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.
Next week: When you think about careers that use math,
do you get stumped right after “accountant”?
In next week’s column, Dr. Gupta will highlight
ten careers which require top-notch quantitative skills.
I guarantee you’ll be surprised!
MORE
INFORMATION
Arvind Gupta is a father of
three, a mathematician and scientific director of MITACS,
a national research network focused on connecting university-based
math researchers with companies and other organizations
to solve real-world challenges. This article first appeared
in the Vancouver Sun on April 7, 2009. Their website is:
www.vancouversun.com
Music without words means leaving behind the mind. And leaving behind the mind is meditation.
Meditation returns you to the source. And the source of all is sound. — Kabir
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