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Physicists at the Max Planck Institute for Dynamics and Self-Organization (MPI-DS) conducted a study to determine the extent to which a piece of music can evoke expectations about its progression. By analyzing over 550 pieces from classical and jazz music, they were able to quantify differences in how compositions of different composers can be anticipated. Leonard Meyer’s theory from almost 70 years ago suggested that emotions and meaning in music arise from an interplay between expectation and surprise, based on the ability to make predictions from past experiences. This led the researchers to investigate whether these philosophical concepts could be empirically quantified using modern data science methods.

The team led by Theo Geisel at the MPI-DS and the University of Göttingen published a paper in Nature Communications detailing their use of time series analysis to infer the autocorrelation function of musical pitch sequences. This function measures the similarity of a tone sequence to previous sequences, creating a “memory” of the piece of music. If this memory decreases slowly with time difference, the time series is easier to anticipate, whereas if it vanishes rapidly, it offers more variation and surprises. The researchers analyzed more than 450 jazz improvisations and 99 classical compositions, finding that the autocorrelation function of pitches initially decreases slowly with time difference before abruptly ending at a certain time limit, where predictability becomes negligible.

The researchers identified transition times in the compositions where predictable behavior changed into unpredictable and uncorrelated behavior. Depending on the composer and type of music, these transition times ranged from a few quarter notes to about 100 quarter notes. Jazz improvisations typically had shorter transition times compared to many classical compositions, making them less predictable. Differences were also observed between composers, with transition times varying between five and twelve quarter notes in compositions by Johann Sebastian Bach and between eight and 22 quarter notes in compositions by Mozart. This suggests that the anticipation and expectation of musical progression tend to last longer in Mozart’s compositions, while Bach’s compositions offer more variability and surprises.

The study also shed light on personal preferences for certain composers based on the variability of their music compositions. Theo Geisel shared an observation from his youth when he expressed a preference for Bach over Mozart to his music teacher and conductor. With the discovery of transition times between highly correlated and uncorrelated behavior in music, Geisel now has a quantitative measure to understand his inclination towards Bach’s compositions. This research not only provides insights into the predictability and variability of music but also offers a new perspective on how different composers create anticipation and surprise in their works.

Overall, the study by the MPI-DS researchers highlights the role of expectation and surprise in the emotional and meaningful aspects of music. By quantifying the anticipation and predictability of musical sequences, they have identified key differences between classical and jazz compositions, as well as between different composers. This research opens up new avenues for exploring the interplay between expectation, surprise, and emotional response in music, providing a deeper understanding of how meaning emerges in musical pieces. The findings offer valuable insights for musicians, composers, and music enthusiasts, enhancing our appreciation and interpretation of the intricacies of musical compositions.

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