Why there are 12 musical notes
And what it has to do with continued fractions
This story was originally published on my personal blog. I’m republishing it here with minor modifications for wider reach.
A standard piano has 88 keys: 52 white ones and 36 black ones. On the left hand side are keys that produce deeper tones with lower sound frequencies, on the right are the keys that produce higher tones. In principle there could be more keys on either end, but at some point the frequencies stop sounding musical to our ears, and more keys become impractical for the performer. Older pianos may have 85 keys and cheaper keyboards exist with even fewer keys. However, what all pianos have in common is the following repeating pattern of seven white keys and five black keys:
If you know a little bit about music, you will also be able to label each key with its corresponding note, as I’ve done in the image.
But have you ever wondered why the keyboard looks like this? Why are there twelve (5 + 7) different notes, and why is there this pattern on the piano? Why do most musical instruments produce the same notes? Sound can be of any pitch, so it seems strange…
