Math patterns in Bach's music

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Johann Sebastian Bach's music exhibits mathematical patterns and structures that contribute to its complexity and the way it conveys information to listeners. Researchers have analyzed Bach's compositions using network theory, representing scores as networks of nodes and edges, where each note is a node and each transition between notes is an edge. They found that Bach's music, particularly toccatas and preludes, has higher information entropy, meaning it is more information-rich and surprising than randomly generated networks. Chorales, on the other hand, are relatively sparse in information but still more information-rich than random networks. These patterns may make it easier for human brains to learn and process the music, as they align with our biased perception of complex informational systems12. Additionally, there is no conclusive evidence that Bach intentionally used the golden ratio or Fibonacci numbers in his compositions, although some scholars have speculated about the use of symmetry and other mathematical principles in his works34. Bach's music also demonstrates various types of symmetry, such as inversion and transposition, which are integral to his compositional techniques5. In summary, Bach's music contains mathematical patterns that contribute to its complexity and the way it communicates information to listeners, but there is no definitive evidence that he intentionally used the golden ratio or Fibonacci numbers in his compositions.
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