What Makes Music Sound So Good?
Music has a strong connection with mathematics, not only is the symbolic musical notation in all its aspects mathematical, but also the first musical scale of 5 tones and 2 semitones is often associated with the ancient Greek mathematician Pythagoras. Other than what we normally can see, there are more mathematical concepts behind the music, like symmetry, Fibonacci Numbers; and the most famous one is the Golden Ratio. We have already noticed that lots of great musicians used Golden Ratio in their music, and as we all know, these great musicians made so much great music in the history. For example, according to a mathematician, J.F. Putz’s research, Mozart used Golden Ratio in the Mozart’s Sonata No. 1. So the question is, what makes the music sound so good? Whether the mathematical concepts behind the music or music itself make it sound so good?
Golden Ratio and classic music
Two quantities are in the Golden Ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one, and the Golden Ratio approximately is 1.618. The negative root of the quadratic equation for Golden Ratio is approximately 0.618. And they are two numbers we often used to find the Golden Ratio in anything.
There are lots of great musicians used Golden Ratio in their music. In a 1996 article in the American Scientist, for example, Mike Kay reported that Mozart’s sonatas were divided into two pars exactly at the Golden Ratio point in almost all cases. Meanwhile, Derek Haylock noted that in Beethoven’s Fifth Symphony, the famous opening “motto” appears in the first and last bars, but also at the Golden Ratio point (0.618) of the way through the symphony, as well as 0.382 of the way. Were they by design or accident? It could be accident if there are only two musicians used golden ratio in their music in the history, but other great musicians like Schubert, Bach and Satie may also have deliberately used Golden Ratio in their music as well. So it could not be accident for them to use Golden Ratio in the music. I cannot say we must use Golden Ratio to make a good piece of music, but I think Golden Ratio is one of the questionable mathematical concepts that make music sound good.
Golden Ratio not only exists in the music, but also exists in lots of other kinds artworks, like paintings, sculptures, architectures. Even we can find Golden Ratio in human body and lots of other creatures on the earth. So maybe the artists did not notice they had used the Golden Ratio in their artworks, as it has been naturally existing in our world. But there are many great artists are not only artist, but also scientist or mathematician. Like Leonardo da Vinci, M. C. Escher, and even Mozart is one of them. It is not well known that Mozart was fascinated by mathematics as well as music. He even mentioned equations in the margins of some of his compositions. There are chances in which he knew of the Golden Ratio and its reputation for conferring elegance in the structure of musical compositions. Normally we only know of these musicians as great artists, but they were also taken to the field of mathematics. This is demonstrated during Renaissance years, it shows an understanding of the use of golden ratio in great classical music.
Noise and music
In early twentieth century, a composer and futurist artist Luigi Russolo made his first piece of noise art called the Art of Noises. He perhaps was the first noise artist in history. He found traditional melodic music confining and envisioned noise music as its future replacement. Today’s music, as it becomes continually more complicated, strives to amalgamate the most dissonant, strange and harsh sounds. In this way, music comes closer to noise sound. Today’s music is going away from the traditional music, and it’s also going away from the mathematical concepts. As the traditional music’s tones are restricted by mathematics, written in the musical scores, and played by the musical instruments. But now, we don’t need any musical scores or instruments to make music, we can produce a very good piece of dance music by only using a computer. And some artists even use noise to make music. Today’s music is so different from the traditional music, but we still call it music.
As the music world is expanding, there are fewer connections between music and maths, but we are still producing good music. The key to make a good musical composition is not reliant on mathematics in musical fundamentals such as notes. Arguably the idea of mathematical concepts behind the music, like golden ratio, probably are the key to make a good composition music.
Golden Ratio and noise
I think there is a way I can test if it is Golden Ratio makes music sound good. Instead of using musical notes or melodies, I will use noise to make a piece of music that integrates Golden Ratio. According to the Golden Ratio, I will divide the time line into several parts, and put a piece of noise sound at the certain part. By using noise rather than musical notes or melodies, I can get rid of the mathematical concepts in the traditional music. There will be no other mathematical concepts in this piece except the Golden Ratio. In this way, I can test if I can make a good piece of music by only using Golden Ratio.
Conclusion
Music is a mathematically based art form, but as the music world is developing, seeking purity of sound is no longer the only goal of music. Music has become more expressive and faded away from the mathematical restrictions. Meanwhile musicians still use mathematical concepts in their compositions’ structures. Golden Ratio, as one of the mathematical concepts musicians often had been used, is not a compulsory element in a good piece of music, but it is one of the mathematical concepts that made music sound good.
References:
Corliss, W. (1996, October). Did Mozart Use The Golden Section? Retrieved October 10, 2010, from http://www.science-frontiers.com/sf107/sf107p14.htm
Knott, R. (2010, September). Fibonacci Numbers and The Golden Section in Art, Architecture and Music. Retrieved October 12, 2010, fromhttp://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibInArt.html#music
Noise (music). (n.d). In Wikipedia. Retrieved October 13, 2010, from http://en.wikipedia.org/wiki/Noise_(music)
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