Music and Mathematics
Following is an excerpt from a terrific article by Jeffrey Rosenthal*, "The magical mathematics of music," published in Plus Magazine.
The astronomer Galileo Galilei observed in 1623 that the entire universe "is written in the language of mathematics", and indeed it is remarkable the extent to which science and society are governed by mathematical ideas. It is perhaps even more surprising that music, with all its passion and emotion, is also based upon mathematical relationships. Such musical notions as octaves, chords, scales, and keys can all be demystified and understood logically using simple mathematics.
Pitch: Wave frequencies
Music appears to be transmitted by magic, escaping from your expensive stereo - or a loudly passing car radio, or a guitar-strumming maestro - and accosting your eardrums in one fell swoop. In fact, sound progresses as a wave through the air, and sound cannot be produced without an atmosphere. (Or, as the horror movies would say: in space no one can hear you scream.)
A sound wave creates minute pockets of higher and lower air pressure, and all the sounds we hear are caused by these pressure changes. With music, the frequency at which these pockets strike your ear controls the pitch that you hear...A basic rule is that higher-pitched notes have a higher frequency, corresponding to more frequent air pocket arrivals...
*Jeffrey Rosenthal is a professor in the Department of Statistics at the University of Toronto, and is an amateur musical performer who plays several instruments. His book Struck by Lightning: The Curious World of Probabilities
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was published in September 2005 by HarperCollins Canada.
