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News from Mathnasium of Stapleton

Pitch Perfect Math

Feb 18, 2019

You hear sounds all day long. Some sounds you probably enjoy (your favorite song -yay!), while others you may not (a 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 (or another medium) that can be heard when they reach an ear. When any object vibrates, it causes movement in the air particles. These particles bump into other particles close to them, which makes them vibrate too, causing them to bump into more air particles. This movement is called sound waves and it keeps going until the particles run out of energy. Picture throwing a penny into a bathtub. The rings of waves expand usually until the reach the end of the bathtub. The same is true with sound. 

Two of the most frequent sounds you probably hear are speech and music. Sound is broken up into a combination of frequencies in speech and music and these frequencies can be calculated by a formula called the Fourier transform, which is named after French mathematician Joseph Fourier. He came up with a measurement to breakdown frequencies into something we call pitch. Pitch is the part of frequency that us humans can hear and is probably something you’ve heard of before in reference to speech or music. When the vibrations are fast, you hear a higher pitches. When vibrations are slow, you hear lower pitches. 

Pitches can be more simple, like those an instrument makes, or they can be more complicated, like in human speech. Music generally carries more simple pitches than. In instruments like the trumpet or flute, ones that require wind movement, vibrating air makes the sound when you blow into them. The particles move back and forth, bumping into each other, creating sound waves. Different pitches are played by pressing keys that open or close holes in the tube. Stringed instruments are played by putting pressure on the strings. The amount of pressure applied changes the strings' length, causing them to vibrate at different frequencies and making different sounds. Pitch is determined by thickness length and thickness of strings.

Speech pitch is not quote as simple as it is in music, because the vibrations are more diverse. Pitch often varies depending on the height of the speaker. Women and children tend to have higher pitches voices because they are generally shorter and men tend to have higher pitched voices because they are generally taller. Societally, we associate lower pitched voices with seriousness and sometimes menacing behavior, whereas high pitched voices are often associated with pleasantness. Can you think of examples of notable high and low pitched voices? 

Pitch in speech also can denote language meaning. One example of this is how pitch creates different meanings in English sentences and phrases. When someone’s voice rises at the end of the phras, it means something different than when their voice pitch falls or remains the same. If someone says “The cat?” with a rising pitch, they are likely asking a question. If someone says “The cat.” they are likely giving an answer. In Mandarin Chinese, changing the pitch of a voice actually helps determine the meaning of singular words. If you say the word ma  the way an English speaker would say it, just reading it sitting by itself on a page, then it means “scold.” If you were to say ma as if you were looking for your mother—ma?— it means “rough.” This is because there are 4 defined pitches in Mandarin that are part of the language itself. 

Despite that we have a certain range of pitches we stay in when talking, there are ways to alter the pitch of your own voice outside of its normal range. The most common way to alter your voice is called pitch shifting. Pitch shifting is a sound recording technique using math that takes your original voice and makes it lower or higher. This is done a lot on TV, radio and in movies, specifically with cartoon characters.One of the most notable examples of pitch shifting is in the voice of Mickey Mouse. The voice of the Disney legacy has been played by many different people, including Walt Disney himself at one point! Are there any characters you can think of who might have pitch shifted voices? 

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-sourceaudio 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!