Bach’s musical genius is linked to mathematics

Music lovers probably already know Johann Sebastian Bach’s compositions are highly mathematical.

While this theory may seem somewhat enigmatic, American researchers set out to test its veracity.

They discovered the music of the German genius is highly methodical, which explains why it is so pleasing to the ear.

Suman Kulkarni, of the University of Pennsylvania, and colleagues translated each of his compositions into an information network, representing each note as a node and each transition between notes as an edge connecting them.

This enabled them to compare the amount of information contained in each of Bach’s works.

The researchers noticed some of his creations were richer than others. This is particularly true of toccatas, free-form compositions that allow the musician to show off their skills.

With this in mind, the research team set out to measure to what extent (and at what moments) listeners experience surprise when they hear Bach’s compositions. As it turns out, the notes follow one another quite logically.

The researchers were able to conclude that, thanks to their mathematical structure, Bach’s pieces deliver information quite effectively.

“Our findings shed light on the information and network properties of Bach’s compositions,” the researchers write in a paper, published in the journal Physical Review Research.

This research could help composers in their creative processes.

“For example, in music composition software, one could add a feature that displays the music network composed thus far and its entropy measures. Composers can then use these measures as feedback in their music writing process.”