Researchers have characterised the musical language of German composer and pianist Ludwig van Beethoven for the first time, applying statistical techniques to unlock recurring patterns.
Researchers from the Ecole Polytechnique Federale de Lausanne (EPFL) in Switzerland found that very few chords govern most of the music, a phenomenon that is also known in linguistics, where very few words dominate language.
The study, published in the journal PLOS ONE, is based on the set of compositions known as the Beethoven String Quartets.
"New state-of-the-art methods in statistics and data science make it possible for us to analyse music in ways that were out of reach for traditional musicology," said Martin Rohrmeier from EPFL.
The Beethoven String Quartets refer to 16 quartets encompassing 70 single movements that Beethoven composed throughout his lifetime.
He completed his first String Quartet composition at the turn of the 19th century when he was almost 30 years old, and the last in 1826 shortly before his death.
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A string quartet is a musical ensemble of four musicians playing string instruments: two violins, the viola, and the cello.
Researchers plowed through the scores of all 16 of Beethoven's String Quartets in digital and annotated form.
The most time-consuming part of the work was to generate the dataset based on ten thousands of annotations by music theoretical experts.
"We essentially generated a large digital resource from Beethoven's music scores to look for patterns," said Fabian C Moss, first author of the study.
When played, the String Quartets represent over eight hours of music.
The scores themselves contain almost 30,000 chord annotations. A chord is a set of notes that sound at the same time, and a note corresponds to a pitch.
In music analysis, chords can be classified according to the role they play in the musical piece.
Two well-known types of chords are called the dominant and the tonic, which have central roles for the build-up of tension and release and for establishing musical phrases.
However, there is a large number of types of chords, including many variants of the dominant and tonic chords. The Beethoven String Quartets contain over 1,000 different types of these chords.
Beethoven's creative choices are now apparent through the filter of statistical analysis, thanks to this new data set generated by the researchers.
As expected from music theory on music from the classical period, the study shows that the compositions are particularly dominated by the dominant and tonic chords and their many variants.
The most frequent transition from one chord to the next happens from the dominant to the tonic.
The researchers also found that chords strongly select for their order and, thus, define the direction of musical time.
However, the statistical methodology characterises Beethoven's specific composition style for the String Quartets, through a distribution of all the chords he used, how often they occur, and how they commonly transition from one to the other.
In other words, it captures Beethoven's composition style with a statistical signature.
"This is just the beginning. We are continuing our work by extending the datasets to cover a broad range of composers and historical periods," Moss said.