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Let's say we want to make some music
first we need some kind of instrument
For quite some time now
We humans have known that one way to make some nice musical sounds is to take a string
Fix it between two points and add some tension
now rocking out on one string can get kinda boring
And early musicians quickly figured out that to make things more interesting. They could add more strings to their instruments
However, just adding more strings does not always make things sound better
We have to make sure that our strings sound good together
we can change the sound each string mix individually by changing that's length or tension
and after a little experimentation it quickly becomes clear that the vast majority of combinations sound terrible
However every now and then for a specific combination of string lengths and tensions something kind of magical happens
All of a sudden the sound of our strings together just makes sense
So if we want to make a music that sounds any good
It's probably a good idea to first tune our instrument in such a way that our strings sound good together
Early instrument makers and musicians solved this problem
Just like we did by guessing and checking until a couple thousand years ago when the Greek mathematician
Pythagoras discovered something remarkable
Pythagoras found a hidden mathematical relationship between the length of each string the tension in each string and the sound the strings made together
Let's see if we can find this hidden mathematical relationship
We can start by making some observations
First I'll make the tensions in each string and as we change the length of each string. We'll note which combinations sound good together
Next we'll make the links of our two strings equal and as we change the tension of each string
We'll note which of these combinations sound good together
Now that we have some data, I'm turning it over to you
Can you see what Pythagoras did?
What is the hidden mathematical connection between the lengths of strings that sound good together?
What is the hidden mathematical connection between the tensions of strings that sound good together?
For a closer look at our data and some other cool stuff check out the PDF linked in the description below
Good luck, and thanks for watching