UvA PhD student composes music based on mathematical models
Bas Cornelissen is a professional baroque singer and a PhD candidate in mathematics. At the UvA, he combines the two. Can you predict the notes of musical pieces using mathematical models? “I could fill in a classical piece 93 percent automatically.”
He is doing the master's in Early Music Singing at the Conservatory of Music and will sing as a soloist in Bach's Johannes Passion at Easter. But this Friday, February 23rd, Bas Cornelissen will receive his doctorate from the UvA in mathematical logic. His research revolves around the question: Can music be measured? “Using a self-devised algorithm, I was able to automatically complete 93 percent of Arvo Pärt's famous piece of music, Summa.”
Cornelissen’s interest in the topic stems from his previous research in measurements of language. But for his dissertation, the baritone was eager to delve deeper into his fascination with music. “I came across Gregorian music and unison church hymns through language. After all, the accents, word groups, and length of religious phrases strongly shaped the melodies that monastics sang.”
Composing computer
Because musical notation had not yet been invented in the Middle Ages, the score primarily stated whether melodies went up or down. “Without musical notation, monks would have only scribbled a few notations on the text to indicate how the music should sound. Such an indication was apparently a sufficient reminder for another church singer of how the song should be sung,” Cornelissen explains.
It soon became apparent in his models that the movement of the music, such as way up, or maybe a little down, could predict the scales quite well. “That predictability dovetailed well with what was scribbled in old manuscripts.”
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Cornelissen studied such church scales, named “modes,” some time ago for a conservatory course. “My teacher said I would have to sing Gregorian music for two years if I wanted to understand those ‘modes.’” The Bach singer didn’t feel like waiting for that. “So I decided to just start understanding the ‘modes’ through my familiar, mathematical models.”
In doing so, the doctoral student developed a simple AI model that can write new, medieval tunes. “You then get simple, but quite nice melodies.” As a trained baritone, Cornelissen could turn that into beautiful music himself. After all, explains the doctoral student, “I can completely choose myself where to take a moment to breathe and what to emphasize musically. With that, you can make that simple church music really beautiful.”
Melodious secrets
Cornelissen can also use his measurements to uncover the secret formulas behind great pieces of music. The riddle of the famous Enigma piece by composer Edward Elgar has not yet been cracked by the PhD student. “But I did discover some formal rules that may underlie works by the contemporary composer Arvo Pärt. They are often based on a set of almost mathematical rules.”
In using these rules, the religious Pärt took inspiration from the melodies of medieval music. “The second voice, which literally accompanies his basic melody, Pärt sees as a guardian angel for his basic melody. The melodies thereby go up or down in intervals, just as in church hymns.”
New music
Singer Cornelissen would also like to compose so well, but his “time is scarce.” So a quiet motivation for his research was being able to create a piece of music from the combination of church hymns and Pärt's mathematical rules, created by Cornelissen's computer model. “I unfortunately did not have the time to finish that project. “In the future, I want to look into whether classical composers are predictable,” the researcher hopes. “If my computer model knows certain bits of melody from Bach's choruses, for example, maybe it can automatically fill in the rest of the music.”
He also hopes other musicians can use his models “to play along.” “Conductors are always trying to make sense of a score. They could use my study of structures to understand a musical work.” The mathematician Cornelissen hopes to model and sing to understand the structures of Bach's Passions after his doctorate. In March, the doctoral candidate-to-be will sing in as many as eight concerts.
