How pieces of music by different composers and genres develop can be anticipated for different periods of time
Compositions by Johann Sebastian Bach are less predictable than those by Wolfgang Amadeus Mozart. And how a jazz piece develops can be anticipated even less. This is what two physicists from the Max Planck Institute for Dynamics and Self-Organization in Göttingen discovered when they used over 550 pieces of classical music and jazz to investigate the extent to which a piece of music raises expectations about its future course.
Music can be uplifting and put you in a good mood, but it can also make you melancholy and sad. But how do these emotions arise and how does meaning emerge in music? Almost 70 years ago, music philosopher Leonard Meyer suggested that both are due to an interplay between expectation and surprise. In the course of evolution, it was crucial for humans to be able to make new predictions based on past experiences. This is how we can also form expectations and predictions about the progression of music based on what we have heard. According to Meyer, emotions and meaning in music arise from the interplay of expectations and their fulfillment or (temporary) non-fulfillment.
For pieces of music by different composers from classical music and jazz, an initial autocorrelation of pitches can be observed, which ends relatively abruptly after a certain time and thus makes further predictability impossible. The point at which a composition develops differently than one might expect depends, among other things, on its creator and the genre. (image generated with AI)
© MPI-DS
A team of scientists led by Theo Geisel at the Max Planck Institute for Dynamics and Selforganization and the University of Göttingen have asked themselves whether these philosophical concepts can be quantified empirically using modern methods of data science. In a paper published recently in the journal Nature Communications, they used time series analysis to infer the autocorrelation function of musical pitch sequences; it measures how similar a tone sequence is to previous sequences. This results in a kind of “memory” of the piece of music. If this memory decreases only slowly with time difference, the time series is easier to anticipate; if it vanishes rapidly, the time series offers more variation and surprises.
Initially musical sequences can be predicted rather well
In total, the researchers Theo Geisel and Corentin Nelias analyzed more than 450 jazz improvisations and 99 classical compositions in this way, including multi-movement symphonies and sonatas. They found that the autocorrelation function of pitches initially decreases very slowly with the time difference. This expresses a high similarity and possibility to anticipate musical sequences. However, they found that there is a time limit, after which this similarity and predictability ends relatively abruptly. For larger time differences, the autocorrelation function and memory are both negligible.
