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Music is written in a notational form that can be easily converted to mathematical symbols. Through doing so it soon becomes apparent that the basis of all music that is commonly thought of as ‘beautiful’ uses repetition.
A motif in music is introduced and then it is repeated and altered. The setting up of expectation of repetition in music and then fulfilling or dashing that expectation explains the dynamic of music. It is a series of patterns essentially that is behind the aesthetics of all music from chamber music to death metal.
This sets up an interesting question: is it possible to write music that is totally absent of pattern? This is different to random music – rather music that has patterns but no pattern is repeated. To do this math is needed, you can watch on UK TV via a UK proxy fast enough to stream video.
John Costas was hired by the US Navy to solve the problem with the sonar ping. For the ping to work a sound with patterns where no pattern was repeated was needed. He solved the problem by using the Prime Number Theory developed by Evariste Galois. Each component of the ping was mathematically related to the next but no pattern was repeated.
The speaker in the talk (Scott Rickard) used the work of Costas that borrowed from Evariste Galois to write a piece of music without repetition. It should be the ugliest piece of music ever written as it is devoid of repeating patterns.
In a sense this music realizes the dream of the composer Schoenberg in his movement called ‘the emancipation of the dissonance’.
After listening to the talk and musical piece on TED it is worth reading the comments
(http://www.ted.com/talks/lang/en/scott_rickard_the_beautiful_math_behind_the_ugliest_music.html) as it details some of the key points of what is pattern? How does the mind perceive pattern? How is math converted to music?