Music and measure theory

There are many facts in math in which I've been able to follow the proof, but have nevertheless been stumped to find an intuitive understanding of what's happening.  Such facts have a funny way of becoming topics I want to create a video about.  In this case, the fact that you can cover a dense set in the real numbers with open intervals whose lengths sum to an arbitrarily small constant absolutely blew my mind.  

After mentally toiling for a while, I finally felt satisfied when I just sat down and thought through what it would feel like to zoom in on an irrational value which was not covered.  Thinking about the conditions for being such an irrational reminded me, surprisingly, of when I learned about why 12 is such a natural number of chromatic notes to have in a scale.