Math in Music Waves

Music has always been a means of cooling me down, pumping me up, or just simply giving me and opportunity to relax. It would be so ever interesting if there was somehow MATH INVOLVED IN THE MUSIC I LISTEN TO ! 

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.

For example, consider the note called "Middle C" (usually the first note learned in piano lessons). This note has a frequency of about 262 Hertz. That means that when Middle C is played, 262 pockets of higher air pressure pound against your ear each second. Equivalently, the pockets of air arrive so quickly that one pocket strikes your ear every 0.00382 seconds. We can draw a graph by putting an X at every time when a pocket of air arrives:

This graph provides a sort of "picture" of Middle C. By itself, it does not tell us much. However, such graphs provide a new perspective on the relationships between different musical notes.

A basic rule is that higher-pitched notes have a higher frequency, corresponding to more frequent air pocket arrivals. For example, the note Middle G (seven semi-tones higher than Middle C) has a frequency of about 392 Hertz, corresponding to 392 air pockets per second, or a time period of 0.00255 of a second between arrivals:

With the higher note (Middle G), the air pockets arrive more frequently - corresponding to a higher frequency, and thus to more X's in the graph.

So how does this help us? Well, by using knowledge of sound frequencies carefully, such musical mysteries as octaves and chords can be unraveled.If you listen carefully to an ambulance siren or a train whistle, you will notice that the noise sounds higher while the vehicle is approaching, and lower after the vehicle has passed by. This is because the approaching movement compresses the X's together, making them arrive more frequently and produce a higher pitch, while the departing movement stretches out the X's and produces a lower pitch. This is musical frequency in action.