Fractal Music: Imitation or Resemblance
While reading Gardner’s chapter 27 on Fractal Music he explained the physics behind white noise verses brown noise. He did this by creating two spinners, explaining the difference between these two types of music. The spinner for white noise was divided into seven parts, and was labeled with the keys of a piano. “Since no tone is related in any way to the sequence of notes that proceeds it, the result is a totally uncorrelated sequence” (pg. 353 The Colossal book of Mathematics). When you spin the spinner each note you land on will be as random as the last note you hit, creating no real pattern in the notes. While the spinner for brown noise was also divided into 7 parts, it was labeled in step sizes. Each time you spin the spinner for brown noise you will either hit a plus or a minus. When the spinner lands on a plus you move up the scale at the given interval, and when you land on a minus you move down the scale at the same interval. This creates a strongly correlated tune although it doesn't represent good music.Voss wanted to compose music in-between the white and brown scales. “In spectral terminology it is called 1/f noise.” (pg. 354) With white noise having a spectral density of 1/f^0 and brown noise having a spectral density of 1/f^2, which mean that 1/f has to be to the first power.The best known fractals are the Peano curves that fill a finite region and Koch’s snowflake. To create Koch’s snowflake you have to “use line segments of two 12 different direction line segments… four of the segments are then divided into two equal parts, creating a line from A to B that consists of 13 long and short segments.” (pg. 355-357) This curve is a lot less regular than Peano’s curve making it much more like a natural phenomenon. Koch’s snowflake and Peano’s curve are not like any fractal that appears in nature like trees, coastline, or star clusters.
What I found were some interesting parts about this chapter, like how the 1/f noise applies to the annual flood levels of the Nile River, the flow of traffic on a Japanese expressway and how Mozart wrote the palindromic and invertible canon as a joke to demonstrate the third way to write a melody. T. Musha conducted a study on traffic flow in one area of an expressway in Japan, this exhibited the 1/f fluctuation like the Nile River. Mozart wrote a canon both backwards and upside down, so that two people could play the music sheet reading it from either the top or bottom of the paper. Mozart was able to construct a sheet of music that would allow two people to play the same song at the same time with the same sheet of people while both people faced each other. Most of the time if a composer tried to write a song like this their rhythms and patterns would be destroyed.
I found it super cool to learn how Mozart would play around with math to manipulate his music to organize a way for multiple musicians to play the same piece at the same time while facing each other. It’s also perplexing to me that there is somehow a correlation between the 1/f noise of an expressway and the 1/f fluctuation of the Nile River. Plato’s suspicion of the fine arts came as a bit of a surprise to me, and I had never even come close to considering the idea that they are imitations of imitations. It is certainly true that a picture of a meal or a bed, for example, do not bring one the same joy or satisfaction as experiencing the physical objects. Conversely, Aristotle felt that the fine arts were of great value simply because they bring one aesthetic pleasure. There is also great value in the fact that one must pour their emotions and passion into their work. While I do see valid points in both oppositions, I must agree with Aristotle because the heart and soul of every artist is present in their work. Imitation is the most sincere form of flattery, and it’s the second best to the original.
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