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What can math tell us about artistry?

Speed read
  • Performances of Bach’s Trio Sonatas for Organ will be digitized and visualized
  • Pipe organ perfectly suited to study due to complexity of skilled performance
  • Data will lead to better understanding of music theory, psychology, and pedagogy

People have been clapping their hands and raising their voices to make music for as long as humans have been standing on two legs. But now, two University of Michigan (UM) researchers are applying modern technology to better understand this ancient art.

<strong>Playing the pipe organ</strong> is one of the most mentally taxing endeavors in all of music, says Professor Forger. Its complexity makes it the perfect instrument for a quantified study of performance differences.Mathematics professor Daniel Forger and chair of the UM Organ Department James Kibbie hope that big data and quantification can provide new answers to long-standing questions about mathematics, music, and performance.

One of the big questions they hope to answer is: When two musicians play the same piece of music, what makes one performance sublime and the other mundane?

“Musicians can sometimes be skeptical that the objective precision of mathematics can relate to their intuitive, creative interpretations,” says Kibbie. “But our project demonstrates that mathematics, specifically big data analysis, can reveal the ways in which individual performers shape and control the music to a far greater extent than ever before.”

The perfect instrument

Classical music maestro Johann Sebastian Bach composed his Trio Sonatas for Organ in the early eighteenth-century, at a time when the sextant counted as disruptive technology. But these sonatas are so foundational to the understanding of Western music that they remain widely taught today.

<strong>Technical excellence.</strong> J. S. Bach wrote the Trio Sonatas for Organ in the 1720s with pedagogy in mind. They remain foundational tools for teaching performance, improvisation, and composition. Courtesy British Museum.Bach wrote the sonatas with pedagogy in mind, and they are fundamental tools for teaching performance, improvisation, and composition. According to Forger, these pieces make an interesting study because they are very challenging—forcing performers to work their hardest—but at the same time the musical structure is very clear.

“I tell my students that performing the works of Bach and most other great composers is a partnership between the composer and the performer,” says Kibbie. “The personal decisions made by the performer are an essential element in bringing the printed score to life.” 

Another reason for choosing the Trio Sonatas is the instrument on which they are played: the pipe organ. Unlike many other instruments, the modern pipe organ is almost perfectly adapted to digital data collection. When a performer presses the keys on a modern organ, that motion is transduced into an electrical pulse that opens and closes the pipes.

That electrical pulse can be recorded, and the collected data will exactly represent the player’s actions. Many instruments even have a play-back feature that allows the performance to be saved onto a USB.

“The pipe organ is so special to this project because the digitization—the creation of data—is done automatically,” says Forger.

Mind-body connection

To build their data library, the team will record performances of the Trio Sonatas played by a variety of performers, from beginning students to international master Kibbie himself. From this dataset, they will study harmony, counterpoint, and music structure from a data science perspective.

<strong>Visualizing Bach.</strong> A network graph of chord progressions in Bach’s Trio Sonatas. Courtesy University of Michigan.“There are lots of questions we want to ask,” says Forger. “From the most basic questions about Bach and his work, all the way to questions of neuroscience.”

As an example, Forger points out that playing the pipe organ is incredibly complex. Besides playing notes with both hands, a score may require them to play additional notes simultaneously with the feet.

“Playing the pipe organ is one of the most mentally taxing endeavors in all of music,” says Forger. “A lot of the decisions a performer has to make are in a very fast time scale. Multiple notes fly by in just one second. But a typical neuron in the brain fires only about once a second. So the really interesting question is: How do you have something on the time scale of one second controlling things that are happening on a much finer time scale?”

Forger has been considering this project for several years and is excited to finally bring it to realization. He says that a large part of what makes this project so compelling is its interdisciplinary nature.

“Michigan is the kind of place where I can say, ‘Hey, I’m teaching a course in a mathematics department, and by the way, I need a pipe organ,’” says Forger. “Michigan is very good at this cutting-edge interdisciplinary work.”    

What is art?

<strong>The Frieze Memorial Organ</strong> in Hill Auditorium on the University of Michigan campus will be used to create big data files of a range of performances—from novice students to internationally-renowned maestros. Researchers will use mathematics to compare performances and analyze common mistakes. Courtesy University of Michigan.In a win-win for the university and the local community, the UM Organ Department is currently giving recitals around Detroit that will be recorded for the project. Once the performances wrap up in March, the team will process the data and the results will be shared with other researchers in data science, music performance, and music psychology.

The results may not provide immediate answers to all of the researcher’s questions, but Kibbie is excited to have a powerful new tool to help him better understand students’ mistakes—and get closer to fathoming the myriad complexities that make a performance great.

“It’s a very ambitious goal, but hopefully we can find some elements of what people typically call artistry,” says Forger. “We’re never going to be able to say, ‘This is art, that’s not art.’ But we can come up with some correlations.”

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