Music is a series of vibrations in the air, which can be reduced to numbers, a series of binary numbers. Rhythm is only one aspect of music that lends itself to mathematical exploration. According to legend, Pythagoras discovered the relationship between harmony and number: each sound has a characteristic speed of vibration, which is pitch for musicians and frequency for physicists. If the ratio of the frequencies of the two sounds is two small numbers, the sounds are harmoniously connected to each other and sound nice when played together.
But beyond that, music carries enormous emotional content, crosses cultural boundaries, and can be enjoyed by anyone without any background information or prior training. According to Gottfried Leibniz, music is the pleasure that the human mind experiences in counting without realizing that it is counting. But it is also a pleasure to consciously analyze what we hear. Therefore, there is a close relationship between music and mathematics.
Bach and Newton
Parallels are often drawn between Bach and Isaac Newton, who was 42 years his senior, on the one hand, because Bach's music is best appreciated by true connoisseurs, just as Newton's writings are also understood by people skilled in the sciences. On the other hand, similar to Newton's scientific innovations, Bach reformed the world of music in terms of composition and performance.
Interestingly, one of the most prominent representatives of German Newtonianism was Johann Heinrich Winkler, the lyricist of one of Bach's cantatas and one of the first scholars elected to the Royal Academy in London as a German.
The two worlds overlapped, and Bach's music and works were influenced by Newtonian culture and the general spirit of discovery of the scientific revolution associated with the name of the English physicist.
And in an Irish blog about mathematics, with the help of artificial intelligence, they sketched what Bach and the mathematician Euler would be like. conversation, who wrote a book on the mathematical theory of music, and since Bach was also fascinated by the relationship between mathematics and music, it turned out that they had a lot to discuss via ChatGPT.
In 2018, his cantatas with physical concepts and theories It has been paired In a lecture series in London. The use of compositional structures and patterns has led to debate about the extent to which the Baroque composer was inspired by mathematics. The program is dedicated to the memory of the writer Douglas Adams, who himself said of Bach: “Beethoven tells you what it is to be Beethoven, and Mozart tells you what it is to be a man. Bach tells us what it is to be the universe.”
Recall and predictability
New research using information theory methods InvestigationWhat makes Bach's music so great. Suman Kulkarni, a researcher at the University of Pennsylvania, wanted to explore the relationships between memory and the structures of musical works with his colleagues, especially in the case of Bach, because he created a wide range of works. According to information theory methods, notes were recorded as nodes and the intervals between them as edges, creating a network that demonstrated that faster Bach toccatas carried more information than slower chorales.
The researchers were also interested in how predictable the music was. In the computer paradigm, participants responded to a series of images displayed on a screen. The researchers then measured how surprising an item in the series was to them. Information networks based on this model have been adapted to music. The connections between each node indicate how likely a listener thinks two related sounds will occur consecutively—or how unexpected it would be if they did. They measured the differences, and found that Bach's pieces conveyed information effectively, making predictability easier. But it is also true that the response depends on the person's musical background and how long he has listened to a particular piece.