Sergio Arellano, Snow College
Mathematical Sciences
Why is music so pleasant to? In Western music, we have used what is called the “tempered scale” for centuries, and even though it has gone through changes, it is still largely based around the mathematical principles that Pythagoras created two thousand years ago. Is it possible that the explanation to this phenomenon has to do with the mathematical basis of music, which is unconsciously perceived by the brain? The human brain is known for detecting the underlying mathematical patterns present in many non-music related disciplines, such as visual arts. Independent of the music world, there is a proportion called the Golden Ratio or Phi. It is found in art and geometry, because human eyes tend to find that this proportion produces beauty. This is not a coincidence; this proportion is found everywhere around us, especially in nature. With this in mind, it makes sense to search for the Golden Ratio in the tempered scale to explain the mind’s intuitive appreciation of music. This research discovered the surprising fact that there is a Phi relationship between the first and third degree of the major scale, in terms of the frequency of sounds. The relationship is this: the sum of the frequencies of the notes of the minor III chord divided by the sum of the frequencies of the major I chord in any given major key, tends to be Phi. Another very surprising result was the importance of the number 24 in the frequencies of the major scale. These two particularities help to shed light on why human ears have an untaught comprehension of music; the underlying perception of mathematical relationships by the mind are related to the natural appreciation of it.