Why do we feel a surge of emotion when listening to certain music? Why do some melodies or chords sound comforting, while others feel inexplicably unsettling?
 

Music is often called the art of emotion. People feel joy while listening to music, and sometimes experience inexplicable sadness or deep movedness. However, an interesting fact is that this world of music, which we perceive emotionally, actually exists within a very precise order. If we look into the deepest structures of music, we find principles of mathematics and physics hidden within, rather than just emotion. This is because the sounds we perceive as beautiful are not created by chance, but are formed within specific ratios and rules—a highly orderly structure.
 

#. The 'Discovery' of Mathematician Pythagoras

The first person to systematically explain this fact was Pythagoras, the ancient Greek philosopher and mathematician. He compared sounds by varying the lengths of strings on a stringed instrument. Through these experiments, he discovered that musical intervals can be explained by specific numerical ratios. In other words, he saw that the beauty of sound was not merely a sensory phenomenon but could be explained within an order of numbers and proportions.
 

For example, if you reduce the length of a string by half, you hear a note one octave higher. This is a simple 2:1 ratio. Additionally, when the frequency ratio of two notes is 3:2, it creates a harmonious and stable relationship, which corresponds to the natural interval we commonly hear as a 'Perfect 5th' (C to G). A 4:3 ratio similarly forms a smooth and stable relationship, heard as the interval of a 'Perfect 4th' (C to F). Thus, the intervals that sound beautiful in music could be explained by simple numerical ratios. This discovery led Pythagoras to an important philosophical insight. He believed that the numerical ratios in music were connected to the order of nature and the universe. For Pythagoras, music was not just an art but a mathematical principle for understanding the cosmic order.
 

#. Vibration at Constant Frequencies

Then, why do some chords sound comfortable while others sound tense or uneasy? The reason for this can also be explained through physics. When two notes sound simultaneously, each sound vibrates at a specific frequency. If the ratio of the two frequencies forms a simple integer relationship, the waves of the two sounds overlap regularly, creating a relatively stable sound. Conversely, the more complex the ratio, the more the waves collide, causing irregular interference. We perceive this phenomenon as dissonance. In other words, the stability of the chords we hear is not merely a matter of sensory preference but is closely linked to the physical properties of sound waves. However, music does not simply follow the laws of nature. Humans have created new tuning systems to use music more freely. A prime example is 'Equal Temperament.' This system divides an octave into 12 equal intervals. Thanks to this, keyboard instruments like the piano can be played freely in any key, allowing composers to use a much wider variety of harmonies and tonalities.
 

#. Johann Sebastian Bach

Johann Sebastian Bach’s 'The Well-Tempered Clavier' is a representative work that demonstrated the possibilities of this tuning system. Subsequently, Western music evolved to use diverse tonalities and harmonies more freely, and the ways of musical expression became even more varied. Taking it a step further, the science of music extends beyond ratios and waves into the realm of the human brain and emotions. Music begins as simple vibrations in the air, but those sounds are transformed into neural signals through the ears and interpreted by the brain, leading to emotion. In other words, the emotion we feel in music is created in the complex process where physical vibrations pass through auditory perception and connect to feelings.
 

#. The Human 'Predictive' Brain

The human 'predictive brain' plays a crucial role in this process. When we listen to music, our brain constantly anticipates what note will follow next. If the melody follows that expectation, we feel a sense of stability; however, if the flow becomes too predictable, we may feel bored. Conversely, if it develops in an unexpected direction, it creates tension or surprise, and these variations sometimes generate musical excitement and movedness. Composers use this balance between expectation and change to craft emotions within music. As such, music is a unique art where emotion and reason meet. Behind the moments we call 'being moved' are the simultaneous workings of numerical ratios, the physics of waves, and the cognitive structure of the human brain. Music is not just an art for the ears but perhaps one of the most beautiful human experiences created by mathematics and science. And perhaps the deep emotion we feel in music is because the order of humanity and the universe resonates through that sound.