There music it is almost always formed by agreements, that is, from several notes played together. But why do some combinations sound better than others? This is not a coincidence, but it depends on the wavelength of the notes that are played: pleasantness depends on the mathematical relationship among them wavelengths. The simplest the relationship, the more the notes “play well together”. This intuition, already known to Pythagorasis the basis of western music and the construction of the agreements that we listen to every day. The agreementsin fact, seem to us “play“Because the wavelengths of the notes involved they combine well among them.
The interpretation of what “sounds well”, however, is not only mathematical, but it is also strongly cultural. In this article we see how Pitagora’s musical theory was born and like some of the “obvious” conventions for us, they are not in other cultures at all.
The myth of the Bottega del Fabbro di Pitagora
According to tradition, the discovery of the link between sound and mathematics dates back to Pythagoras, The famous Greek mathematician and philosopher. There legend handed down by Giamblico di Calcide it says that while walking near the workshop of a blacksmith, Pitagora noticed that some sounds produced by hammers They combined on the fire in a pleasant way, while others were unpleasant. In particular, he realized that the blows of two hammers they played well together if one was large and heavy twice the other. It is said that Pythagoras was so impressed by this fact that it decides to study the relationship between sounds and mathematics.
Beyond the legend, we know that the Pythagorean school he studied in depth the relationship between sound And mathematical proportions Using a tool called “monochord“: One rope tense on a sound box, with a mobile bridge that allows you to divide the rope two parts of variable length.
The Pythagoreans discovered that dividing the rope In simple relationships – halfway, two thirds, three quarters – they got sounds particularly pleasant, called consonants. They concluded that the notes that sound good together correspond to relationships between simple numbers, while the dissonant combinations derive from more complex or irrational relationships. The notes thus identified, called harmonichave become the foundation of western musical theory.
Because the notes play well together (for the Westerners)
Today we know that the harmonic notes they have proportional wavelengths. It is precisely this characteristic that makes two or more pleasant harmonic notes played with each other. When we play two or more notes simultaneously and their ratio of wavelengths is simple, our brain interprets the sound as a harmonious, coherent.
In 2012, a Canadian research group showed that for listeners westernthe combinations of three or more known (or agreements) they appear pleasant When the frequencies that compose them are linked by harmonic relationships. This effect is also the result of cultural habit: we grew up listening to music built on these relationships. Western musical theory, in fact, is based from the origins on the intuitions of the Pythagoreans. Even today, the agreements that we consider “natural” resume the same mathematical proportions identified by Pythagoras.
This vision of musical harmony, however, is partial. A recent study of the Max Planck Institute has shown that the consonance It does not depend only on the relationship between the frequencies, but also on stampthat is, from the distinctive sound characteristics of an instrument. For example, it has been observed that non -western tools such as i gong can generate non -harmonious sounds which are however pleasant. This suggests that our idea of ”consonance” is the result of a combination between physical factors and cultural influences.
Is it true that the greatest agreements are happy and sad minor ones?
Another very widespread belief in western music is that it is enough to change the agreements from greater to lesser to make one “sad” song. But this association between agreements and emotions Is it really universal? Or is it something we learn culturally?
In our musical context, we are used to connecting the greatest agreements to positive sensations (joy, serenity) and minor ones to negative emotions (sadness, melancholy). However, recent studies suggest that it is a cultural conventionnot of a natural and universal response.
A 2021 study compared the emotional reactions of English participants and two groups of northern Pakistan (Kho and Kalash). While the British clearly associated the greatest agreements with happiness and minor ones with sadness, the subjects Pakistani they did not show this distinction. A second study from 2022 involved the Uruwaa population of the Papua New Guinea with poor exposure to western music. Also in this case, the major/happy/minor association was not perceived as in western champions. Indeed, the more the participants were culturally far from western music, the less they recognized this difference.
These results suggest that the major-positive, minor-negative association is a cultural product, not an innate experience. If certain sounds are continuously associated with specific emotions in the media, advertising or popular music, we end up internalizing their emotional meaning.
