Researchers at the Max Planck Institute for Dynamics and Self-Organization (MPI-DS) have explored how much a piece of music can create expectations regarding its unfolding. They discovered varying levels of predictability in the works of different composers. Overall, the team quantitatively examined over 550 musical pieces spanning classical and jazz styles.
It’s well-known that music elicits emotions, but what is the source of these feelings, and how is meaning developed in music? Nearly seven decades ago, music philosopher Leonard Meyer proposed that both phenomena stem from a dynamic between anticipation and surprise. Throughout human evolution, the ability to formulate new predictions based on past experiences was vital. Similarly, we can build expectations about how music will progress based on prior listening experiences. According to Meyer, the emotions and significance in music come from the balance of anticipating outcomes and experiencing their realization or, at times, their unexpected absence.
A research team led by Theo Geisel at MPI-DS and the University of Göttingen questioned whether these philosophical ideas can be measured with contemporary data science techniques. In a recent study published in Nature Communications, they employed time series analysis to derive the autocorrelation function of melodic pitch sequences, which indicates how closely a sequence resembles earlier sequences. This generates a kind of “memory” associated with the musical piece. If this memory fades gradually over time, it suggests a smoother predictability; conversely, if it diminishes quickly, it indicates more surprises and variety in the music.
The researchers, Theo Geisel and Corentin Nelias, analyzed over 450 jazz improvisations and 99 classical works, including multi-movement symphonies and sonatas, using this methodology. Their findings revealed that the autocorrelation function of pitches tends to decrease slowly at first, indicating a significant level of similarity and predictability in musical sequences. However, they also discovered a cutoff point, beyond which this strong correlation and predictability drop off sharply. For longer time differences, both the autocorrelation function and the associated memory become insignificant.
What’s intriguing are the measured transition times indicating where the music shifts from predictably correlated behavior to unpredictably random behavior. The transition times varied between just a few quarter notes to approximately 100 quarter notes depending on the piece. The jazz improvisations generally displayed shorter transition times compared to many classical pieces, rendering them less predictable. Notably, differences were also observed between various composers. For instance, transition times in multiple works by Johann Sebastian Bach ranged from five to twelve quarter notes, while those in Mozart’s works varied from eight to 22 quarter notes. This indicates that listeners might expect Mozart’s pieces to maintain predictive elements for a longer duration compared to Bach’s works, which contain more surprises and variability.
Theo Geisel, who spearheaded this research, sees this finding as a personal reflection of his own experiences in music appreciation during high school: “In my youth, I surprised my music teacher and conductor of our school orchestra by admitting that I often found it hard to engage with Mozart’s compositions,” he shares. “With the discovery of transition times between highly correlated and uncorrelated behaviors, we have identified a quantitative measure to assess the variability in musical pieces, which clarifies why I have always preferred Bach over Mozart.”
