tangles, spirals, and so on. Many of these sculptures represent different mathematical
concepts, from polyhedral geometry and topological knots to fractal designs.In what ways does mathematicsapply to music?
There are many ways in which mathematics applies to music—from harmonics to the
concept of octaves and scales. There is a most interesting connection in that both
music and mathematics are experienced as pure objects of the brain—and both have
meaning outside of the brain only through artificial connections.For example, there is a “mathematical” reason why certain note combinations
sound harmonious to most people. One good example is a violin string: When it is
plucked, the string vibrates back and forth, creating mechanical energy that travels
through the air as wave patterns. The number of times the waves reach a person’s ear
is called the frequency, which is measured in Hertz (Hz, or cycles per second); if more
waves are heard within a certain time period, the note’s pitch sounds higher.Chords sound harmonious to us because of waves and ratios. For example, take
378 the C major chord, in which the note middle C is 261.6 Hz, the note E is 329.6 Hz, and
What is the “Mozart Effect”?
T
he Mozart Effect is a term coined in the 1950s by physician and researcher
Alfred A. Tomatis (1920–2001). It refers to the supposed increase in brain
development that children under age three experience when they listen to music
composed by Wolfgang Amadeus Mozart (1756–1791). A more recent interpreta-
tion originated in 1993 from physicist Gordon Shaw and Frances Rauscher, a
former concert cellist and expert on cognitive development. After a few dozen
students listened to the first ten minutes of Mozart’s Sonata for Two Pianos in D
Major (K.448), the researchers determined that the students experienced a
short-term enhancement of their spatial-temporal reasoning (based on a certain
IQ test). But many other researchers claim that no one has ever been able to
reproduce these results.
Over the years, the Mozart Effect has reached further into the public “psyche,”
with highly debated claims of better health, memory improvement, and therapeu-
tic uses of music, especially classical music. Proponents also claim the Mozart
Effect can be applied to learning such subjects as mathematics. They believe that
exposure to certain types of music—especially classical music early in life—leads
to higher future scores in spatial visualization, abstract reasoning, and sundry
other mathematical concepts. But all these claims remain highly contested.