创造音乐和谐的数学规则可能比我们想象的更具可塑性。
西方音乐理论传统上认为，当和弦包含由特定音程分隔的音符时，它们听起来最悦耳。也就是说，音符的频率有简单的比例——比如2:1(一个八度)或3:2(一个五度)。
但新的研究表明，人们真正喜欢的和声取决于音符的音色。音色是由特定乐器发出的声音的独特味道——这就是为什么同样的音调在钢琴、吉他或锣上发出的声音不同。
These findings, reported February 19 in Nature Communications, show that the recipe for a beautiful harmony is more nuanced than a simple set of mathematical relationships. The results may also help explain why different cultures around the world — whose instruments yield different timbres — have developed diverse musical scales.
Researchers know that culture plays a role in people’s tastes for different blends of notes, says Tuomas Eerola, who studies music cognition at Durham University in England but was not involved in the new research. “This study really nicely shows that it’s not just any arbitrary [cultural influence]. It might come from the type of instruments being used in certain cultures.”
More than 4,000 online participants from the United States completed a battery of harmony perception tests, where they listened to notes crafted on a computer to have different timbres. In one test, people rated the pleasantness of chords containing realistic synthetic notes similar to those produced by Western instruments. To the researchers’ surprise, people seemed to prefer intervals slightly different from those tuned to simple, “ideal” frequency ratios.
People might prefer these intervals because when musical notes that are slightly off “ideal” ratios interact, they cause the sound to slowly pulsate, giving a chord some added texture. “Not too much, but a little bit of deviation from the integer ratio that creates a little bit of roughness,” says study coauthor Nori Jacoby. “When you have that, you feel it’s more pleasant.” Jacoby is a cognitive scientist who studies auditory perception at the Max Planck Institute for Empirical Aesthetics in Frankfurt am Main, Germany.
In another experiment, people listened to chords that contained synthetic notes modeled after a non-Western instrument: the bonang. This collection of gongs is played in the Javanese version of an Indonesian musical ensemble called a gamelan. When study participants listened to chords with bonanglike timbres, they preferred intervals with vastly different frequency ratios than Western “ideal” ratios.
Those chord preferences did map pretty well onto a musical scale used in Javanese gamelans called the slendro scale. This scale has five notes per octave — compared with Westerners’ twelve, including sharps and flats — with frequency ratios that are not even close to simple integer ratios. (The slendro scale cannot be played on Western instruments like the piano, because some of its notes would fall between the keys.)
“That was a really striking phenomenon,” Jacoby says. Even though Western participants likely had little or no prior exposure to Javanese gamelan music, they seemed to intuitively prefer chords at home in that musical style while listening to an artificial bonang. “This is suggesting something about the origin of musical scales,” Jacoby says, “that they can be strongly influenced by the kind of instrument they’re used for.”
The idea that timbre influences people’s preference for “perfect” versus “imperfect” ratios in musical intervals matches the experience of tuning and playing gamelan instruments, says Ki Midiyanto, a Central Javanese musician and expert in gamelan music at the University of California, Berkeley.
The tuning of bronze gamelan instruments such as the bonang “is done by feel, and significant differences between sets of instruments is the norm,” Midiyanto says. “This variation is both desirable aesthetically, and to some degree inevitable, as instrument tuning does not remain completely stable over time.”
In fact, it’s common to purposely stretch an octave slightly farther apart than the “ideal” frequency ratio in higher-pitched bronze instruments to create a nicer combined timbre when all the instruments of a gamelan are played together, Midiyanto says. But that’s never done with stringed instruments in gamelan ensembles, such as the siter and celempung.
Jacoby’s team carried out further experiments that showed tampering with timbre influenced the preferred harmonies of 68 people from South Korea, too — offering early evidence that timbral effects generalize 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.
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