Feb 25 2013
Researchers have found deep connection between music and mathematics
A musical engineer can mean both — an engineer who loves music and a musician who loves technology. Mark Bocko and Dave Headlam, both professors at the University of Rochester’s Music Research Lab, are musical engineers. They perform musically-informed research. Bocko wants to understand, through computers, what musicians do to create sound. He wants to capture the essence of the physics of how the instrument works. He studies how the more subtle inputs and the changes of the blowing pressure over time, and how things are connected together. He tries to better understand what’s critical, and what’s not, in a music file. Headlam wants to add another sense to music training. He wants music students to spend time not only with their ears, but also with their eyes. He wants them to better coordinate their ears with their eyes. Says Headlam, “So, you can imagine if you are playing something, you are looking at a screen, at some sort of oscilloscope display, and you see your line as you’re playing, and then you see your teacher’s line, and then those lines gradually come together as you are hearing what you want to do. Then, at a certain point, they come together. In that way you have accomplished your goal by combining your sight and your hearing.”
Many engineers have a penchant and passion for listening to and making music. Musically inclined neural scientists say that music stimulates right brain function, enhancing the ability to solve logical and mathematical problems. It could be due to the mathematical nature of music that engineers love music. Elain Chew says that music’s imminently quantifiable attributes make it an ideal medium for studying human creativity and cognition. “The dynamics of musical ensemble offer models of human collaboration”, thinks Chew.
We are not sure why music evokes emotion. A study conducted by Nidhya Logeswaran and Joydeep Bhattacharya from the University of London tells us that music can affect our visual images. After listening to happy or sad musical excerpts, the participants of the study were shown a photograph of a face. They were then asked to rate the emotional content of the face (1 meaning extremely sad and 7 extremely happy). Logeshwaran and Bhattacharya found that music powerfully influenced the emotional ratings of the faces. Happy music made happy faces seem even happier, while sad music exaggerated the melancholy of a frown.
Music has pitch and beat. It seems music also has mathematical shapes. Researchers have found deep connection between music and mathematics. They say music does have geometry. Pythagoras discovered that pleasing musical intervals could be described using simple ratios. Now, the researchers are trying to find mathematical sense of music. Music researchers Clifton Callender at Florida State University, Ian Quinn at Yale University, and Dmitri Tymoczko at Princeton University say that mathematics is a more fundamental language of nature than music. Their “geometrical music theory” can turn music into shapes. For Tymoczko, the history of music represents “a long process of exploring different symmetries and different geometries”. He says his method “might allow you to visualise some of the differences between John Lennon and Paul McCartney. McCartney’s tunes tend to look more traditional, Lennon’s tend to be a little more rock.” The method developed by these researchers can assign mathematical structure so they can be represented by points in complex geometrical spaces, like the ‘X’ and ‘Y’ coordinates in two dimensional space. “The music of the spheres isn’t really a metaphor — some musical spaces really are spheres,” says Tymoczko, who is also a composer. zz
(The writer is a biotechnologist
and ED, Birla Institute of
Scientific Research, Jaipur)