This fine gentleman is Pythagoras. Born in 570 BCE, he is most commonly known for his work in mathematics, specifically his theory about the geometry of right triangles which states that the area of the square on the hypotenuse is equal to the (blah blah blah math math math) or a^2+b^2=c^2.
Most of us have come across the Pythagorean theorem at some point in our learning lifetimes. BUT: did you know that Pythagoras and his followers were also interested in the mathematics of every day life and the things around us— leading him to discover many of the systems which make up the foundation of Western music? Take a look at just a few of the ways Pythagoras used mathematics to explain the sounds we hear!
Blacksmiths’ hammers and Guitar string
Legend has it that one day Pythagoras took a stroll through the market and the sounds of the blacksmiths’ hammers as they struck the anvil caught his ear. He noticed that different hammers produced different sounds. This brought about an idea that we take for granted today: that the speed of vibration and the size of the object producing the sound affects the ‘pitch’ of sounds in music.
Think of it like this: Imagine you have two different sized buckets, one large and one small. We expect that when we hit the larger bucket that the sound we get will be lower than that of the smaller bucket. Just like in music when we hear low sounds we know they come from a large instrument like a tuba or a string bass.
Pythagoras discovered very important properties of relationships between notes as well. After experimenting with musical tones and ratios on several stringed instruments he found that the sound of a stretched string gets lower as it gets longer. He also noticed that when he placed his finger on the string and plucked it, that the relationship between the original tone of the string and the note created could be put into numerical terms. We know this relationship today not by the numerical value, but by the term ‘interval’.
We can see this idea in action in the construction and performance of the guitar. To make sound, press on the strings of the guitar at the frets and strum. The note created has an exact relationship to the original note of the string. Wherever you placed your hand, that note is at a certain interval like a perfect fifth or minor third. Now you can thank Pythagoras every time you hear a rocking guitar solo!
Check out this video from the Science Channel talking more about Pythagoras’ theories!
Pythagoras thought in ways very similar to our mission here at The Right Brain Initiative. He saw that everything was connected, from mathematics to music. We hope we can excite our students about learning by showing them these very same connections, just as we hope we have excited you to go learn more about Pythagoras!
Itching for more ways to learn more about the sounds around us? So are we! Here’s a Brain Food exercise you can do anywhere to explore how the space you’re in changes your voice.
Travis Opocensky is a percussion instructor in the Portland area and a Psychology student at Portland State University. He blogs and tweets for The Right Brain Initiative through the Performing Arts Advocacy Capstone class at Portland State.