Thanks for the summary, that is really interesting. Also, I don't think the OP is making any claim that the piano keyboard is the result of any kind of natural

Thanks for the summary, that is really interesting. Also, I don't think the OP is making any claim that the piano keyboard is the result of any kind of natural phenomenon. They're just pointing out that you can create the same piano keyboard that we have using mathematical derivation, which is also interesting.