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Sweet Math Music

Feb 25, 2019

You hear sounds all day long. Some sounds you probably enjoy (your favorite song - yay!), while others you may not (the neighbor’s dog barking for 3 hours - ugh). Have you ever stopped to think about what sound actually is though? 

Sound is what we call vibrations that travel through air that can be heard when they reach an ear. Movement in air particles is caused when any object vibrates. When the particles move, they bump into other particles close to them, which makes them vibrate, too. This effect of particles all bumping into each other is called sound waves and sound waves, like a ripple, keep going until the particles run out of energy. Picture throwing a stone into a still lake. The rings of waves expand indefinitely. The same is true with sound. 

Two of the most frequent sounds we hear as humans are speech and music. In speech and music, sound is broken up into a combination of frequencies.These frequencies can be measured by something called the Fourier transform, which is named after French mathematician Joseph Fourier who came up with a formula to breakdown frequencies into something we call pitch. Pitch is the part of frequency that us humans can hear.

Music generally carries less complicated pitches than speech. Instruments like the piano are very straight forward and pretty much stay the same vibration once the key is touched. Other instruments, like wind instruments, produce more complex sounds with many frequencies at once, allowing you to hear multiple pitches from one sound. Combining differnt souds together, like the sound of a band creates multiple pitches at one time. However, from each individual instrument, pitch is usually a single vibration. 

Speech pitch is more complicated, because the vibrations are more diverse. Pitch tends to correlate with the height of the speaker and generally higher for short speakers such as children and lower for taller women and men. We also have attached meaning to voice pitches. In our society, lower pitched voices tend to convey seriousness and sometimes menace, whereas high pitched voices tend to convey less seriousness. Can you think of examples of notable high and low pitched voices? 

Speech pitch also often affects language meaning. One example of this is in English sentences and phrases. A rising pitch at the end of the phrase means something different than a falling pitch. “The car?” generally means you’re asking a question, but saying that same phrase with a falling pitch, as in, “The car.” Means you’re giving an answer, versus asking a question. There are also languages, such as Mandarin Chinese, where the changing pitch of a speaker actually helps determine the meaning of a singular word. A word with a higher pitch has a totally different meaning from an otherwise identical word with a lower pitch. In Mandarin Chinese, there are actually 4 defined pitches and pitch is just as important as the word itself.

There are several ways to alter the pitch of your own voice, and several characters, especially ones who are cartoon characters, are played by people who have normal pitched voices that have been altered. The most common technique for altering voices these days is called pitch shifting. Pitch shifting is a sound recording technique using math in which the original pitch of a voice and/or sound is raised or lowered. It’s done using measured electronic devices and can alter the pitch of voices so much, that they aren’t even recognizable by their owners! One of the most widely known examples of pitch shifting is in the voice of Mickey Mouse. Walt Disney himself actually played his voice at one point, and, now the Mickey Mouse voice legacy carries on as a result of pitch shifting. 

Has all this got you curious about pitches and how to pitch shift your own voice? Perhaps you have a video you want to make or a friend you want to send an e-card too with an altered funny voice? Audacity is an open-source audio editor that can help you with the basics of pitch shifting your voice. Have fun and remember, sound, vibrations and pitch can all be explained by math!