Whether it’s a symphony or your favorite pop song, most of the music we know and love today is made with 12 notes. So why not 5 or not 22, but 12 notes? Why is this pleasure bestowed upon us based on such a limited collection of sounds? The reason why music is made with these particulars notes is the mathematics in human aesthetic perception. This number of notes can be further increased by following a simple rule. In fact, the number of notes varies from culture to culture. Arab and Indian music has more notes in one octave than Western music. However, the 12 notes used in Western music constitute the essential notes in many other cultures.
Math Behind Music Theory
Musical notes are just the names given to certain frequencies of sound waves in music. For example, high-pitched notes have a high frequency. The distance between notes is called “intervals” and there is an aesthetic created by these intervals. When the distances of the notes are positioned using more aesthetically perceived intervals, firstly 7 notes in the major scale and then 12 notes appear. The frequencies of the notes are chosen according to a certain rule to make them sound pleasant when selecting the notes. The notes should be selected in a way that their distances from each other contain the maximum number of harmonious intervals.
The most harmonious interval between intervals is an octave. The lower or upper octaves of a note sound ‘same’ to the ear, but only in higher or lower versions. The reason for this harmony is the simplicity in the ratio of frequencies. The simpler the ratio of the two frequencies to each other, the more dopamine the human brain tends to secrete while hearing these two notes at the same time or listening to the melodies made from these two notes. In the case of octaves, this ratio is 2 and it has the simplest ratio among the intervals. While the note of A4 is 440 hertz, A3 with a lower octave is 220 hertz and the A5 with an upper octave is 880 hertz.
The octave interval always gives us the same note. Therefore, we need a different interval to find different notes. After the octave, the most harmonious intervals are the perfect fifth and the perfect fourth. Most melodies, songs and and classical pieces contain the perfect fourth and perfect fifth intervals. On the other hand, the dissonant intervals; minor & major seconds, and minor & major sevenths. These intervals are respectively; one, two, eight, and nine halftones long. It is difficult to listen to these dissonant intervals. However, composers use the tension and chaotic feeling created by the dissonant intervals to increase the feeling of dissolution created by harmonious intervals. Harmonious intervals following dissonant intervals are often used to make music catchy and create more emotions. If a music piece consists only of harmonious intervals, it will sound nice but that’s all.
Is It Inspiration or Math?
Since the aesthetics of music are largely based on simple mathematical rules, artificial intelligence can easily learn these patterns. If we feed the AI with enough data, it can learn mathematics we think of as inspiration in a shorter time than us. Here is an Rachmaninov piece reconstructed by Artificial Intelligence.