the new research, states that culture influences people’s preferences for different combinations of notes. This research interestingly demonstrates that culture could be influenced by the kinds of instruments used in particular cultures.

In the study, over 4,000 online participants from the United States completed harmony perception tests which involved listening to notes with different timbres generated by a computer. One test required people to rate the pleasantness of chords containing realistic synthetic notes resembling those created by Western musical instruments. Surprisingly, researchers found that people seemed to prefer intervals that were slightly dissimilar from those tuned to basic, “ideal” frequency ratios.

Study coauthor Nori Jacoby, a cognitive scientist at the Max Planck Institute for Empirical Aesthetics in Frankfurt am Main, Germany, surmises that people may prefer these intervals due to the way slightly off “ideal” ratio musical notes interact. This interaction causes the sound to pulsate slowly, providing a chord with added texture.

In another part of the study, participants were made to listen to chords containing synthetic notes modeled on a non-Western instrument known as the bonang. This gong collection is part of the Indonesian gamelan musical ensemble. Participants who listened to chords featuring bonang-like timbres preferred intervals with frequency ratios that were starkly different from Western “ideal” ratios.

Jacoby observed that these chord preferences align quite well with a musical scale utilized in Javanese gamelans, termed the slendro scale. This scale features five notes per octave, as opposed to the twelve notes of the Western scale, with frequency ratios that don't resemble simple integer ratios at all.

Jacoby asserts that the frequency preferences of participants not familiar with Javanese gamelan music imply something about the origin of musical scales. They suggest that they might be greatly influenced by the nature of the instrument used.

Ki Midiyanto, a Central Javanese musician and gamelan music expert at the University of California, Berkeley, also believes that the timbre might influence preference for “perfect” versus “imperfect” ratios in musical intervals.

According to Midiyanto, the process of tuning bronze gamelan instruments like the bonang is completed by feel and significant tuning differences are expected and aesthetically attractive. He adds that instrument tuning is bound to change with time.

Midiyanto explains that it's common to deliberately stretch an octave slightly farther apart than the so-called “ideal” frequency ratio in high-pitched bronze instruments. This practice creates a more pleasing combined timbre when all the gamelan instruments are played together. However, this is not performed with stringed instruments in gamelan ensembles.

Further experiments by Jacoby’s team established that manipulating timbre influenced the harmonies preferred by a group of 68 South Korean participants, suggesting that these findings are applicable across cultures.

“It’s a clever use of crowdsourcing and really large-scale online experiments,” Eerola says. “They’ve raised the bar for future studies quite a bit.” In the future, Eerola would like to see similar investigations with people from other parts of the world who may not have as much exposure to Western music as those in South Korea. 

Other future studies, the researchers say, could explore how people’s experience of harmony changes when chords are embedded within the larger context of a song, or probe other perceptions of harmony beyond simple pleasantness — such as how different chords evoke happiness, nostalgia or other feelings.