The interesting connection between math and music

By Arvind Gupta , Special to the Vancouver Sun April 7, 2009

From the rich complexity of the Bach fugues to the catchy songs of the Beatles, music and mathematics overlap in all kinds of interesting ways.

Beyond the basic uses of mathematics in music theory and notation (such as chords, time signatures, or dotted half-notes representing a count of three), music has also been the source of research in many areas of mathematics such as abstract algebra, set theory and number theory.

Would you believe that research has shown that certain pieces of music end up being more popular and mainstream due to their ‘mathematical’ structure?

For example, Pachelbel’s Canon in D — sure to be a top choice for brides again this summer — is said to reach the masses because of its repetitive structure, a trend very apparent in music today. No doubt the amazing popularity of hip-hop music, with its rhythmic beats and looping breaks, is partially due to our innate mathematical need for rhythm and patterns.

Jason Brown, professor of mathematics at Dalhousie University, used a mathematical tool called a “Fourier Transform” to analyse and solve the decades-old mystery of which instruments and notes actually make up that wild opening chord of the Beatles’ song A Hard Day’s Night. Hint: it’s more than George Harrison’s 12-string guitar. Brown is now using his sound-wave analysis of Beatles music as inspiration for new songs. (Check out his piece A Million Whys online to see how it’s working.)

In the field of cognitive research, the mind-body connections between music and mathematics have fuelled continuing debate surrounding the so-called “Mozart Effect,” which was first popularized in the early 1990s. In some studies, test subjects performed better on spatial-temporal tasks — such as visualizing a boat in one’s mind and then building it with Lego pieces — immediately following exposure to a Mozart sonata.

This might be explained by the fact that the same parts of the brain are active when listening to Mozart as when engaged in spatial-temporal reasoning.

Dr. Frances Rauscher of the University of Wisconsin Oshkosh has been heavily involved in research on music and cognitive performance. She gives far more credit to the active playing of instruments than simply passive listening.

In her 2006 article published in the Educational Psychologist, she explains that “young children provided with instrumental instruction score significantly higher on tasks measuring spatial-temporal cognition, hand-eye coordination and arithmetic.” Part of this is due to the amount of overlap between music skills and math skills. For example, Rauscher says the part-whole concept that is necessary for understanding fractions, decimals and per cents is highly relevant in understanding rhythm. “A literate musician is required to continually mentally subdivide beat to arrive at the correct interpretation of rhythmic notation,” she writes. “The context has changed, but the structure of the problem is essentially the same as any part-whole problem posed mathematically.”

The visual and spatial skills that a child exercises every time he practises an instrument and plays music strengthen his mental-physical connection.

The link between the physical practice of music and strong mathematical abilities are demonstrated in studies that show that kids who play a musical instrument can perform more complex arithmetical operations than those who do not play an instrument. The slow work of practice, the attention to detail and the discipline it takes to learn an instrument are also excellent preparation for the practice involved in building strong math skills.

The math-music connection shines in the field of education as well. Research shows that children who learn their academics through music and dance retain the information better than children who learn the same concepts by verbal instruction.

You may have noticed this yourself if your children are in a school participating in the Learning Through The Arts program established by the Royal Conservatory of Music. In LTTA, teachers and professional artists collaborate on lessons using art, dance, story and song to explore math, science and other subject areas.

So the next time you find yourself wanting to get up and dance to the music, remember that those pleasurable patterns of rhythm, beat, harmony and melody are actually embodied mathematical expressions.

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