Researchers at the École Polytechnique Fédérale de Lausanne (EPFL) have studied Beethoven's style of composing music, to gain a better understanding of the patterns that create musical structures in classical Western music.
What was their technique? Statistics.
Music and math are not typical allies, but in having them work side by side, the group of researchers have been able to statistically characterize the musical language of Beethoven for the first time in history.
The researchers exclusively studied the Beethoven String Quartets, which Beethoven composed throughout his entire life, from the age of 30 until 1826, right before he passed away.
A string quartet is a musical ensemble encompassing two violins, one viola and one cello. Beethoven, in his lifetime, composed 16 quartets with 70 single movements, which amasses to just over eight hours of music.
What is the point of this study?
"The aim of our lab is to understand how music works," says Martin Rohrmeier, the lead in EPFL's Digital and Cognitive Musicology Lab (DCML).
He continues, "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. The young field of Digital Musicology is currently advancing a whole new range of methods and perspectives."
So how does one statistically study Beethoven's music?
The team went through all of the late musical genius' 16 scores (containing almost 30,000 chord annotations in total) in both digital and annotated form (musical notes as we read them in a score).
"We essentially generated a large digital resource from Beethoven's music scores to look for patterns," says Fabian C. Moss, who is first author of the PLOS ONE study.
"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," explains co-author Markus Neuwirth.
Thank you for the music
From the data and filter of statistical analysis, it is now clear how Beethoven made his note-worthy choices.
What the study also discovered was that the music is not run by many different chords, something it shares with linguistics. For example, when only a small number of words dominate a language.
What has also been possible to detect, through the use of statistical methodology, is the characterization of Beethoven's particular way of composing the String Quartets. This was done by noting the distribution and frequency of the chords he chose, and how commonly they transitioned from one another.
That is to say, Beethoven's style of composing has been laid bare in a statistical signature.
"This is just the beginning," explains Moss.
"We are continuing our work by extending the datasets to cover a broad range of composers and historical periods, and invite other researchers to join our search for the statistical basis of the inner workings of music."