New research challenges Pythagoras’s ancient theory on musical consonance, revealing our preference for slight imperfections in chords rather than the perfect integer ratios traditionally associated with beautiful music. The study, conducted by researchers from Cambridge University, Princeton, and the Max Planck Institute for Empirical Aesthetics, highlights how the mathematical relationships deemed crucial for a chord’s beauty disappear with instruments unfamiliar to Western traditions, such as the Javanese gamelan’s bonang.
Traditionally, the Ancient Greek philosopher Pythagoras believed that pleasant-sounding combinations of notes, known as consonance, are produced by special relationships between simple numbers. However, recent studies have questioned this theory and sought psychological explanations. Despite this, the idea that integer ratios make chords sound beautiful and deviation from them makes music dissonant has persisted.
The researchers’ findings challenge Pythagoras’s theory in two key ways. First, they discovered that listeners actually favor chords with slight deviations from perfect mathematical ratios, finding beauty in minor imperfections. It seems that we prefer a little imperfection because it gives life to the sounds, which is attractive to us. Second, the role played by these mathematical relationships disappears when considering certain musical instruments that are less familiar to Western musicians, audiences, and scholars.
Instruments such as bells, gongs, xylophones, and other pitched percussion instruments, including the bonang from the Javanese gamelan, do not adhere to traditional mathematical relationships. The shape of these instruments means that when they resonate, their frequency components don’t respect those traditional mathematical relationships. This discovery opens up exciting opportunities for exploring new harmonic languages that resonate with listeners without prior musical training.
The researchers created an online laboratory where over 4,000 participants from the US and South Korea took part in 23 behavioral experiments. The experiments aimed to determine participants’ preferences for perfectly tuned intervals versus slightly sharp or slightly flat ones. Surprisingly, the researchers found a significant preference for slight imperfection, challenging the notion that consonance must be perfectly in line with mathematical ratios. The study also explored harmony perception with Western and non-Western musical instruments, revealing that the consonances of instruments like the bonang cannot be replicated on a Western piano due to differences in the scales used.
The implications of these findings are significant. They suggest that there are many more kinds of harmony in the world than previously thought, and that different cultures have developed their own unique concepts of harmony. This challenges the notion of a universal harmonic language based solely on mathematical ratios.
Moreover, the study indicates that individuals without musical training can instinctively appreciate the unique consonances of non-Western instruments. This challenges the belief that musical appreciation and understanding require formal training. As Dr. Peter Harrison, one of the researchers, explains, “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.”
These research findings have implications for the music industry. Musicians and producers are encouraged to experiment with diverse instruments to create innovative musical expressions. The research suggests that merging Western harmony with melodies from different cultures can be more successful if special attention is given to the chosen instruments’ timbre. By using instruments that offer new harmonies and combining them with Western instruments, musicians and producers can create music that harmonizes both Western and local scale systems.
In conclusion, the research challenges long-held beliefs regarding musical consonance and offers valuable insights into the complexity of harmonic relationships. It suggests that there is a wide range of harmonies to explore beyond traditional Western norms, and that listeners can instinctively appreciate the unique consonances of non-Western instruments. This opens up new possibilities for musicians and producers to create innovative and culturally diverse music that resonates with a global audience. By embracing these findings, the music industry can stimulate new musical expressions that listeners intuitively enjoy.
