blogs.scientificamerican.com/roots-of-unity/2014/11/30/the-saddest-thing-i-know-about-the-integers/, posted 2014 by peter in math music
The integers are a unique factorization domain, so we can’t tune pianos. That is the saddest thing I know about the integers.
I talked to a Girl Scout troop about math earlier this month, and one of our topics was the intersection of math and music. I chose the way we perceive ratios of sound wave frequencies as intervals. We interpret frequencies that have the ratio 2:1 as octaves. (Larger frequencies sound higher.) We interpret frequencies that have the ratio 3:2 as perfect fifths. And sadly, I had to break it to the girls that these two facts mean that no piano is in tune. In other words, you can tuna fish, but you can’t tune a piano.