Famed Classical/Romantic composer Ludwig van Beethoven had a distinct statistical signature to his compositional style, according to an innovative analysis published in a recent paper in PLOS ONE. The study is part of the rise of so-called "digital humanities," although much of the work to date in this burgeoning subfield has focused on textual analysis.

"New state-of-the-art methods in statistics and data science make it possible for us to analyze music in ways that were out of reach for traditional musicology," said co-author Martin Rohrmeier, head of EPFL's Digital Humanities Institute, which is devoted to achieving a better understanding of how music works. "The young field of digital musicology is currently advancing a whole range of methods and perspectives."

Per co-author Markus Neuwirth, "Our approach exemplifies the growing research field of digital humanities, in which data-science methods and digital technologies are used to advance our understanding of real-world sources, such as literary texts, music, or paintings under new digital perspectives."

For their study, the Swiss team focused on the composer's 16 string quartets—over eight hours of music in total, with 70 individual movements. From there, they built up a dataset (the Annotated Beethoven Corpus, or ABC) based on nearly 30,000 chord annotations made by music theorists. Then they applied a variety of statistical techniques to hunt for patterns within that dataset.

The team focused its efforts on looking for structural regularities in the dataset, noting that tonal harmony is the most central concept when it comes to Western music, most dominant from the mid-18th through the late 19th century. But the researchers note in their paper that previous theoretical approaches to this subject "suffer from a lack of empirical foundation," relying more on qualitative descriptions of just a few examples. In contrast, they believe they can offer a more "quantifiable and testable hypothesis."

So what makes Beethoven sound like Beethoven? The Swiss researchers relied on a harmonic perspective to decode the maestro's distinctive compositional style. Dominant and tonic chords (aka V and I chords) are the most common in classical music, playing a vital role in musical phraseology, and there are many variants within those two broad classifications. The researchers assigned a symbol to each chord in the musical scores, counting how often each appeared. According to the EPFL team, Beethoven's string quarters contain more than 1,000 different types of chords.

"We found that, indeed, dominant and tonic chords are very, very common in this dataset," said co-author Fabian Moss, who also happens to be an accomplished pianist. "We also found that very few chords make up the largest portion of the data. And we found, importantly, that the order in which the chords appear matters a lot, so you cannot play the music backwards."

Furthermore, by studying the distribution of chords Beethoven used in his string quartets—how often each occurred, for instance, and how often one transitioned to another—they were able to define a statistical signature for the composer. In the future, the Swiss team hopes to expand the application of their statistical techniques to other 19th-century composers, such as Frederic Chopin or Franz Liszt, and perhaps add other musical dimensions into the mix, like rhythm, meter, and instrumentation.

DOI: PLOS ONE, 2019. 10.1371/journal.pone.0217242 (About DOIs).

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