Professor describes the math behind music

Guest professor Marc de Graef, from Carnegie Mellon University’s Materials Science and Engineering Department, delivered a presentation about the numbers behind musicality in the Gilman Atrium on Friday evening.

The event was hosted by the Hopkins Extreme Materials Institute and the Department of Mechanical Engineering. It sought to build connections between faculty members and graduate students.

“The motivation for doing these sort of performances is so that graduate students can see that the faculty are real people too, and not just people on a pedestal,” de Graef said. “We can really celebrate passions outside of our fields.”

De Graef introduced the audience to the concept of harmonious and discordant chords by strumming various major and minor chords on his guitar. De Graef then incorporated the various chords into a short bluegrass Dutch jig.

De Graef proceeded to explain the fundamentals behind music theory. He first introduced the concept of the Western C-D-E-F-G-A-B scale, in which each octave was the direct equivalent of doubling the pitch. De Graef also explained the mathematics behind the scale, showing how half-steps in the modern C-D-E-F-G-A-B scale, which runs from C to C#, can be described intuitively by multiplying the initial pitch by 122. De Graef discussed how the perfect fifth chord interval could be perfectly quantified by following the pattern and multiplying the base note by 1225. De Graef illustrated his point by playing Scarborough Fair in A.

From there, de Graef transitioned to the purely mathematical discussion about music. De Graef and Norman D. Cook of Kansai University in Japan published research studies showing how overlaying pitch calculations on a hexagonal semitone coordinate axis granted a center area that contained all non-dissonant chords. De Graef initially made a spur-of-the-moment decision to contact Cook after reading an article in bimonthly science and technology magazine American Scientist in which Cook discussed why some three-tone chords sounded better than others.

Their research, which used a triad tension plot, showed how all the major and minor chords lie on or near areas with low triad tension, while the augmented, diminished and suspended fourth chords lie on or near areas with local tension maxima. De Graef showed the tensions and chord progressions by playing “Bach’s Air” in G.

While de Graef was in college, he spent time traveling around the Dutch countryside playing with a bluegrass band called The Duelin.

When de Graef entered graduate school, he was mentored by a formal musician named Kostas Chatzopoulos, who provided him with a more classical approach to music.

After graduate school, de Graef moved to the United States, where he worked as a post-doctoral researcher at the University of California, Santa Barbara. De Graef began working at Carnegie Mellon University in 1993, and after becoming a full tenured professor in 2002, de Graef began bringing his guitar to work in order to practice his musicality.

To conclude his presentation, de Graef showed a viral Youtube video by The Axis of Awesome titled “4 Chords.” De Graef said that he dislikes modern music, which is overly reliant on redundant and overused chords. When the video ended, de Graef circulated around the room to answer questions.

Student attendees enjoyed de Graef’s style of lecturing, which involved using his guitar to provide examples of the points that he was making.

“I loved the integration of the mathematics and the music [in the presentation],” freshman Stephane Teste said. “My favorite part was when he talked about the math and then proceeded to play something to quantify his example, to show how it wasn’t abstract. Plus, I loved the music.”

Many music students also learned about new mathematical approaches to centuries-old musical concepts, such as the circle of fifths.

“I thought [the presentation] was interesting,” freshman Aki Songunro said. “I’m taking a music theory class, so most of the concepts were familiar, but I did learn something new about the frequencies. It was interesting seeing how what’s more harmonious and dissonant can be modeled mathematically.”